From 9b74235eeec75938311530a540a66ee9e27bc9e3 Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Fri, 31 May 2024 00:41:05 -0400 Subject: [PATCH 01/24] Add start of dynamics code --- cmake/recipes/filib.cmake | 2 +- notebooks/abd.ipynb | 1102 +++++++++++++++++ src/ipc/CMakeLists.txt | 1 + src/ipc/dynamics/CMakeLists.txt | 6 + src/ipc/dynamics/affine/CMakeLists.txt | 12 + src/ipc/dynamics/affine/affine_body.hpp | 30 + .../affine/orthogonality_potential.cpp | 168 +++ .../affine/orthogonality_potential.hpp | 33 + src/ipc/dynamics/rigid/CMakeLists.txt | 11 + src/ipc/dynamics/rigid/rigid_body.cpp | 47 + src/ipc/dynamics/rigid/rigid_body.hpp | 23 + src/ipc/utils/CMakeLists.txt | 2 + src/ipc/utils/interval.hpp | 16 +- src/ipc/utils/sinc.cpp | 149 +++ src/ipc/utils/sinc.hpp | 44 + tests/src/tests/CMakeLists.txt | 1 + tests/src/tests/dynamics/CMakeLists.txt | 5 + .../src/tests/dynamics/affine/CMakeLists.txt | 10 + .../affine/test_orthogonality_potential.cpp | 80 ++ tests/src/tests/utils/CMakeLists.txt | 1 + tests/src/tests/utils/test_sinc.cpp | 151 +++ 21 files changed, 1889 insertions(+), 5 deletions(-) create mode 100644 notebooks/abd.ipynb create mode 100644 src/ipc/dynamics/CMakeLists.txt create mode 100644 src/ipc/dynamics/affine/CMakeLists.txt create mode 100644 src/ipc/dynamics/affine/affine_body.hpp create mode 100644 src/ipc/dynamics/affine/orthogonality_potential.cpp create mode 100644 src/ipc/dynamics/affine/orthogonality_potential.hpp create mode 100644 src/ipc/dynamics/rigid/CMakeLists.txt create mode 100644 src/ipc/dynamics/rigid/rigid_body.cpp create mode 100644 src/ipc/dynamics/rigid/rigid_body.hpp create mode 100644 src/ipc/utils/sinc.cpp create mode 100644 src/ipc/utils/sinc.hpp create mode 100644 tests/src/tests/dynamics/CMakeLists.txt create mode 100644 tests/src/tests/dynamics/affine/CMakeLists.txt create mode 100644 tests/src/tests/dynamics/affine/test_orthogonality_potential.cpp create mode 100644 tests/src/tests/utils/test_sinc.cpp diff --git a/cmake/recipes/filib.cmake b/cmake/recipes/filib.cmake index dcbcc522e..67e2dbb00 100644 --- a/cmake/recipes/filib.cmake +++ b/cmake/recipes/filib.cmake @@ -7,4 +7,4 @@ endif() message(STATUS "Third-party: creating target 'filib::filib'") include(CPM) -CPMAddPackage("gh:zfergus/filib#1cd377a7c833a68dc47217829e333f4886c5c46d") \ No newline at end of file +CPMAddPackage("gh:zfergus/filib#fe1d1bfa56ef8c00fbcea2deec69a6b4f9da2207") \ No newline at end of file diff --git a/notebooks/abd.ipynb b/notebooks/abd.ipynb new file mode 100644 index 000000000..315d2a265 --- /dev/null +++ b/notebooks/abd.ipynb @@ -0,0 +1,1102 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [], + "source": [ + "import sympy\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}a_{00} & a_{01} & a_{02}\\\\a_{10} & a_{11} & a_{12}\\\\a_{20} & a_{21} & a_{22}\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[a00, a01, a02],\n", + "[a10, a11, a12],\n", + "[a20, a21, a22]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "A = sympy.symbols([f\"a{i}{j}\" for i in range(3) for j in range(3)])\n", + "A = np.array(A).reshape(3, 3)\n", + "display(sympy.Matrix(A))" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": {}, + "outputs": [], + "source": [ + "def frobenius_norm(A):\n", + " sum = 0\n", + " for i in range(A.shape[0]):\n", + " for j in range(A.shape[1]):\n", + " sum += A[i, j]**2\n", + " return sympy.sqrt(sum)\n", + "\n", + "standard_version = frobenius_norm(A @ A.T - np.eye(3))**2" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [], + "source": [ + "paper_version = sum((A[i].dot(A[i]) - 1)**2 for i in range(3)) \\\n", + " + sum((A[i].dot(A[j]))**2 for i in range(3) for j in range(3) if i != j)" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 0$" + ], + "text/plain": [ + "0" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "(standard_version - paper_version).simplify()" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle 12 a_{00}^{2} + 4 a_{01}^{2} + 4 a_{02}^{2} + 4 a_{10}^{2} + 4 a_{20}^{2} - 4.0$" + ], + "text/plain": [ + "12*a00**2 + 4*a01**2 + 4*a02**2 + 4*a10**2 + 4*a20**2 - 4.0" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 8 a_{00} a_{01} + 4 a_{10} a_{11} + 4 a_{20} a_{21}$" + ], + "text/plain": [ + "8*a00*a01 + 4*a10*a11 + 4*a20*a21" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 8 a_{00} a_{02} + 4 a_{10} a_{12} + 4 a_{20} a_{22}$" + ], + "text/plain": [ + "8*a00*a02 + 4*a10*a12 + 4*a20*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 8 a_{00} a_{10} + 4 a_{01} a_{11} + 4 a_{02} a_{12}$" + ], + "text/plain": [ + "8*a00*a10 + 4*a01*a11 + 4*a02*a12" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{01} a_{10}$" + ], + "text/plain": [ + "4*a01*a10" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{02} a_{10}$" + ], + "text/plain": [ + "4*a02*a10" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 8 a_{00} a_{20} + 4 a_{01} a_{21} + 4 a_{02} a_{22}$" + ], + "text/plain": [ + "8*a00*a20 + 4*a01*a21 + 4*a02*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{01} a_{20}$" + ], + "text/plain": [ + "4*a01*a20" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{02} a_{20}$" + ], + "text/plain": [ + "4*a02*a20" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 8 a_{00} a_{01} + 4 a_{10} a_{11} + 4 a_{20} a_{21}$" + ], + "text/plain": [ + "8*a00*a01 + 4*a10*a11 + 4*a20*a21" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{00}^{2} + 12 a_{01}^{2} + 4 a_{02}^{2} + 4 a_{11}^{2} + 4 a_{21}^{2} - 4.0$" + ], + "text/plain": [ + "4*a00**2 + 12*a01**2 + 4*a02**2 + 4*a11**2 + 4*a21**2 - 4.0" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 8 a_{01} 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a_{10} a_{22}$" + ], + "text/plain": [ + "4*a10*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{00}^{2} + 4 a_{10}^{2} + 12 a_{20}^{2} + 4 a_{21}^{2} + 4 a_{22}^{2} - 4.0$" + ], + "text/plain": [ + "4*a00**2 + 4*a10**2 + 12*a20**2 + 4*a21**2 + 4*a22**2 - 4.0" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{00} a_{01} + 4 a_{10} a_{11} + 8 a_{20} a_{21}$" + ], + "text/plain": [ + "4*a00*a01 + 4*a10*a11 + 8*a20*a21" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{00} a_{02} + 4 a_{10} a_{12} + 8 a_{20} a_{22}$" + ], + "text/plain": [ + "4*a00*a02 + 4*a10*a12 + 8*a20*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{01} a_{20}$" + ], + "text/plain": [ + "4*a01*a20" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{00} a_{20} + 8 a_{01} a_{21} + 4 a_{02} a_{22}$" + ], + "text/plain": [ + "4*a00*a20 + 8*a01*a21 + 4*a02*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{01} a_{22}$" + ], + "text/plain": [ + "4*a01*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{11} a_{20}$" + ], + "text/plain": [ + "4*a11*a20" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{10} a_{20} + 8 a_{11} a_{21} + 4 a_{12} a_{22}$" + ], + "text/plain": [ + "4*a10*a20 + 8*a11*a21 + 4*a12*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{11} a_{22}$" + ], + "text/plain": [ + "4*a11*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{00} a_{01} + 4 a_{10} a_{11} + 8 a_{20} a_{21}$" + ], + "text/plain": [ + "4*a00*a01 + 4*a10*a11 + 8*a20*a21" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{01}^{2} + 4 a_{11}^{2} + 4 a_{20}^{2} + 12 a_{21}^{2} + 4 a_{22}^{2} - 4.0$" + ], + "text/plain": [ + "4*a01**2 + 4*a11**2 + 4*a20**2 + 12*a21**2 + 4*a22**2 - 4.0" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{01} a_{02} + 4 a_{11} a_{12} + 8 a_{21} a_{22}$" + ], + "text/plain": [ + "4*a01*a02 + 4*a11*a12 + 8*a21*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{02} a_{20}$" + ], + "text/plain": [ + "4*a02*a20" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{02} a_{21}$" + ], + "text/plain": [ + "4*a02*a21" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{00} a_{20} + 4 a_{01} a_{21} + 8 a_{02} a_{22}$" + ], + "text/plain": [ + "4*a00*a20 + 4*a01*a21 + 8*a02*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{12} a_{20}$" + ], + "text/plain": [ + "4*a12*a20" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{12} a_{21}$" + ], + "text/plain": [ + "4*a12*a21" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{10} a_{20} + 4 a_{11} a_{21} + 8 a_{12} a_{22}$" + ], + "text/plain": [ + "4*a10*a20 + 4*a11*a21 + 8*a12*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{00} a_{02} + 4 a_{10} a_{12} + 8 a_{20} a_{22}$" + ], + "text/plain": [ + "4*a00*a02 + 4*a10*a12 + 8*a20*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{01} a_{02} + 4 a_{11} a_{12} + 8 a_{21} a_{22}$" + ], + "text/plain": [ + "4*a01*a02 + 4*a11*a12 + 8*a21*a22" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle 4 a_{02}^{2} + 4 a_{12}^{2} + 4 a_{20}^{2} + 4 a_{21}^{2} + 12 a_{22}^{2} - 4.0$" + ], + "text/plain": [ + "4*a02**2 + 4*a12**2 + 4*a20**2 + 4*a21**2 + 12*a22**2 - 4.0" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "for i in range(9):\n", + " for j in range(9):\n", + " display(standard_version.diff(A[i//3, i%3]).diff(A[j//3, j%3]))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.7" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/src/ipc/CMakeLists.txt b/src/ipc/CMakeLists.txt index 07a4d55fd..37ad80ba1 100644 --- a/src/ipc/CMakeLists.txt +++ b/src/ipc/CMakeLists.txt @@ -19,6 +19,7 @@ add_subdirectory(ccd) add_subdirectory(candidates) add_subdirectory(collisions) add_subdirectory(distance) +add_subdirectory(dynamics) add_subdirectory(friction) add_subdirectory(implicits) add_subdirectory(potentials) diff --git a/src/ipc/dynamics/CMakeLists.txt b/src/ipc/dynamics/CMakeLists.txt new file mode 100644 index 000000000..e43145b22 --- /dev/null +++ b/src/ipc/dynamics/CMakeLists.txt @@ -0,0 +1,6 @@ +################################################################################ +# Subfolders +################################################################################ + +add_subdirectory(affine) +add_subdirectory(rigid) \ No newline at end of file diff --git a/src/ipc/dynamics/affine/CMakeLists.txt b/src/ipc/dynamics/affine/CMakeLists.txt new file mode 100644 index 000000000..344ab319e --- /dev/null +++ b/src/ipc/dynamics/affine/CMakeLists.txt @@ -0,0 +1,12 @@ +set(SOURCES + affine_body.hpp + orthogonality_potential.cpp + orthogonality_potential.hpp +) + +source_group(TREE "${CMAKE_CURRENT_SOURCE_DIR}" PREFIX "Source Files" FILES ${SOURCES}) +target_sources(ipc_toolkit PRIVATE ${SOURCES}) + +################################################################################ +# Subfolders +################################################################################ \ No newline at end of file diff --git a/src/ipc/dynamics/affine/affine_body.hpp b/src/ipc/dynamics/affine/affine_body.hpp new file mode 100644 index 000000000..0f005876d --- /dev/null +++ b/src/ipc/dynamics/affine/affine_body.hpp @@ -0,0 +1,30 @@ +#pragma once + +#include + +namespace ipc::affine { + +struct AffineBody { + MatrixMax3d A; // Affine matrix + VectorMax3d p; // Translation vector + double volume; // Volume of the body + + AffineBody() = default; + + AffineBody(const MatrixMax3d& A, const VectorMax3d& p, const double volume) + : A(A) + , p(p) + , volume(volume) + { + } + + Eigen::MatrixXd + transform_vertices(const Eigen::MatrixXd& rest_positions) const + { + // Compute: A x̄ + p + // transpose because x is row-ordered + return (rest_positions * A.transpose()).rowwise() + p.transpose(); + } +}; + +} // namespace ipc::affine \ No newline at end of file diff --git a/src/ipc/dynamics/affine/orthogonality_potential.cpp b/src/ipc/dynamics/affine/orthogonality_potential.cpp new file mode 100644 index 000000000..f98d428e5 --- /dev/null +++ b/src/ipc/dynamics/affine/orthogonality_potential.cpp @@ -0,0 +1,168 @@ +#include "orthogonality_potential.hpp" + +#include +#include +#include + +namespace ipc::affine { + +double +OrthogonalityPotential::operator()(const std::vector& bodies) const +{ + if (bodies.empty()) { + return 0; + } + + tbb::enumerable_thread_specific storage(0); + + tbb::parallel_for( + tbb::blocked_range(size_t(0), bodies.size()), + [&](const tbb::blocked_range& r) { + double& local_potential = storage.local(); + for (size_t i = r.begin(); i < r.end(); ++i) { + // Quadrature weight is premultiplied by local potential + local_potential += (*this)(bodies[i]); + } + }); + + return storage.combine([](double a, double b) { return a + b; }); +} + +Eigen::VectorXd +OrthogonalityPotential::gradient(const std::vector& bodies) const +{ + if (bodies.empty()) { + return Eigen::VectorXd(); + } + + const int dim = bodies[0].A.rows(); + const int ndof_per_body = dim * dim + dim; + Eigen::VectorXd grad(ndof_per_body * bodies.size()); + + tbb::parallel_for( + tbb::blocked_range(size_t(0), bodies.size()), + [&](const tbb::blocked_range& r) { + for (size_t i = r.begin(); i < r.end(); ++i) { + grad.segment(ndof_per_body * i, ndof_per_body) = + this->gradient(bodies[i]); + } + }); + + return grad; +} + +Eigen::SparseMatrix OrthogonalityPotential::hessian( + const std::vector& bodies, + const bool project_hessian_to_psd) const +{ + if (bodies.empty()) { + return Eigen::SparseMatrix(); + } + + const int dim = bodies[0].A.rows(); + const int ndof_per_body = dim * dim + dim; + const int ndof = ndof_per_body * bodies.size(); + + tbb::enumerable_thread_specific>> + storage; + + tbb::parallel_for( + tbb::blocked_range(size_t(0), bodies.size()), + [&](const tbb::blocked_range& r) { + auto& hess_triplets = storage.local(); + + for (size_t i = r.begin(); i < r.end(); ++i) { + const MatrixMax9d local_hess = this->hessian(bodies[i]); + for (size_t hi = 0; hi < local_hess.rows(); ++hi) { + for (size_t hj = 0; hj < local_hess.rows(); ++hj) { + hess_triplets.emplace_back( + ndof_per_body * i + hi, ndof_per_body * i + hj, + local_hess(hi, hj)); + } + } + } + }); + + Eigen::SparseMatrix hess(ndof, ndof); + for (const auto& local_hess_triplets : storage) { + Eigen::SparseMatrix local_hess(ndof, ndof); + local_hess.setFromTriplets( + local_hess_triplets.begin(), local_hess_triplets.end()); + hess += local_hess; + } + return hess; +} + +// -- Single body methods --------------------------------------------- + +double OrthogonalityPotential::operator()(const AffineBody& body) const +{ + const auto& [A, p, volume] = body; + const auto I = MatrixMax3d::Identity(A.rows(), A.cols()); + return stiffness * volume * (A * A.transpose() - I).squaredNorm(); + + // double r = 0; + // for (int i = 0; i < A.cols(); i++) { + // for (int j = 0; j < A.cols(); j++) { + // const double dot = A.col(i).dot(A.col(j)) - int(i == j); + // r += dot * dot; + // } + // } + // return stiffness * volume * r; +} + +VectorMax12d OrthogonalityPotential::gradient(const AffineBody& body) const +{ + const auto& [A, p, volume] = body; + VectorMax12d grad = VectorMax12d::Zero(A.size() + p.size()); + + const auto I = MatrixMax3d::Identity(A.rows(), A.cols()); + const MatrixMax3d G = stiffness * volume * 4 * (A * A.transpose() - I) * A; + grad.tail(A.size()) = G.reshaped(); + + // for (int i = 0; i < A.cols(); i++) { + // auto grad_ai = grad.segment(i * A.rows() + p.size(), A.rows()); + // for (int j = 0; j < A.cols(); j++) { + // grad_ai += (A.col(i).dot(A.col(j)) - int(i == j)) * A.col(j); + // } + // grad_ai *= 4 * stiffness * volume; + // } + + return grad; +} + +MatrixMax12d OrthogonalityPotential::hessian(const AffineBody& body) const +{ + const auto& [A, p, volume] = body; + const int dim = A.rows(); + assert(p.size() == dim); + const int ndof = A.size() + p.size(); + const auto I = MatrixMax3d::Identity(A.rows(), A.cols()); + + MatrixMax12d hess = MatrixMax12d::Zero(ndof, ndof); + // NOTE: top left block is with respect to p (translation) and is zero + + for (int i = 0; i < A.cols(); i++) { + for (int j = 0; j < A.cols(); j++) { + auto hess_aij = + hess.block(i * dim + p.size(), j * dim + p.size(), dim, dim); + + hess_aij += (int(i == j) + 1) * A.col(j) * A.col(i).transpose() + + (A.col(i).dot(A.col(j)) - int(i == j)) * I; + + if (i == j) { + for (int k = 0; k < A.cols(); k++) { + if (i != k) { + hess_aij += A.col(k) * A.col(k).transpose(); + } + } + } + + hess_aij *= 4 * stiffness * volume; + } + } + + return hess; +} + +} // namespace ipc::affine \ No newline at end of file diff --git a/src/ipc/dynamics/affine/orthogonality_potential.hpp b/src/ipc/dynamics/affine/orthogonality_potential.hpp new file mode 100644 index 000000000..dde69f6ac --- /dev/null +++ b/src/ipc/dynamics/affine/orthogonality_potential.hpp @@ -0,0 +1,33 @@ +#pragma once + +#include + +namespace ipc::affine { + +class OrthogonalityPotential { +public: + OrthogonalityPotential(const double stiffness) : stiffness(stiffness) { } + virtual ~OrthogonalityPotential() = default; + + // -- Cumulative methods --------------------------------------------------- + + double operator()(const std::vector& bodies) const; + + Eigen::VectorXd gradient(const std::vector& bodies) const; + + Eigen::SparseMatrix hessian( + const std::vector& bodies, + const bool project_hessian_to_psd = false) const; + + // -- Single body methods --------------------------------------------- + + double operator()(const AffineBody& body) const; + + VectorMax12d gradient(const AffineBody& body) const; + + MatrixMax12d hessian(const AffineBody& body) const; + + double stiffness; +}; + +} // namespace ipc::affine \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/CMakeLists.txt b/src/ipc/dynamics/rigid/CMakeLists.txt new file mode 100644 index 000000000..910d603c6 --- /dev/null +++ b/src/ipc/dynamics/rigid/CMakeLists.txt @@ -0,0 +1,11 @@ +set(SOURCES + rigid_body.cpp + rigid_body.hpp +) + +source_group(TREE "${CMAKE_CURRENT_SOURCE_DIR}" PREFIX "Source Files" FILES ${SOURCES}) +target_sources(ipc_toolkit PRIVATE ${SOURCES}) + +################################################################################ +# Subfolders +################################################################################ \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/rigid_body.cpp b/src/ipc/dynamics/rigid/rigid_body.cpp new file mode 100644 index 000000000..cc7dcb921 --- /dev/null +++ b/src/ipc/dynamics/rigid/rigid_body.cpp @@ -0,0 +1,47 @@ +#include "rigid_body.hpp" + +#include + +namespace ipc::rigid { + +namespace { + inline Eigen::Matrix3d cross_product_matrix(const Eigen::Vector3d& x) + { + Eigen::Matrix3d X; + X << 0, -x.z(), x.y(), // + x.z(), 0, -x.x(), // + -x.y(), x.x(), 0; + return X; + } +} // namespace + +Eigen::MatrixXd +RigidBody::transform_vertices(const Eigen::MatrixXd& rest_positions) const +{ + // Compute: R(θ) x̄ + p + // transpose because x is row-ordered + const int dim = rest_positions.cols(); + + assert( + (dim == 2 && rotation_vector.size() == 1) + || (dim == 3 && rotation_vector.size() == 3)); + + // Convert the rotation vector to a rotation matrix + MatrixMax3d R(dim, dim); + if (dim == 2) { + const double theta = rotation_vector(0); + R << sin(theta), -cos(theta), cos(theta), sin(theta); + } else { + assert(dim == 3); + const double sinc_angle = sinc_normx(rotation_vector); + const double sinc_half_angle = sinc_normx((rotation_vector / 2).eval()); + const Eigen::Matrix3d K = cross_product_matrix(rotation_vector); + const Eigen::Matrix3d K2 = K * K; + R = sinc_angle * K + 0.5 * sinc_half_angle * sinc_half_angle * K2; + R.diagonal().array() += 1.0; + } + + return (rest_positions * R.transpose()).rowwise() + position.transpose(); +} + +} // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/rigid_body.hpp b/src/ipc/dynamics/rigid/rigid_body.hpp new file mode 100644 index 000000000..6dafd5cab --- /dev/null +++ b/src/ipc/dynamics/rigid/rigid_body.hpp @@ -0,0 +1,23 @@ +#pragma once + +#include + +namespace ipc::rigid { + +struct RigidBody { + VectorMax3d rotation_vector; // Affine matrix + VectorMax3d position; // Translation vector + + RigidBody() = default; + + RigidBody(const VectorMax3d& r, const VectorMax3d& p) + : rotation_vector(r) + , position(p) + { + } + + Eigen::MatrixXd + transform_vertices(const Eigen::MatrixXd& rest_positions) const; +}; + +} // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/utils/CMakeLists.txt b/src/ipc/utils/CMakeLists.txt index 68d98b273..b7b742469 100644 --- a/src/ipc/utils/CMakeLists.txt +++ b/src/ipc/utils/CMakeLists.txt @@ -13,6 +13,8 @@ set(SOURCES merge_thread_local.hpp save_obj.cpp save_obj.hpp + sinc.cpp + sinc.hpp unordered_map_and_set.cpp unordered_map_and_set.hpp vertex_to_min_edge.cpp diff --git a/src/ipc/utils/interval.hpp b/src/ipc/utils/interval.hpp index a4bf00ec4..e28552252 100644 --- a/src/ipc/utils/interval.hpp +++ b/src/ipc/utils/interval.hpp @@ -33,6 +33,13 @@ class Interval : public interval { this->SUP = y; } + static Interval empty() + { + return Interval( + std::numeric_limits::infinity(), + -std::numeric_limits::infinity()); + } + // friend std::ostream& operator<<(std::ostream& out, const Interval& i) // { // return out << "[" << i.INF << ", " << i.SUP << "]"; @@ -57,13 +64,13 @@ typedef Matrix3 Matrix3I; typedef MatrixMax3 MatrixMax3I; typedef MatrixX MatrixXI; -/// @brief Compute the L2 norm of a 3-dimensional interval -/// @param v The 3-dimensional interval +/// @brief Compute the L2 norm of a n-dimensional interval +/// @param v The n-dimensional interval /// @return The L2 norm of the interval filib::Interval squared_norm(const Eigen::Ref& v); // L2 norm -/// @brief Compute the L2 norm of a 3-dimensional interval -/// @param v The 3-dimensional interval +/// @brief Compute the L2 norm of a n-dimensional interval +/// @param v The n-dimensional interval /// @return The L2 norm of the interval filib::Interval norm(const Eigen::Ref& v); // L2 norm @@ -80,6 +87,7 @@ template struct ScalarBinaryOpTraits { typedef filib::Interval ReturnType; }; + } // namespace Eigen #endif \ No newline at end of file diff --git a/src/ipc/utils/sinc.cpp b/src/ipc/utils/sinc.cpp new file mode 100644 index 000000000..b44f90b26 --- /dev/null +++ b/src/ipc/utils/sinc.cpp @@ -0,0 +1,149 @@ +#include "sinc.hpp" + +namespace ipc { + +namespace { + // We use these bounds because for example 1 + x^2 = 1 for x < sqrt(ϵ). + static constexpr double taylor_0_bound = + std::numeric_limits::epsilon(); + static const double taylor_2_bound = sqrt(taylor_0_bound); + static const double taylor_n_bound = sqrt(taylor_2_bound); + + // WARNING: Assumes x is a single value and uses interval arithmetic to + // account for rounding. + filib::Interval sinc_interval_taylor(double x_double) + { + const filib::Interval x(x_double); + + if (abs(x.INF) >= taylor_n_bound) { + return sin(x) / x; + } + + // approximation by taylor series in x at 0 up to order 5 + // 1 - x² / 6 + x⁴ / 120 = 1 + x² / 6 * (x² / 20 - 1) + const filib::Interval squared_x = sqr(x); + return 1.0 + squared_x / 6.0 * (squared_x / 20.0 - 1.0); + } + + // Compute sinc'(x) / x + inline double dsinc_over_x(double x) + { + static const double eps = 1e-4; + + double x2 = x * x; + if (abs(x) > eps) { + return (x * cos(x) - sin(x)) / (x2 * x); + } + + // approximation by taylor series in x at 0 up to order 5 + return x2 * (-x2 / 840.0 + 1.0 / 30.0) - 1.0 / 3.0; + } + + // Compute sinc"(x) / x² - sinc'(x) / x³ + inline double ddsinc_over_x2_minus_dsinc_over_x3(double x) + { + static const double eps = 0.1; + + double x2 = x * x; + double x4 = x2 * x2; + if (abs(x) > eps) { + return ((3 - x2) * sin(x) - 3 * x * cos(x)) / (x4 * x); + } + + // approximation by taylor series in x at 0 up to order 5 + return x4 / 7560.0 - x2 / 210.0 + 1.0 / 15.0; + } +} // namespace + +double sinc(const double& x) +{ + if (abs(x) >= taylor_n_bound) { + return sin(x) / x; + } + + // approximation by taylor series in x at 0 up to order 1 + double result = 1; + + if (abs(x) >= taylor_0_bound) { + const double squared_x = x * x; + + // approximation by taylor series in x at 0 up to order 3 + result -= squared_x / 6.0; + + if (abs(x) >= taylor_2_bound) { + // approximation by taylor series in x at 0 up to order 5 + result += (squared_x * squared_x) / 120.0; + } + } + + return result; +} + +filib::Interval sinc(const filib::Interval& x) +{ + // Define two regions and use even symmetry of sinc. + + // A bound on sinc where it is monotonic ([0, ~4.4934]) + constexpr double monotonic_bound = 4.4934094579; + + // A conservative lower bound for sinc(x) + // https://www.wolframalpha.com/input/?i=min+sin%28x%29%2Fx+between+4+and+5 + const filib::Interval bounds(-0.217233628211221659, 1.0); + + filib::Interval y = filib::Interval::empty(), x_pos = x; + if (x.INF < 0) { + if (x.SUP <= 0) { + return sinc(-x); // sinc is an even function + } + // Split + y = sinc(filib::Interval(0, -x.INF)); + x_pos = filib::Interval(0, x.SUP); + } + + // Split the domain into two intervals: + // 1) x ∩ [0, monotonic_bound] + // 2) x ∩ [monotonic_bound, ∞) + + // Case 1 (Monotonic): + filib::Interval x_gt_monotonic = x_pos; + if (x_pos.INF <= monotonic_bound) { + filib::Interval x_monotonic = x_pos; + if (x_monotonic.SUP > monotonic_bound) { + x_monotonic = filib::Interval(x_monotonic.INF, monotonic_bound); + x_gt_monotonic = filib::Interval(monotonic_bound, x_pos.SUP); + } else { + x_gt_monotonic = filib::Interval::empty(); + } + + // sinc is monotonically decreasing, so flip lower() and upper(). + filib::Interval monotonic_y = (sinc_interval_taylor(x_monotonic.SUP) + | sinc_interval_taylor(x_monotonic.INF)) + & bounds; + + // Combine the two intervals as a convex hull + y |= monotonic_y; + } + + // Case 2 (Not necessarily monotonic): + if (!empty(x_gt_monotonic)) { + // x_gt_monotonic is larger than one, so the division should be well + // behaved. + y |= sin(x_gt_monotonic) / x_gt_monotonic; + } + + return intsec(y, bounds); +} + +VectorMax3d sinc_normx_grad(const VectorMax3d& x) +{ + return dsinc_over_x(x.norm()) * x; +} + +MatrixMax3d sinc_normx_hess(const VectorMax3d& x) +{ + double normx = x.norm(); + return ddsinc_over_x2_minus_dsinc_over_x3(normx) * x * x.transpose() + + dsinc_over_x(normx) * MatrixMax3d::Identity(x.size(), x.size()); +} + +} // namespace ipc diff --git a/src/ipc/utils/sinc.hpp b/src/ipc/utils/sinc.hpp new file mode 100644 index 000000000..61cf86ebb --- /dev/null +++ b/src/ipc/utils/sinc.hpp @@ -0,0 +1,44 @@ +#pragma once + +#include + +namespace ipc { + +/// @brief Compute the sinc function: \f$ \frac{\sin(x)}{x} \f$ +/// @param x The value for which to compute the sinc function +/// @return The value of sinc(x) +double sinc(const double& x); + +#ifdef IPC_TOOLKIT_WITH_FILIB + +/// @brief Compute the sinc function: \f$ \frac{\sin(x)}{x} \f$ over an interval +/// @param x The interval for which to compute the sinc function +/// @return The interval of sinc(x) +filib::Interval sinc(const filib::Interval& x); + +#endif + +/// @brief Compute the sinc of the norm of a vector (\f$\operatorname{sinc}(\|x\|)\f$) +/// @tparam T The type of the elements of the vector +/// @param x The vector for which to compute the sinc of the norm +/// @return The value of \f$\operatorname{sinc}(\|x\|)\f$ +template T sinc_normx(const VectorMax3& x) +{ + if constexpr (std::is_same_v) { + return sinc(x.norm()); + } else { + return sinc(norm(x)); + } +} + +/// @brief Compute the gradient of the sinc of the norm of a vector +/// @param x The vector for which to compute the gradient of the sinc of the norm +/// @return The gradient of the sinc of the norm of the vector +VectorMax3d sinc_normx_grad(const VectorMax3d& x); + +/// @brief Compute the Hessian of the sinc of the norm of a vector +/// @param x The vector for which to compute the Hessian of the sinc of the norm +/// @return The Hessian of the sinc of the norm of the vector +MatrixMax3d sinc_normx_hess(const VectorMax3d& x); + +} // namespace ipc \ No newline at end of file diff --git a/tests/src/tests/CMakeLists.txt b/tests/src/tests/CMakeLists.txt index 3b0028455..e333fea61 100644 --- a/tests/src/tests/CMakeLists.txt +++ b/tests/src/tests/CMakeLists.txt @@ -29,6 +29,7 @@ add_subdirectory(candidates) add_subdirectory(ccd) add_subdirectory(collisions) add_subdirectory(distance) +add_subdirectory(dynamics) add_subdirectory(friction) add_subdirectory(potential) add_subdirectory(utils) \ No newline at end of file diff --git a/tests/src/tests/dynamics/CMakeLists.txt b/tests/src/tests/dynamics/CMakeLists.txt new file mode 100644 index 000000000..fd6c3e17c --- /dev/null +++ b/tests/src/tests/dynamics/CMakeLists.txt @@ -0,0 +1,5 @@ +################################################################################ +# Subfolders +################################################################################ + +add_subdirectory(affine) \ No newline at end of file diff --git a/tests/src/tests/dynamics/affine/CMakeLists.txt b/tests/src/tests/dynamics/affine/CMakeLists.txt new file mode 100644 index 000000000..25797a113 --- /dev/null +++ b/tests/src/tests/dynamics/affine/CMakeLists.txt @@ -0,0 +1,10 @@ +set(SOURCES + test_orthogonality_potential.cpp +) + +source_group(TREE "${CMAKE_CURRENT_SOURCE_DIR}" PREFIX "Source Files" FILES ${SOURCES}) +target_sources(ipc_toolkit_tests PRIVATE ${SOURCES}) + +################################################################################ +# Subfolders +################################################################################ \ No newline at end of file diff --git a/tests/src/tests/dynamics/affine/test_orthogonality_potential.cpp b/tests/src/tests/dynamics/affine/test_orthogonality_potential.cpp new file mode 100644 index 000000000..074e67f1d --- /dev/null +++ b/tests/src/tests/dynamics/affine/test_orthogonality_potential.cpp @@ -0,0 +1,80 @@ +#include + +#include + +#include + +#include + +TEST_CASE("Orthogonality potential", "[abd]") +{ + using namespace ipc; + using namespace ipc::affine; + + AffineBody body(MatrixMax9d::Random(3, 3), VectorMax9d::Random(3), 1); + + VectorMax12d dof(12); + dof.head(3) = body.p; + dof.segment(3, 3) = body.A.col(0); + dof.segment(6, 3) = body.A.col(1); + dof.segment(9, 3) = body.A.col(2); + + OrthogonalityPotential V_perp(1); + + // ------------------------------------------------------------------------- + // Gradient + // ------------------------------------------------------------------------- + + const Eigen::VectorXd grad_V_perp = V_perp.gradient(body); + REQUIRE(grad_V_perp.squaredNorm() > 1e-8); + + // Compute the gradient using finite differences + Eigen::VectorXd fgrad_V_perp; + { + auto f = [&V_perp, &body](const Eigen::VectorXd& x) { + AffineBody fd_body; + fd_body.p = x.head(3); + fd_body.A.resize(3, 3); + fd_body.A.col(0) = x.segment(3, 3); + fd_body.A.col(1) = x.segment(6, 3); + fd_body.A.col(2) = x.segment(9, 3); + fd_body.volume = body.volume; + return V_perp(fd_body); + }; + fd::finite_gradient(dof, f, fgrad_V_perp); + } + + CHECK(fd::compare_gradient(grad_V_perp, fgrad_V_perp)); + if (!fd::compare_gradient(grad_V_perp, fgrad_V_perp)) { + logger().error("grad_V_perp: {}", grad_V_perp); + logger().error("fgrad_V_perp: {}", fgrad_V_perp); + } + + // ------------------------------------------------------------------------- + // Hessian + // ------------------------------------------------------------------------- + + const Eigen::MatrixXd hess_V_perp = V_perp.hessian(body); + REQUIRE(hess_V_perp.squaredNorm() > 1e-3); + + // Compute the gradient using finite differences + Eigen::MatrixXd fhess_V_perp; + { + auto f = [&](const Eigen::VectorXd& x) { + AffineBody fd_body; + fd_body.p = x.head(3); + fd_body.A.resize(3, 3); + fd_body.A.col(0) = x.segment(3, 3); + fd_body.A.col(1) = x.segment(6, 3); + fd_body.A.col(2) = x.segment(9, 3); + fd_body.volume = body.volume; + return V_perp.gradient(fd_body); + }; + fd::finite_jacobian(dof, f, fhess_V_perp); + } + + CHECK(fd::compare_hessian(hess_V_perp, fhess_V_perp, 1e-3)); + if (!fd::compare_hessian(hess_V_perp, fhess_V_perp, 1e-3)) { + tests::print_compare_nonzero(hess_V_perp, fhess_V_perp); + } +} \ No newline at end of file diff --git a/tests/src/tests/utils/CMakeLists.txt b/tests/src/tests/utils/CMakeLists.txt index 2175e0184..52d639fc8 100644 --- a/tests/src/tests/utils/CMakeLists.txt +++ b/tests/src/tests/utils/CMakeLists.txt @@ -1,6 +1,7 @@ set(SOURCES # Tests test_interval.cpp + test_sinc.cpp test_utils.cpp # Benchmarks diff --git a/tests/src/tests/utils/test_sinc.cpp b/tests/src/tests/utils/test_sinc.cpp new file mode 100644 index 000000000..8a3e7c622 --- /dev/null +++ b/tests/src/tests/utils/test_sinc.cpp @@ -0,0 +1,151 @@ +#include +#include +#include + +#include + +#include +#include + +// #include +#include + +using namespace ipc; + +TEST_CASE("sinc(double)", "[sinc][double]") +{ + CHECK(sinc(0) == Catch::Approx(1)); + CHECK(sinc(1e-8) == Catch::Approx(1)); + CHECK(sinc(igl::PI / 2) == Catch::Approx(2 / igl::PI)); + CHECK(sinc(igl::PI) == Catch::Approx(0).margin(1e-16)); +} + +TEST_CASE("sinc(Interval)", "[sinc][interval]") +{ + // All of these cases fall within the monotonic bound on sinc, so they are + // a tight bound (ignoring rounding). + filib::Interval x, expected_y; + + SECTION("y=[1, 1]") + { + SECTION("[0, 0]") { x = filib::Interval(0); }; + SECTION("[0, 1e-8]") { x = filib::Interval(0, 1e-8); }; + SECTION("[-1e-8, 0]") { x = filib::Interval(-1e-8, 0); }; + SECTION("[-1e-8, 1e-8]") { x = filib::Interval(-1e-8, 1e-8); }; + expected_y = filib::Interval(1); + } + SECTION("y=[0, 1]") + { + SECTION("[0, π]") { x = filib::Interval(0, igl::PI); } + SECTION("[-π, 0]") { x = filib::Interval(-igl::PI, 0); } + SECTION("[-π, π]") { x = filib::Interval(-igl::PI, igl::PI); } + expected_y = filib::Interval(0, 1); + } + SECTION("y=[2/pi, 1]") + { + const double PI_2 = igl::PI / 2; + SECTION("[0, π/2]") { x = filib::Interval(0, PI_2); } + SECTION("[-π/2, 0]") { x = filib::Interval(-PI_2, 0); } + SECTION("[-π/2, π/2]") { x = filib::Interval(-PI_2, PI_2); } + expected_y = filib::Interval(2 / igl::PI, 1); + } + + CAPTURE(x.INF, x.SUP); + filib::Interval y = sinc(x); + CHECK(y.INF == Catch::Approx(expected_y.INF).margin(1e-8)); + CHECK(y.SUP == Catch::Approx(expected_y.SUP).margin(1e-8)); +} + +TEST_CASE("Interval sinc with looser bounds", "[sinc][interval]") +{ + filib::Interval x, expected_y; + + SECTION("Non-monotonic") + { + const double a = GENERATE(-5, -1, 0); + x = filib::Interval(a, 5); + expected_y = filib::Interval(-0.217233628211221659, 1); + } + SECTION("Monotonic outside bounds") + { + x = filib::Interval(5, 7); + expected_y = filib::Interval(sinc(5), sinc(7)); + } + SECTION("Monotonic far outside bounds") + { + x = filib::Interval(21, 22); + expected_y = filib::Interval(sinc(22), sinc(21)); + } + + filib::Interval y = sinc(x); + CAPTURE(x.INF, x.SUP, y.INF, y.SUP, expected_y.INF, expected_y.SUP); + CHECK(in(expected_y, y)); + // Loosest bound + CHECK(in(y, filib::Interval(-0.23, 1))); + if (x.INF > 0) { + // Tighter bound if x.INF > 1 + CHECK(in(y, filib::Interval(-1 / x.INF, 1 / x.INF))); + } +} + +TEST_CASE("Interval sinc_normx", "[sinc][interval]") +{ + VectorMax3 x = VectorMax3::Zero(3); + filib::Interval expected_y; + + SECTION("Zero") + { + // x is already zero + expected_y = filib::Interval(1); + } + SECTION("Positive") + { + x(1) = filib::Interval(igl::PI); + expected_y = filib::Interval(0); + } + SECTION("Negative") + { + x(1) = filib::Interval(-igl::PI); + expected_y = filib::Interval(0); + } + SECTION("Mixed") + { + x(1) = filib::Interval(-igl::PI, igl::PI); + expected_y = filib::Interval(0, 1); + } + + filib::Interval y = sinc_normx(x); + CAPTURE(y.INF, y.SUP, expected_y.INF, expected_y.SUP); + CHECK(expected_y.INF == Catch::Approx(y.INF).margin(1e-8)); + CHECK(expected_y.SUP == Catch::Approx(y.SUP).margin(1e-8)); +} + +TEST_CASE("∇sinc(||x||)", "[sinc][vector][diff]") +{ + double sign = GENERATE(-1, 1); + double val = GENERATE(0, 1e-8, igl::PI / 2, igl::PI, 5, 20, 100); + int index = GENERATE(0, 1, 2); + Eigen::Vector3d x = Eigen::Vector3d::Zero(); + x(index) = sign * val; + + Eigen::VectorXd fgrad(3); + fd::finite_gradient(x, sinc_normx, fgrad); + + Eigen::Vector3d grad = sinc_normx_grad(x); + CHECK(fd::compare_gradient(grad, fgrad)); +} + +TEST_CASE("∇²sinc(||x||)", "[sinc][vector][diff]") +{ + double sign = GENERATE(-1, 1); + double val = GENERATE(0, 1e-8, igl::PI / 2, igl::PI, 5, 20, 100); + int index = GENERATE(0, 1, 2); + Eigen::Vector3d x = Eigen::Vector3d::Zero(); + x(index) = sign * val; + + Eigen::MatrixXd fhess(3, 3); + fd::finite_hessian(x, sinc_normx, fhess); + + Eigen::Matrix3d hess = sinc_normx_hess(x); + CHECK(fd::compare_hessian(hess, fhess)); +} \ No newline at end of file From 75d0588010daeb4a601072f1204336ee95eacdc0 Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Fri, 31 May 2024 00:49:14 -0400 Subject: [PATCH 02/24] Add comments to OrthogonalityPotential::hessian --- src/ipc/dynamics/affine/orthogonality_potential.cpp | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/src/ipc/dynamics/affine/orthogonality_potential.cpp b/src/ipc/dynamics/affine/orthogonality_potential.cpp index f98d428e5..6a9d60ad5 100644 --- a/src/ipc/dynamics/affine/orthogonality_potential.cpp +++ b/src/ipc/dynamics/affine/orthogonality_potential.cpp @@ -147,12 +147,13 @@ MatrixMax12d OrthogonalityPotential::hessian(const AffineBody& body) const auto hess_aij = hess.block(i * dim + p.size(), j * dim + p.size(), dim, dim); + // Extra outer product term if i == j hess_aij += (int(i == j) + 1) * A.col(j) * A.col(i).transpose() + (A.col(i).dot(A.col(j)) - int(i == j)) * I; if (i == j) { for (int k = 0; k < A.cols(); k++) { - if (i != k) { + if (i != k) { // Already added the i == k term above hess_aij += A.col(k) * A.col(k).transpose(); } } From 8b3a1b24d920b975bf503586eaf7937f8ceb8b0e Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Wed, 5 Jun 2024 20:03:49 -0400 Subject: [PATCH 03/24] Add J matrix to AffineBody class --- notebooks/abd.ipynb | 581 +++++++++++++++++------- src/ipc/dynamics/affine/affine_body.hpp | 34 ++ 2 files changed, 441 insertions(+), 174 deletions(-) diff --git a/notebooks/abd.ipynb b/notebooks/abd.ipynb index 315d2a265..825d7c805 100644 --- a/notebooks/abd.ipynb +++ b/notebooks/abd.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "code", - "execution_count": 36, + "execution_count": 237, "metadata": {}, "outputs": [], "source": [ @@ -12,19 +12,19 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 238, "metadata": {}, "outputs": [ { "data": { "text/latex": [ - "$\\displaystyle \\left[\\begin{matrix}a_{00} & a_{01} & a_{02}\\\\a_{10} & a_{11} & a_{12}\\\\a_{20} & a_{21} & a_{22}\\end{matrix}\\right]$" + "$\\displaystyle \\left[\\begin{matrix}a_{1x} & a_{1y} & a_{1z}\\\\a_{2x} & a_{2y} & a_{2z}\\\\a_{3x} & a_{3y} & a_{3z}\\end{matrix}\\right]$" ], "text/plain": [ "Matrix([\n", - "[a00, a01, a02],\n", - "[a10, a11, a12],\n", - "[a20, a21, a22]])" + "[a_{1x}, a_{1y}, a_{1z}],\n", + "[a_{2x}, a_{2y}, a_{2z}],\n", + "[a_{3x}, a_{3y}, a_{3z}]])" ] }, "metadata": {}, @@ -32,14 +32,14 @@ } ], "source": [ - "A = sympy.symbols([f\"a{i}{j}\" for i in range(3) for j in range(3)])\n", + "A = sympy.symbols([f\"a_{{{i}{j}}}\" for i in range(1, 4) for j in \"xyz\"])\n", "A = np.array(A).reshape(3, 3)\n", "display(sympy.Matrix(A))" ] }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 239, "metadata": {}, "outputs": [], "source": [ @@ -55,7 +55,7 @@ }, { "cell_type": "code", - "execution_count": 39, + "execution_count": 240, "metadata": {}, "outputs": [], "source": [ @@ -65,7 +65,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 241, "metadata": {}, "outputs": [ { @@ -77,7 +77,7 @@ "0" ] }, - "execution_count": 40, + "execution_count": 241, "metadata": {}, "output_type": "execute_result" } @@ -88,16 +88,16 @@ }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 242, "metadata": {}, "outputs": [ { "data": { "text/latex": [ - "$\\displaystyle 12 a_{00}^{2} + 4 a_{01}^{2} + 4 a_{02}^{2} + 4 a_{10}^{2} + 4 a_{20}^{2} - 4.0$" + "$\\displaystyle 12 a_{1x}^{2} + 4 a_{1y}^{2} + 4 a_{1z}^{2} + 4 a_{2x}^{2} + 4 a_{3x}^{2} - 4.0$" ], "text/plain": [ - "12*a00**2 + 4*a01**2 + 4*a02**2 + 4*a10**2 + 4*a20**2 - 4.0" + "12*a_{1x}**2 + 4*a_{1y}**2 + 4*a_{1z}**2 + 4*a_{2x}**2 + 4*a_{3x}**2 - 4.0" ] }, "metadata": {}, @@ -106,10 +106,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 8 a_{00} a_{01} + 4 a_{10} a_{11} + 4 a_{20} a_{21}$" + "$\\displaystyle 8 a_{1x} a_{1y} + 4 a_{2x} a_{2y} + 4 a_{3x} a_{3y}$" ], "text/plain": [ - "8*a00*a01 + 4*a10*a11 + 4*a20*a21" + "8*a_{1x}*a_{1y} + 4*a_{2x}*a_{2y} + 4*a_{3x}*a_{3y}" ] }, "metadata": {}, @@ -118,10 +118,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 8 a_{00} a_{02} + 4 a_{10} a_{12} + 4 a_{20} a_{22}$" + "$\\displaystyle 8 a_{1x} a_{1z} + 4 a_{2x} a_{2z} + 4 a_{3x} a_{3z}$" ], "text/plain": [ - "8*a00*a02 + 4*a10*a12 + 4*a20*a22" + "8*a_{1x}*a_{1z} + 4*a_{2x}*a_{2z} + 4*a_{3x}*a_{3z}" ] }, "metadata": {}, @@ -130,10 +130,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 8 a_{00} a_{10} + 4 a_{01} a_{11} + 4 a_{02} a_{12}$" + "$\\displaystyle 8 a_{1x} a_{2x} + 4 a_{1y} a_{2y} + 4 a_{1z} a_{2z}$" ], "text/plain": [ - "8*a00*a10 + 4*a01*a11 + 4*a02*a12" + "8*a_{1x}*a_{2x} + 4*a_{1y}*a_{2y} + 4*a_{1z}*a_{2z}" ] }, "metadata": {}, @@ -142,10 +142,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01} a_{10}$" + "$\\displaystyle 4 a_{1y} a_{2x}$" ], "text/plain": [ - "4*a01*a10" + "4*a_{1y}*a_{2x}" ] }, "metadata": {}, @@ -154,10 +154,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{02} a_{10}$" + "$\\displaystyle 4 a_{1z} a_{2x}$" ], "text/plain": [ - "4*a02*a10" + "4*a_{1z}*a_{2x}" ] }, "metadata": {}, @@ -166,10 +166,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 8 a_{00} a_{20} + 4 a_{01} a_{21} + 4 a_{02} a_{22}$" + "$\\displaystyle 8 a_{1x} a_{3x} + 4 a_{1y} a_{3y} + 4 a_{1z} a_{3z}$" ], "text/plain": [ - "8*a00*a20 + 4*a01*a21 + 4*a02*a22" + "8*a_{1x}*a_{3x} + 4*a_{1y}*a_{3y} + 4*a_{1z}*a_{3z}" ] }, "metadata": {}, @@ -178,10 +178,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01} a_{20}$" + "$\\displaystyle 4 a_{1y} a_{3x}$" ], "text/plain": [ - "4*a01*a20" + "4*a_{1y}*a_{3x}" ] }, "metadata": {}, @@ -190,10 +190,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{02} a_{20}$" + "$\\displaystyle 4 a_{1z} a_{3x}$" ], "text/plain": [ - "4*a02*a20" + "4*a_{1z}*a_{3x}" ] }, "metadata": {}, @@ -202,10 +202,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 8 a_{00} a_{01} + 4 a_{10} a_{11} + 4 a_{20} a_{21}$" + "$\\displaystyle 8 a_{1x} a_{1y} + 4 a_{2x} a_{2y} + 4 a_{3x} a_{3y}$" ], "text/plain": [ - "8*a00*a01 + 4*a10*a11 + 4*a20*a21" + "8*a_{1x}*a_{1y} + 4*a_{2x}*a_{2y} + 4*a_{3x}*a_{3y}" ] }, "metadata": {}, @@ -214,10 +214,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00}^{2} + 12 a_{01}^{2} + 4 a_{02}^{2} + 4 a_{11}^{2} + 4 a_{21}^{2} - 4.0$" + "$\\displaystyle 4 a_{1x}^{2} + 12 a_{1y}^{2} + 4 a_{1z}^{2} + 4 a_{2y}^{2} + 4 a_{3y}^{2} - 4.0$" ], "text/plain": [ - "4*a00**2 + 12*a01**2 + 4*a02**2 + 4*a11**2 + 4*a21**2 - 4.0" + "4*a_{1x}**2 + 12*a_{1y}**2 + 4*a_{1z}**2 + 4*a_{2y}**2 + 4*a_{3y}**2 - 4.0" ] }, "metadata": {}, @@ -226,10 +226,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 8 a_{01} a_{02} + 4 a_{11} a_{12} + 4 a_{21} a_{22}$" + "$\\displaystyle 8 a_{1y} a_{1z} + 4 a_{2y} a_{2z} + 4 a_{3y} a_{3z}$" ], "text/plain": [ - "8*a01*a02 + 4*a11*a12 + 4*a21*a22" + "8*a_{1y}*a_{1z} + 4*a_{2y}*a_{2z} + 4*a_{3y}*a_{3z}" ] }, "metadata": {}, @@ -238,10 +238,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{11}$" + "$\\displaystyle 4 a_{1x} a_{2y}$" ], "text/plain": [ - "4*a00*a11" + "4*a_{1x}*a_{2y}" ] }, "metadata": {}, @@ -250,10 +250,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{10} + 8 a_{01} a_{11} + 4 a_{02} a_{12}$" + "$\\displaystyle 4 a_{1x} a_{2x} + 8 a_{1y} a_{2y} + 4 a_{1z} a_{2z}$" ], "text/plain": [ - "4*a00*a10 + 8*a01*a11 + 4*a02*a12" + "4*a_{1x}*a_{2x} + 8*a_{1y}*a_{2y} + 4*a_{1z}*a_{2z}" ] }, "metadata": {}, @@ -262,10 +262,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{02} a_{11}$" + "$\\displaystyle 4 a_{1z} a_{2y}$" ], "text/plain": [ - "4*a02*a11" + "4*a_{1z}*a_{2y}" ] }, "metadata": {}, @@ -274,10 +274,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{21}$" + "$\\displaystyle 4 a_{1x} a_{3y}$" ], "text/plain": [ - "4*a00*a21" + "4*a_{1x}*a_{3y}" ] }, "metadata": {}, @@ -286,10 +286,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{20} + 8 a_{01} a_{21} + 4 a_{02} a_{22}$" + "$\\displaystyle 4 a_{1x} a_{3x} + 8 a_{1y} a_{3y} + 4 a_{1z} a_{3z}$" ], "text/plain": [ - "4*a00*a20 + 8*a01*a21 + 4*a02*a22" + "4*a_{1x}*a_{3x} + 8*a_{1y}*a_{3y} + 4*a_{1z}*a_{3z}" ] }, "metadata": {}, @@ -298,10 +298,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{02} a_{21}$" + "$\\displaystyle 4 a_{1z} a_{3y}$" ], "text/plain": [ - "4*a02*a21" + "4*a_{1z}*a_{3y}" ] }, "metadata": {}, @@ -310,10 +310,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 8 a_{00} a_{02} + 4 a_{10} a_{12} + 4 a_{20} a_{22}$" + "$\\displaystyle 8 a_{1x} a_{1z} + 4 a_{2x} a_{2z} + 4 a_{3x} a_{3z}$" ], "text/plain": [ - "8*a00*a02 + 4*a10*a12 + 4*a20*a22" + "8*a_{1x}*a_{1z} + 4*a_{2x}*a_{2z} + 4*a_{3x}*a_{3z}" ] }, "metadata": {}, @@ -322,10 +322,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 8 a_{01} a_{02} + 4 a_{11} a_{12} + 4 a_{21} a_{22}$" + "$\\displaystyle 8 a_{1y} a_{1z} + 4 a_{2y} a_{2z} + 4 a_{3y} a_{3z}$" ], "text/plain": [ - "8*a01*a02 + 4*a11*a12 + 4*a21*a22" + "8*a_{1y}*a_{1z} + 4*a_{2y}*a_{2z} + 4*a_{3y}*a_{3z}" ] }, "metadata": {}, @@ -334,10 +334,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00}^{2} + 4 a_{01}^{2} + 12 a_{02}^{2} + 4 a_{12}^{2} + 4 a_{22}^{2} - 4.0$" + "$\\displaystyle 4 a_{1x}^{2} + 4 a_{1y}^{2} + 12 a_{1z}^{2} + 4 a_{2z}^{2} + 4 a_{3z}^{2} - 4.0$" ], "text/plain": [ - "4*a00**2 + 4*a01**2 + 12*a02**2 + 4*a12**2 + 4*a22**2 - 4.0" + "4*a_{1x}**2 + 4*a_{1y}**2 + 12*a_{1z}**2 + 4*a_{2z}**2 + 4*a_{3z}**2 - 4.0" ] }, "metadata": {}, @@ -346,10 +346,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{12}$" + "$\\displaystyle 4 a_{1x} a_{2z}$" ], "text/plain": [ - "4*a00*a12" + "4*a_{1x}*a_{2z}" ] }, "metadata": {}, @@ -358,10 +358,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01} a_{12}$" + "$\\displaystyle 4 a_{1y} a_{2z}$" ], "text/plain": [ - "4*a01*a12" + "4*a_{1y}*a_{2z}" ] }, "metadata": {}, @@ -370,10 +370,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{10} + 4 a_{01} a_{11} + 8 a_{02} a_{12}$" + "$\\displaystyle 4 a_{1x} a_{2x} + 4 a_{1y} a_{2y} + 8 a_{1z} a_{2z}$" ], "text/plain": [ - "4*a00*a10 + 4*a01*a11 + 8*a02*a12" + "4*a_{1x}*a_{2x} + 4*a_{1y}*a_{2y} + 8*a_{1z}*a_{2z}" ] }, "metadata": {}, @@ -382,10 +382,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{22}$" + "$\\displaystyle 4 a_{1x} a_{3z}$" ], "text/plain": [ - "4*a00*a22" + "4*a_{1x}*a_{3z}" ] }, "metadata": {}, @@ -394,10 +394,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01} a_{22}$" + "$\\displaystyle 4 a_{1y} a_{3z}$" ], "text/plain": [ - "4*a01*a22" + "4*a_{1y}*a_{3z}" ] }, "metadata": {}, @@ -406,10 +406,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{20} + 4 a_{01} a_{21} + 8 a_{02} a_{22}$" + "$\\displaystyle 4 a_{1x} a_{3x} + 4 a_{1y} a_{3y} + 8 a_{1z} a_{3z}$" ], "text/plain": [ - "4*a00*a20 + 4*a01*a21 + 8*a02*a22" + "4*a_{1x}*a_{3x} + 4*a_{1y}*a_{3y} + 8*a_{1z}*a_{3z}" ] }, "metadata": {}, @@ -418,10 +418,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 8 a_{00} a_{10} + 4 a_{01} a_{11} + 4 a_{02} a_{12}$" + "$\\displaystyle 8 a_{1x} a_{2x} + 4 a_{1y} a_{2y} + 4 a_{1z} a_{2z}$" ], "text/plain": [ - "8*a00*a10 + 4*a01*a11 + 4*a02*a12" + "8*a_{1x}*a_{2x} + 4*a_{1y}*a_{2y} + 4*a_{1z}*a_{2z}" ] }, "metadata": {}, @@ -430,10 +430,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{11}$" + "$\\displaystyle 4 a_{1x} a_{2y}$" ], "text/plain": [ - "4*a00*a11" + "4*a_{1x}*a_{2y}" ] }, "metadata": {}, @@ -442,10 +442,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{12}$" + "$\\displaystyle 4 a_{1x} a_{2z}$" ], "text/plain": [ - "4*a00*a12" + "4*a_{1x}*a_{2z}" ] }, "metadata": {}, @@ -454,10 +454,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00}^{2} + 12 a_{10}^{2} + 4 a_{11}^{2} + 4 a_{12}^{2} + 4 a_{20}^{2} - 4.0$" + "$\\displaystyle 4 a_{1x}^{2} + 12 a_{2x}^{2} + 4 a_{2y}^{2} + 4 a_{2z}^{2} + 4 a_{3x}^{2} - 4.0$" ], "text/plain": [ - "4*a00**2 + 12*a10**2 + 4*a11**2 + 4*a12**2 + 4*a20**2 - 4.0" + "4*a_{1x}**2 + 12*a_{2x}**2 + 4*a_{2y}**2 + 4*a_{2z}**2 + 4*a_{3x}**2 - 4.0" ] }, "metadata": {}, @@ -466,10 +466,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{01} + 8 a_{10} a_{11} + 4 a_{20} a_{21}$" + "$\\displaystyle 4 a_{1x} a_{1y} + 8 a_{2x} a_{2y} + 4 a_{3x} a_{3y}$" ], "text/plain": [ - "4*a00*a01 + 8*a10*a11 + 4*a20*a21" + "4*a_{1x}*a_{1y} + 8*a_{2x}*a_{2y} + 4*a_{3x}*a_{3y}" ] }, "metadata": {}, @@ -478,10 +478,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{02} + 8 a_{10} a_{12} + 4 a_{20} a_{22}$" + "$\\displaystyle 4 a_{1x} a_{1z} + 8 a_{2x} a_{2z} + 4 a_{3x} a_{3z}$" ], "text/plain": [ - "4*a00*a02 + 8*a10*a12 + 4*a20*a22" + "4*a_{1x}*a_{1z} + 8*a_{2x}*a_{2z} + 4*a_{3x}*a_{3z}" ] }, "metadata": {}, @@ -490,10 +490,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 8 a_{10} a_{20} + 4 a_{11} a_{21} + 4 a_{12} a_{22}$" + "$\\displaystyle 8 a_{2x} a_{3x} + 4 a_{2y} a_{3y} + 4 a_{2z} a_{3z}$" ], "text/plain": [ - "8*a10*a20 + 4*a11*a21 + 4*a12*a22" + "8*a_{2x}*a_{3x} + 4*a_{2y}*a_{3y} + 4*a_{2z}*a_{3z}" ] }, "metadata": {}, @@ -502,10 +502,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{11} a_{20}$" + "$\\displaystyle 4 a_{2y} a_{3x}$" ], "text/plain": [ - "4*a11*a20" + "4*a_{2y}*a_{3x}" ] }, "metadata": {}, @@ -514,10 +514,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{12} a_{20}$" + "$\\displaystyle 4 a_{2z} a_{3x}$" ], "text/plain": [ - "4*a12*a20" + "4*a_{2z}*a_{3x}" ] }, "metadata": {}, @@ -526,10 +526,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01} a_{10}$" + "$\\displaystyle 4 a_{1y} a_{2x}$" ], "text/plain": [ - "4*a01*a10" + "4*a_{1y}*a_{2x}" ] }, "metadata": {}, @@ -538,10 +538,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{10} + 8 a_{01} a_{11} + 4 a_{02} a_{12}$" + "$\\displaystyle 4 a_{1x} a_{2x} + 8 a_{1y} a_{2y} + 4 a_{1z} a_{2z}$" ], "text/plain": [ - "4*a00*a10 + 8*a01*a11 + 4*a02*a12" + "4*a_{1x}*a_{2x} + 8*a_{1y}*a_{2y} + 4*a_{1z}*a_{2z}" ] }, "metadata": {}, @@ -550,10 +550,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01} a_{12}$" + "$\\displaystyle 4 a_{1y} a_{2z}$" ], "text/plain": [ - "4*a01*a12" + "4*a_{1y}*a_{2z}" ] }, "metadata": {}, @@ -562,10 +562,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{01} + 8 a_{10} a_{11} + 4 a_{20} a_{21}$" + "$\\displaystyle 4 a_{1x} a_{1y} + 8 a_{2x} a_{2y} + 4 a_{3x} a_{3y}$" ], "text/plain": [ - "4*a00*a01 + 8*a10*a11 + 4*a20*a21" + "4*a_{1x}*a_{1y} + 8*a_{2x}*a_{2y} + 4*a_{3x}*a_{3y}" ] }, "metadata": {}, @@ -574,10 +574,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01}^{2} + 4 a_{10}^{2} + 12 a_{11}^{2} + 4 a_{12}^{2} + 4 a_{21}^{2} - 4.0$" + "$\\displaystyle 4 a_{1y}^{2} + 4 a_{2x}^{2} + 12 a_{2y}^{2} + 4 a_{2z}^{2} + 4 a_{3y}^{2} - 4.0$" ], "text/plain": [ - "4*a01**2 + 4*a10**2 + 12*a11**2 + 4*a12**2 + 4*a21**2 - 4.0" + "4*a_{1y}**2 + 4*a_{2x}**2 + 12*a_{2y}**2 + 4*a_{2z}**2 + 4*a_{3y}**2 - 4.0" ] }, "metadata": {}, @@ -586,10 +586,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01} a_{02} + 8 a_{11} a_{12} + 4 a_{21} a_{22}$" + "$\\displaystyle 4 a_{1y} a_{1z} + 8 a_{2y} a_{2z} + 4 a_{3y} a_{3z}$" ], "text/plain": [ - "4*a01*a02 + 8*a11*a12 + 4*a21*a22" + "4*a_{1y}*a_{1z} + 8*a_{2y}*a_{2z} + 4*a_{3y}*a_{3z}" ] }, "metadata": {}, @@ -598,10 +598,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{10} a_{21}$" + "$\\displaystyle 4 a_{2x} a_{3y}$" ], "text/plain": [ - "4*a10*a21" + "4*a_{2x}*a_{3y}" ] }, "metadata": {}, @@ -610,10 +610,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{10} a_{20} + 8 a_{11} a_{21} + 4 a_{12} a_{22}$" + "$\\displaystyle 4 a_{2x} a_{3x} + 8 a_{2y} a_{3y} + 4 a_{2z} a_{3z}$" ], "text/plain": [ - "4*a10*a20 + 8*a11*a21 + 4*a12*a22" + "4*a_{2x}*a_{3x} + 8*a_{2y}*a_{3y} + 4*a_{2z}*a_{3z}" ] }, "metadata": {}, @@ -622,10 +622,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{12} a_{21}$" + "$\\displaystyle 4 a_{2z} a_{3y}$" ], "text/plain": [ - "4*a12*a21" + "4*a_{2z}*a_{3y}" ] }, "metadata": {}, @@ -634,10 +634,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{02} a_{10}$" + "$\\displaystyle 4 a_{1z} a_{2x}$" ], "text/plain": [ - "4*a02*a10" + "4*a_{1z}*a_{2x}" ] }, "metadata": {}, @@ -646,10 +646,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{02} a_{11}$" + "$\\displaystyle 4 a_{1z} a_{2y}$" ], "text/plain": [ - "4*a02*a11" + "4*a_{1z}*a_{2y}" ] }, "metadata": {}, @@ -658,10 +658,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{10} + 4 a_{01} a_{11} + 8 a_{02} a_{12}$" + "$\\displaystyle 4 a_{1x} a_{2x} + 4 a_{1y} a_{2y} + 8 a_{1z} a_{2z}$" ], "text/plain": [ - "4*a00*a10 + 4*a01*a11 + 8*a02*a12" + "4*a_{1x}*a_{2x} + 4*a_{1y}*a_{2y} + 8*a_{1z}*a_{2z}" ] }, "metadata": {}, @@ -670,10 +670,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{02} + 8 a_{10} a_{12} + 4 a_{20} a_{22}$" + "$\\displaystyle 4 a_{1x} a_{1z} + 8 a_{2x} a_{2z} + 4 a_{3x} a_{3z}$" ], "text/plain": [ - "4*a00*a02 + 8*a10*a12 + 4*a20*a22" + "4*a_{1x}*a_{1z} + 8*a_{2x}*a_{2z} + 4*a_{3x}*a_{3z}" ] }, "metadata": {}, @@ -682,10 +682,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01} a_{02} + 8 a_{11} a_{12} + 4 a_{21} a_{22}$" + "$\\displaystyle 4 a_{1y} a_{1z} + 8 a_{2y} a_{2z} + 4 a_{3y} a_{3z}$" ], "text/plain": [ - "4*a01*a02 + 8*a11*a12 + 4*a21*a22" + "4*a_{1y}*a_{1z} + 8*a_{2y}*a_{2z} + 4*a_{3y}*a_{3z}" ] }, "metadata": {}, @@ -694,10 +694,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{02}^{2} + 4 a_{10}^{2} + 4 a_{11}^{2} + 12 a_{12}^{2} + 4 a_{22}^{2} - 4.0$" + "$\\displaystyle 4 a_{1z}^{2} + 4 a_{2x}^{2} + 4 a_{2y}^{2} + 12 a_{2z}^{2} + 4 a_{3z}^{2} - 4.0$" ], "text/plain": [ - "4*a02**2 + 4*a10**2 + 4*a11**2 + 12*a12**2 + 4*a22**2 - 4.0" + "4*a_{1z}**2 + 4*a_{2x}**2 + 4*a_{2y}**2 + 12*a_{2z}**2 + 4*a_{3z}**2 - 4.0" ] }, "metadata": {}, @@ -706,10 +706,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{10} a_{22}$" + "$\\displaystyle 4 a_{2x} a_{3z}$" ], "text/plain": [ - "4*a10*a22" + "4*a_{2x}*a_{3z}" ] }, "metadata": {}, @@ -718,10 +718,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{11} a_{22}$" + "$\\displaystyle 4 a_{2y} a_{3z}$" ], "text/plain": [ - "4*a11*a22" + "4*a_{2y}*a_{3z}" ] }, "metadata": {}, @@ -730,10 +730,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{10} a_{20} + 4 a_{11} a_{21} + 8 a_{12} a_{22}$" + "$\\displaystyle 4 a_{2x} a_{3x} + 4 a_{2y} a_{3y} + 8 a_{2z} a_{3z}$" ], "text/plain": [ - "4*a10*a20 + 4*a11*a21 + 8*a12*a22" + "4*a_{2x}*a_{3x} + 4*a_{2y}*a_{3y} + 8*a_{2z}*a_{3z}" ] }, "metadata": {}, @@ -742,10 +742,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 8 a_{00} a_{20} + 4 a_{01} a_{21} + 4 a_{02} a_{22}$" + "$\\displaystyle 8 a_{1x} a_{3x} + 4 a_{1y} a_{3y} + 4 a_{1z} a_{3z}$" ], "text/plain": [ - "8*a00*a20 + 4*a01*a21 + 4*a02*a22" + "8*a_{1x}*a_{3x} + 4*a_{1y}*a_{3y} + 4*a_{1z}*a_{3z}" ] }, "metadata": {}, @@ -754,10 +754,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{21}$" + "$\\displaystyle 4 a_{1x} a_{3y}$" ], "text/plain": [ - "4*a00*a21" + "4*a_{1x}*a_{3y}" ] }, "metadata": {}, @@ -766,10 +766,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{22}$" + "$\\displaystyle 4 a_{1x} a_{3z}$" ], "text/plain": [ - "4*a00*a22" + "4*a_{1x}*a_{3z}" ] }, "metadata": {}, @@ -778,10 +778,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 8 a_{10} a_{20} + 4 a_{11} a_{21} + 4 a_{12} a_{22}$" + "$\\displaystyle 8 a_{2x} a_{3x} + 4 a_{2y} a_{3y} + 4 a_{2z} a_{3z}$" ], "text/plain": [ - "8*a10*a20 + 4*a11*a21 + 4*a12*a22" + "8*a_{2x}*a_{3x} + 4*a_{2y}*a_{3y} + 4*a_{2z}*a_{3z}" ] }, "metadata": {}, @@ -790,10 +790,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{10} a_{21}$" + "$\\displaystyle 4 a_{2x} a_{3y}$" ], "text/plain": [ - "4*a10*a21" + "4*a_{2x}*a_{3y}" ] }, "metadata": {}, @@ -802,10 +802,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{10} a_{22}$" + "$\\displaystyle 4 a_{2x} a_{3z}$" ], "text/plain": [ - "4*a10*a22" + "4*a_{2x}*a_{3z}" ] }, "metadata": {}, @@ -814,10 +814,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00}^{2} + 4 a_{10}^{2} + 12 a_{20}^{2} + 4 a_{21}^{2} + 4 a_{22}^{2} - 4.0$" + "$\\displaystyle 4 a_{1x}^{2} + 4 a_{2x}^{2} + 12 a_{3x}^{2} + 4 a_{3y}^{2} + 4 a_{3z}^{2} - 4.0$" ], "text/plain": [ - "4*a00**2 + 4*a10**2 + 12*a20**2 + 4*a21**2 + 4*a22**2 - 4.0" + "4*a_{1x}**2 + 4*a_{2x}**2 + 12*a_{3x}**2 + 4*a_{3y}**2 + 4*a_{3z}**2 - 4.0" ] }, "metadata": {}, @@ -826,10 +826,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{01} + 4 a_{10} a_{11} + 8 a_{20} a_{21}$" + "$\\displaystyle 4 a_{1x} a_{1y} + 4 a_{2x} a_{2y} + 8 a_{3x} a_{3y}$" ], "text/plain": [ - "4*a00*a01 + 4*a10*a11 + 8*a20*a21" + "4*a_{1x}*a_{1y} + 4*a_{2x}*a_{2y} + 8*a_{3x}*a_{3y}" ] }, "metadata": {}, @@ -838,10 +838,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{02} + 4 a_{10} a_{12} + 8 a_{20} a_{22}$" + "$\\displaystyle 4 a_{1x} a_{1z} + 4 a_{2x} a_{2z} + 8 a_{3x} a_{3z}$" ], "text/plain": [ - "4*a00*a02 + 4*a10*a12 + 8*a20*a22" + "4*a_{1x}*a_{1z} + 4*a_{2x}*a_{2z} + 8*a_{3x}*a_{3z}" ] }, "metadata": {}, @@ -850,10 +850,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01} a_{20}$" + "$\\displaystyle 4 a_{1y} a_{3x}$" ], "text/plain": [ - "4*a01*a20" + "4*a_{1y}*a_{3x}" ] }, "metadata": {}, @@ -862,10 +862,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{20} + 8 a_{01} a_{21} + 4 a_{02} a_{22}$" + "$\\displaystyle 4 a_{1x} a_{3x} + 8 a_{1y} a_{3y} + 4 a_{1z} a_{3z}$" ], "text/plain": [ - "4*a00*a20 + 8*a01*a21 + 4*a02*a22" + "4*a_{1x}*a_{3x} + 8*a_{1y}*a_{3y} + 4*a_{1z}*a_{3z}" ] }, "metadata": {}, @@ -874,10 +874,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01} a_{22}$" + "$\\displaystyle 4 a_{1y} a_{3z}$" ], "text/plain": [ - "4*a01*a22" + "4*a_{1y}*a_{3z}" ] }, "metadata": {}, @@ -886,10 +886,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{11} a_{20}$" + "$\\displaystyle 4 a_{2y} a_{3x}$" ], "text/plain": [ - "4*a11*a20" + "4*a_{2y}*a_{3x}" ] }, "metadata": {}, @@ -898,10 +898,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{10} a_{20} + 8 a_{11} a_{21} + 4 a_{12} a_{22}$" + "$\\displaystyle 4 a_{2x} a_{3x} + 8 a_{2y} a_{3y} + 4 a_{2z} a_{3z}$" ], "text/plain": [ - "4*a10*a20 + 8*a11*a21 + 4*a12*a22" + "4*a_{2x}*a_{3x} + 8*a_{2y}*a_{3y} + 4*a_{2z}*a_{3z}" ] }, "metadata": {}, @@ -910,10 +910,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{11} a_{22}$" + "$\\displaystyle 4 a_{2y} a_{3z}$" ], "text/plain": [ - "4*a11*a22" + "4*a_{2y}*a_{3z}" ] }, "metadata": {}, @@ -922,10 +922,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{01} + 4 a_{10} a_{11} + 8 a_{20} a_{21}$" + "$\\displaystyle 4 a_{1x} a_{1y} + 4 a_{2x} a_{2y} + 8 a_{3x} a_{3y}$" ], "text/plain": [ - "4*a00*a01 + 4*a10*a11 + 8*a20*a21" + "4*a_{1x}*a_{1y} + 4*a_{2x}*a_{2y} + 8*a_{3x}*a_{3y}" ] }, "metadata": {}, @@ -934,10 +934,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01}^{2} + 4 a_{11}^{2} + 4 a_{20}^{2} + 12 a_{21}^{2} + 4 a_{22}^{2} - 4.0$" + "$\\displaystyle 4 a_{1y}^{2} + 4 a_{2y}^{2} + 4 a_{3x}^{2} + 12 a_{3y}^{2} + 4 a_{3z}^{2} - 4.0$" ], "text/plain": [ - "4*a01**2 + 4*a11**2 + 4*a20**2 + 12*a21**2 + 4*a22**2 - 4.0" + "4*a_{1y}**2 + 4*a_{2y}**2 + 4*a_{3x}**2 + 12*a_{3y}**2 + 4*a_{3z}**2 - 4.0" ] }, "metadata": {}, @@ -946,10 +946,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01} a_{02} + 4 a_{11} a_{12} + 8 a_{21} a_{22}$" + "$\\displaystyle 4 a_{1y} a_{1z} + 4 a_{2y} a_{2z} + 8 a_{3y} a_{3z}$" ], "text/plain": [ - "4*a01*a02 + 4*a11*a12 + 8*a21*a22" + "4*a_{1y}*a_{1z} + 4*a_{2y}*a_{2z} + 8*a_{3y}*a_{3z}" ] }, "metadata": {}, @@ -958,10 +958,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{02} a_{20}$" + "$\\displaystyle 4 a_{1z} a_{3x}$" ], "text/plain": [ - "4*a02*a20" + "4*a_{1z}*a_{3x}" ] }, "metadata": {}, @@ -970,10 +970,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{02} a_{21}$" + "$\\displaystyle 4 a_{1z} a_{3y}$" ], "text/plain": [ - "4*a02*a21" + "4*a_{1z}*a_{3y}" ] }, "metadata": {}, @@ -982,10 +982,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{20} + 4 a_{01} a_{21} + 8 a_{02} a_{22}$" + "$\\displaystyle 4 a_{1x} a_{3x} + 4 a_{1y} a_{3y} + 8 a_{1z} a_{3z}$" ], "text/plain": [ - "4*a00*a20 + 4*a01*a21 + 8*a02*a22" + "4*a_{1x}*a_{3x} + 4*a_{1y}*a_{3y} + 8*a_{1z}*a_{3z}" ] }, "metadata": {}, @@ -994,10 +994,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{12} a_{20}$" + "$\\displaystyle 4 a_{2z} a_{3x}$" ], "text/plain": [ - "4*a12*a20" + "4*a_{2z}*a_{3x}" ] }, "metadata": {}, @@ -1006,10 +1006,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{12} a_{21}$" + "$\\displaystyle 4 a_{2z} a_{3y}$" ], "text/plain": [ - "4*a12*a21" + "4*a_{2z}*a_{3y}" ] }, "metadata": {}, @@ -1018,10 +1018,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{10} a_{20} + 4 a_{11} a_{21} + 8 a_{12} a_{22}$" + "$\\displaystyle 4 a_{2x} a_{3x} + 4 a_{2y} a_{3y} + 8 a_{2z} a_{3z}$" ], "text/plain": [ - "4*a10*a20 + 4*a11*a21 + 8*a12*a22" + "4*a_{2x}*a_{3x} + 4*a_{2y}*a_{3y} + 8*a_{2z}*a_{3z}" ] }, "metadata": {}, @@ -1030,10 +1030,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{00} a_{02} + 4 a_{10} a_{12} + 8 a_{20} a_{22}$" + "$\\displaystyle 4 a_{1x} a_{1z} + 4 a_{2x} a_{2z} + 8 a_{3x} a_{3z}$" ], "text/plain": [ - "4*a00*a02 + 4*a10*a12 + 8*a20*a22" + "4*a_{1x}*a_{1z} + 4*a_{2x}*a_{2z} + 8*a_{3x}*a_{3z}" ] }, "metadata": {}, @@ -1042,10 +1042,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{01} a_{02} + 4 a_{11} a_{12} + 8 a_{21} a_{22}$" + "$\\displaystyle 4 a_{1y} a_{1z} + 4 a_{2y} a_{2z} + 8 a_{3y} a_{3z}$" ], "text/plain": [ - "4*a01*a02 + 4*a11*a12 + 8*a21*a22" + "4*a_{1y}*a_{1z} + 4*a_{2y}*a_{2z} + 8*a_{3y}*a_{3z}" ] }, "metadata": {}, @@ -1054,10 +1054,10 @@ { "data": { "text/latex": [ - "$\\displaystyle 4 a_{02}^{2} + 4 a_{12}^{2} + 4 a_{20}^{2} + 4 a_{21}^{2} + 12 a_{22}^{2} - 4.0$" + "$\\displaystyle 4 a_{1z}^{2} + 4 a_{2z}^{2} + 4 a_{3x}^{2} + 4 a_{3y}^{2} + 12 a_{3z}^{2} - 4.0$" ], "text/plain": [ - "4*a02**2 + 4*a12**2 + 4*a20**2 + 4*a21**2 + 12*a22**2 - 4.0" + "4*a_{1z}**2 + 4*a_{2z}**2 + 4*a_{3x}**2 + 4*a_{3y}**2 + 12*a_{3z}**2 - 4.0" ] }, "metadata": {}, @@ -1070,6 +1070,239 @@ " display(standard_version.diff(A[i//3, i%3]).diff(A[j//3, j%3]))" ] }, + { + "cell_type": "code", + "execution_count": 243, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}x_{1} & y_{1} & z_{1}\\\\x_{2} & y_{2} & z_{2}\\\\x_{3} & y_{3} & z_{3}\\\\x_{4} & y_{4} & z_{4}\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[x1, y1, z1],\n", + "[x2, y2, z2],\n", + "[x3, y3, z3],\n", + "[x4, y4, z4]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = np.array(sympy.symbols([f\"{d}{i}\" for i in range(1, 5) for d in \"xyz\"])).reshape(-1, 3)\n", + "display(sympy.Matrix(x))" + ] + }, + { + "cell_type": "code", + "execution_count": 244, + "metadata": {}, + "outputs": [], + "source": [ + "p = np.array(sympy.symbols(\"p_x p_y p_z\"))\n", + "dof = np.hstack((p, A.flatten(order=\"C\")))" + ] + }, + { + "cell_type": "code", + "execution_count": 245, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{array}{cccccccccccc}1 & 0 & 0 & x_{1} & y_{1} & z_{1} & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 0 & 0 & x_{2} & y_{2} & z_{2} & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 0 & 0 & x_{3} & y_{3} & z_{3} & 0 & 0 & 0 & 0 & 0 & 0\\\\1 & 0 & 0 & x_{4} & y_{4} & z_{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0 & 0 & x_{1} & y_{1} & z_{1} & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0 & 0 & x_{2} & y_{2} & z_{2} & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0 & 0 & x_{3} & y_{3} & z_{3} & 0 & 0 & 0\\\\0 & 1 & 0 & 0 & 0 & 0 & x_{4} & y_{4} & z_{4} & 0 & 0 & 0\\\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & x_{1} & y_{1} & z_{1}\\\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & x_{2} & y_{2} & z_{2}\\\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & x_{3} & y_{3} & z_{3}\\\\0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & x_{4} & y_{4} & z_{4}\\end{array}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[1, 0, 0, x1, y1, z1, 0, 0, 0, 0, 0, 0],\n", + "[1, 0, 0, x2, y2, z2, 0, 0, 0, 0, 0, 0],\n", + "[1, 0, 0, x3, y3, z3, 0, 0, 0, 0, 0, 0],\n", + "[1, 0, 0, x4, y4, z4, 0, 0, 0, 0, 0, 0],\n", + "[0, 1, 0, 0, 0, 0, x1, y1, z1, 0, 0, 0],\n", + "[0, 1, 0, 0, 0, 0, x2, y2, z2, 0, 0, 0],\n", + "[0, 1, 0, 0, 0, 0, x3, y3, z3, 0, 0, 0],\n", + "[0, 1, 0, 0, 0, 0, x4, y4, z4, 0, 0, 0],\n", + "[0, 0, 1, 0, 0, 0, 0, 0, 0, x1, y1, z1],\n", + "[0, 0, 1, 0, 0, 0, 0, 0, 0, x2, y2, z2],\n", + "[0, 0, 1, 0, 0, 0, 0, 0, 0, x3, y3, z3],\n", + "[0, 0, 1, 0, 0, 0, 0, 0, 0, x4, y4, z4]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}a_{1x} x_{1} + a_{1y} y_{1} + a_{1z} z_{1} + p_{x}\\\\a_{1x} x_{2} + a_{1y} y_{2} + a_{1z} z_{2} + p_{x}\\\\a_{1x} x_{3} + a_{1y} y_{3} + a_{1z} z_{3} + p_{x}\\\\a_{1x} x_{4} + a_{1y} y_{4} + a_{1z} z_{4} + p_{x}\\\\a_{2x} x_{1} + a_{2y} y_{1} + a_{2z} z_{1} + p_{y}\\\\a_{2x} x_{2} + a_{2y} y_{2} + a_{2z} z_{2} + p_{y}\\\\a_{2x} x_{3} + a_{2y} y_{3} + a_{2z} z_{3} + p_{y}\\\\a_{2x} x_{4} + a_{2y} y_{4} + a_{2z} z_{4} + p_{y}\\\\a_{3x} x_{1} + a_{3y} y_{1} + a_{3z} z_{1} + p_{z}\\\\a_{3x} x_{2} + a_{3y} y_{2} + a_{3z} z_{2} + p_{z}\\\\a_{3x} x_{3} + a_{3y} y_{3} + a_{3z} z_{3} + p_{z}\\\\a_{3x} x_{4} + a_{3y} y_{4} + a_{3z} z_{4} + p_{z}\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[a_{1x}*x1 + a_{1y}*y1 + a_{1z}*z1 + p_x],\n", + "[a_{1x}*x2 + a_{1y}*y2 + a_{1z}*z2 + p_x],\n", + "[a_{1x}*x3 + a_{1y}*y3 + a_{1z}*z3 + p_x],\n", + "[a_{1x}*x4 + a_{1y}*y4 + a_{1z}*z4 + p_x],\n", + "[a_{2x}*x1 + a_{2y}*y1 + a_{2z}*z1 + p_y],\n", + "[a_{2x}*x2 + a_{2y}*y2 + a_{2z}*z2 + p_y],\n", + "[a_{2x}*x3 + a_{2y}*y3 + a_{2z}*z3 + p_y],\n", + "[a_{2x}*x4 + a_{2y}*y4 + a_{2z}*z4 + p_y],\n", + "[a_{3x}*x1 + a_{3y}*y1 + a_{3z}*z1 + p_z],\n", + "[a_{3x}*x2 + a_{3y}*y2 + a_{3z}*z2 + p_z],\n", + "[a_{3x}*x3 + a_{3y}*y3 + a_{3z}*z3 + p_z],\n", + "[a_{3x}*x4 + a_{3y}*y4 + a_{3z}*z4 + p_z]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}a_{1x} x_{1} + a_{1y} y_{1} + a_{1z} z_{1} + p_{x}\\\\a_{1x} x_{2} + a_{1y} y_{2} + a_{1z} z_{2} + p_{x}\\\\a_{1x} x_{3} + a_{1y} y_{3} + a_{1z} z_{3} + p_{x}\\\\a_{1x} x_{4} + a_{1y} y_{4} + a_{1z} z_{4} + p_{x}\\\\a_{2x} x_{1} + a_{2y} y_{1} + a_{2z} z_{1} + p_{y}\\\\a_{2x} x_{2} + a_{2y} y_{2} + a_{2z} z_{2} + p_{y}\\\\a_{2x} x_{3} + a_{2y} y_{3} + a_{2z} z_{3} + p_{y}\\\\a_{2x} x_{4} + a_{2y} y_{4} + a_{2z} z_{4} + p_{y}\\\\a_{3x} x_{1} + a_{3y} y_{1} + a_{3z} z_{1} + p_{z}\\\\a_{3x} x_{2} + a_{3y} y_{2} + a_{3z} z_{2} + p_{z}\\\\a_{3x} x_{3} + a_{3y} y_{3} + a_{3z} z_{3} + p_{z}\\\\a_{3x} x_{4} + a_{3y} y_{4} + a_{3z} z_{4} + p_{z}\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[a_{1x}*x1 + a_{1y}*y1 + a_{1z}*z1 + p_x],\n", + "[a_{1x}*x2 + a_{1y}*y2 + a_{1z}*z2 + p_x],\n", + "[a_{1x}*x3 + a_{1y}*y3 + a_{1z}*z3 + p_x],\n", + "[a_{1x}*x4 + a_{1y}*y4 + a_{1z}*z4 + p_x],\n", + "[a_{2x}*x1 + a_{2y}*y1 + a_{2z}*z1 + p_y],\n", + "[a_{2x}*x2 + a_{2y}*y2 + a_{2z}*z2 + p_y],\n", + "[a_{2x}*x3 + a_{2y}*y3 + a_{2z}*z3 + p_y],\n", + "[a_{2x}*x4 + a_{2y}*y4 + a_{2z}*z4 + p_y],\n", + "[a_{3x}*x1 + a_{3y}*y1 + a_{3z}*z1 + p_z],\n", + "[a_{3x}*x2 + a_{3y}*y2 + a_{3z}*z2 + p_z],\n", + "[a_{3x}*x3 + a_{3y}*y3 + a_{3z}*z3 + p_z],\n", + "[a_{3x}*x4 + a_{3y}*y4 + a_{3z}*z4 + p_z]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[0],\n", + "[0],\n", + "[0],\n", + "[0],\n", + "[0],\n", + "[0],\n", + "[0],\n", + "[0],\n", + "[0],\n", + "[0],\n", + "[0],\n", + "[0]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{matrix}\\left[\\begin{matrix}1\\\\1\\\\1\\\\1\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right] & \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\1\\\\1\\\\1\\\\1\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right] & \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\1\\\\1\\\\1\\\\1\\end{matrix}\\right] & \\left[\\begin{matrix}x_{1}\\\\x_{2}\\\\x_{3}\\\\x_{4}\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right] & \\left[\\begin{matrix}y_{1}\\\\y_{2}\\\\y_{3}\\\\y_{4}\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right] & \\left[\\begin{matrix}z_{1}\\\\z_{2}\\\\z_{3}\\\\z_{4}\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right] & \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\x_{1}\\\\x_{2}\\\\x_{3}\\\\x_{4}\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right] & \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\y_{1}\\\\y_{2}\\\\y_{3}\\\\y_{4}\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right] & \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\z_{1}\\\\z_{2}\\\\z_{3}\\\\z_{4}\\\\0\\\\0\\\\0\\\\0\\end{matrix}\\right] & \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\x_{1}\\\\x_{2}\\\\x_{3}\\\\x_{4}\\end{matrix}\\right] & \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\y_{1}\\\\y_{2}\\\\y_{3}\\\\y_{4}\\end{matrix}\\right] & \\left[\\begin{matrix}0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\0\\\\z_{1}\\\\z_{2}\\\\z_{3}\\\\z_{4}\\end{matrix}\\right]\\end{matrix}\\right]$" + ], + "text/plain": [ + "[[[1], [1], [1], [1], [0], [0], [0], [0], [0], [0], [0], [0]], [[0], [0], [0], [0], [1], [1], [1], [1], [0], [0], [0], [0]], [[0], [0], [0], [0], [0], [0], [0], [0], [1], [1], [1], [1]], [[x1], [x2], [x3], [x4], [0], [0], [0], [0], [0], [0], [0], [0]], [[y1], [y2], [y3], [y4], [0], [0], [0], [0], [0], [0], [0], [0]], [[z1], [z2], [z3], [z4], [0], [0], [0], [0], [0], [0], [0], [0]], [[0], [0], [0], [0], [x1], [x2], [x3], [x4], [0], [0], [0], [0]], [[0], [0], [0], [0], [y1], [y2], [y3], [y4], [0], [0], [0], [0]], [[0], [0], [0], [0], [z1], [z2], [z3], [z4], [0], [0], [0], [0]], [[0], [0], [0], [0], [0], [0], [0], [0], [x1], [x2], [x3], [x4]], [[0], [0], [0], [0], [0], [0], [0], [0], [y1], [y2], [y3], [y4]], [[0], [0], [0], [0], [0], [0], [0], [0], [z1], [z2], [z3], [z4]]]" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "J = np.zeros((x.size, 12), dtype=object)\n", + "\n", + "for i in range(x.shape[0]):\n", + " for j in range(x.shape[1]):\n", + " J[x.shape[0]*j + i, j] = 1\n", + "\n", + "# J[:, 3:] = np.kron(np.eye(3, dtype=int), x)\n", + "for i in range(x.shape[0]):\n", + " for j in range(x.shape[1]):\n", + " for k in range(A.shape[0]):\n", + " J[i + k * x.shape[0], j + k * x.shape[1] + p.size] = x[i, j]\n", + "\n", + "display(sympy.Matrix(J))\n", + "\n", + "linear_version = J @ dof\n", + "affine_version = (x @ A.T + p).flatten(order=\"F\")\n", + "\n", + "display(sympy.Matrix(linear_version))\n", + "display(sympy.Matrix(affine_version))\n", + "display(sympy.Matrix(linear_version - affine_version))\n", + "\n", + "display(sympy.Matrix(linear_version).diff(dof))" + ] + }, + { + "cell_type": "code", + "execution_count": 246, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left. \\frac{\\partial}{\\partial \\xi_{1}} f{\\left(\\xi_{1},a_{1x} x_{2} + a_{1y} y_{2} + a_{1z} z_{2} + p_{x},a_{1x} x_{3} + a_{1y} y_{3} + a_{1z} z_{3} + p_{x},a_{1x} x_{4} + a_{1y} y_{4} + a_{1z} z_{4} + p_{x},a_{2x} x_{1} + a_{2y} y_{1} + a_{2z} z_{1} + p_{y},a_{2x} x_{2} + a_{2y} y_{2} + a_{2z} z_{2} + p_{y},a_{2x} x_{3} + a_{2y} y_{3} + a_{2z} z_{3} + p_{y},a_{2x} x_{4} + a_{2y} y_{4} + a_{2z} z_{4} + p_{y},a_{3x} x_{1} + a_{3y} y_{1} + a_{3z} z_{1} + p_{z},a_{3x} x_{2} + a_{3y} y_{2} + a_{3z} z_{2} + p_{z},a_{3x} x_{3} + a_{3y} y_{3} + a_{3z} z_{3} + p_{z},a_{3x} x_{4} + a_{3y} y_{4} + a_{3z} z_{4} + p_{z} \\right)} \\right|_{\\substack{ \\xi_{1}=a_{1x} x_{1} + a_{1y} y_{1} + a_{1z} z_{1} + p_{x} }} + \\left. \\frac{\\partial}{\\partial \\xi_{2}} f{\\left(a_{1x} x_{1} + a_{1y} y_{1} + a_{1z} z_{1} + p_{x},\\xi_{2},a_{1x} x_{3} + a_{1y} y_{3} + a_{1z} z_{3} + p_{x},a_{1x} x_{4} + a_{1y} y_{4} + a_{1z} z_{4} + p_{x},a_{2x} x_{1} + a_{2y} y_{1} + a_{2z} z_{1} + p_{y},a_{2x} x_{2} + a_{2y} y_{2} + a_{2z} z_{2} + p_{y},a_{2x} x_{3} + a_{2y} y_{3} + a_{2z} z_{3} + p_{y},a_{2x} x_{4} + a_{2y} y_{4} + a_{2z} z_{4} + p_{y},a_{3x} x_{1} + a_{3y} y_{1} + a_{3z} z_{1} + p_{z},a_{3x} x_{2} + a_{3y} y_{2} + a_{3z} z_{2} + p_{z},a_{3x} x_{3} + a_{3y} y_{3} + a_{3z} z_{3} + p_{z},a_{3x} x_{4} + a_{3y} y_{4} + a_{3z} z_{4} + p_{z} \\right)} \\right|_{\\substack{ \\xi_{2}=a_{1x} x_{2} + a_{1y} y_{2} + a_{1z} z_{2} + p_{x} }} + \\left. \\frac{\\partial}{\\partial \\xi_{3}} f{\\left(a_{1x} x_{1} + a_{1y} y_{1} + a_{1z} z_{1} + p_{x},a_{1x} x_{2} + a_{1y} y_{2} + a_{1z} z_{2} + p_{x},\\xi_{3},a_{1x} x_{4} + a_{1y} y_{4} + a_{1z} z_{4} + p_{x},a_{2x} x_{1} + a_{2y} y_{1} + a_{2z} z_{1} + p_{y},a_{2x} x_{2} + a_{2y} y_{2} + a_{2z} z_{2} + p_{y},a_{2x} x_{3} + a_{2y} y_{3} + a_{2z} z_{3} + p_{y},a_{2x} x_{4} + a_{2y} y_{4} + a_{2z} z_{4} + p_{y},a_{3x} x_{1} + a_{3y} y_{1} + a_{3z} z_{1} + p_{z},a_{3x} x_{2} + a_{3y} y_{2} + a_{3z} z_{2} + p_{z},a_{3x} x_{3} + a_{3y} y_{3} + a_{3z} z_{3} + p_{z},a_{3x} x_{4} + a_{3y} y_{4} + a_{3z} z_{4} + p_{z} \\right)} \\right|_{\\substack{ \\xi_{3}=a_{1x} x_{3} + a_{1y} y_{3} + a_{1z} z_{3} + p_{x} }} + \\left. \\frac{\\partial}{\\partial \\xi_{4}} f{\\left(a_{1x} x_{1} + a_{1y} y_{1} + a_{1z} z_{1} + p_{x},a_{1x} x_{2} + a_{1y} y_{2} + a_{1z} z_{2} + p_{x},a_{1x} x_{3} + a_{1y} y_{3} + a_{1z} z_{3} + p_{x},\\xi_{4},a_{2x} x_{1} + a_{2y} y_{1} + a_{2z} z_{1} + p_{y},a_{2x} x_{2} + a_{2y} y_{2} + a_{2z} z_{2} + p_{y},a_{2x} x_{3} + a_{2y} y_{3} + a_{2z} z_{3} + p_{y},a_{2x} x_{4} + a_{2y} y_{4} + a_{2z} z_{4} + p_{y},a_{3x} x_{1} + a_{3y} y_{1} + a_{3z} z_{1} + p_{z},a_{3x} x_{2} + a_{3y} y_{2} + a_{3z} z_{2} + p_{z},a_{3x} x_{3} + a_{3y} y_{3} + a_{3z} z_{3} + p_{z},a_{3x} x_{4} + a_{3y} y_{4} + a_{3z} z_{4} + p_{z} \\right)} \\right|_{\\substack{ \\xi_{4}=a_{1x} x_{4} + a_{1y} y_{4} + a_{1z} z_{4} + p_{x} }}$" + ], + "text/plain": [ + "Subs(Derivative(f(_xi_1, a_{1x}*x2 + a_{1y}*y2 + a_{1z}*z2 + p_x, a_{1x}*x3 + a_{1y}*y3 + a_{1z}*z3 + p_x, a_{1x}*x4 + a_{1y}*y4 + a_{1z}*z4 + p_x, a_{2x}*x1 + a_{2y}*y1 + a_{2z}*z1 + p_y, a_{2x}*x2 + a_{2y}*y2 + a_{2z}*z2 + p_y, a_{2x}*x3 + a_{2y}*y3 + a_{2z}*z3 + p_y, a_{2x}*x4 + a_{2y}*y4 + a_{2z}*z4 + p_y, a_{3x}*x1 + a_{3y}*y1 + a_{3z}*z1 + p_z, a_{3x}*x2 + a_{3y}*y2 + a_{3z}*z2 + p_z, a_{3x}*x3 + a_{3y}*y3 + a_{3z}*z3 + p_z, a_{3x}*x4 + a_{3y}*y4 + a_{3z}*z4 + p_z), _xi_1), _xi_1, a_{1x}*x1 + a_{1y}*y1 + a_{1z}*z1 + p_x) + Subs(Derivative(f(a_{1x}*x1 + a_{1y}*y1 + a_{1z}*z1 + p_x, _xi_2, a_{1x}*x3 + a_{1y}*y3 + a_{1z}*z3 + p_x, a_{1x}*x4 + a_{1y}*y4 + a_{1z}*z4 + p_x, a_{2x}*x1 + a_{2y}*y1 + a_{2z}*z1 + p_y, a_{2x}*x2 + a_{2y}*y2 + a_{2z}*z2 + p_y, a_{2x}*x3 + a_{2y}*y3 + a_{2z}*z3 + p_y, a_{2x}*x4 + a_{2y}*y4 + a_{2z}*z4 + p_y, a_{3x}*x1 + a_{3y}*y1 + a_{3z}*z1 + p_z, a_{3x}*x2 + a_{3y}*y2 + a_{3z}*z2 + p_z, a_{3x}*x3 + a_{3y}*y3 + a_{3z}*z3 + p_z, a_{3x}*x4 + a_{3y}*y4 + a_{3z}*z4 + p_z), _xi_2), _xi_2, a_{1x}*x2 + a_{1y}*y2 + a_{1z}*z2 + p_x) + Subs(Derivative(f(a_{1x}*x1 + a_{1y}*y1 + a_{1z}*z1 + p_x, a_{1x}*x2 + a_{1y}*y2 + a_{1z}*z2 + p_x, _xi_3, a_{1x}*x4 + a_{1y}*y4 + a_{1z}*z4 + p_x, a_{2x}*x1 + a_{2y}*y1 + a_{2z}*z1 + p_y, a_{2x}*x2 + a_{2y}*y2 + a_{2z}*z2 + p_y, a_{2x}*x3 + a_{2y}*y3 + a_{2z}*z3 + p_y, a_{2x}*x4 + a_{2y}*y4 + a_{2z}*z4 + p_y, a_{3x}*x1 + a_{3y}*y1 + a_{3z}*z1 + p_z, a_{3x}*x2 + a_{3y}*y2 + a_{3z}*z2 + p_z, a_{3x}*x3 + a_{3y}*y3 + a_{3z}*z3 + p_z, a_{3x}*x4 + a_{3y}*y4 + a_{3z}*z4 + p_z), _xi_3), _xi_3, a_{1x}*x3 + a_{1y}*y3 + a_{1z}*z3 + p_x) + Subs(Derivative(f(a_{1x}*x1 + a_{1y}*y1 + a_{1z}*z1 + p_x, a_{1x}*x2 + a_{1y}*y2 + a_{1z}*z2 + p_x, a_{1x}*x3 + a_{1y}*y3 + a_{1z}*z3 + p_x, _xi_4, a_{2x}*x1 + a_{2y}*y1 + a_{2z}*z1 + p_y, a_{2x}*x2 + a_{2y}*y2 + a_{2z}*z2 + p_y, a_{2x}*x3 + a_{2y}*y3 + a_{2z}*z3 + p_y, a_{2x}*x4 + a_{2y}*y4 + a_{2z}*z4 + p_y, a_{3x}*x1 + a_{3y}*y1 + a_{3z}*z1 + p_z, a_{3x}*x2 + a_{3y}*y2 + a_{3z}*z2 + p_z, a_{3x}*x3 + a_{3y}*y3 + a_{3z}*z3 + p_z, a_{3x}*x4 + a_{3y}*y4 + a_{3z}*z4 + p_z), _xi_4), _xi_4, a_{1x}*x4 + a_{1y}*y4 + a_{1z}*z4 + p_x)" + ] + }, + "execution_count": 246, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "sympy.Function(\"f\")(*(J @ dof)).diff(dof[0])" + ] + }, + { + "cell_type": "code", + "execution_count": 247, + "metadata": {}, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\left[\\begin{array}{cccccccccccc}\\rho & 0 & 0 & \\frac{\\rho \\left(x_{1} + x_{2} + x_{3} + x_{4}\\right)}{4} & \\frac{\\rho \\left(y_{1} + y_{2} + y_{3} + y_{4}\\right)}{4} & \\frac{\\rho \\left(z_{1} + z_{2} + z_{3} + z_{4}\\right)}{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & \\rho & 0 & 0 & 0 & 0 & \\frac{\\rho \\left(x_{1} + x_{2} + x_{3} + x_{4}\\right)}{4} & \\frac{\\rho \\left(y_{1} + y_{2} + y_{3} + y_{4}\\right)}{4} & \\frac{\\rho \\left(z_{1} + z_{2} + z_{3} + z_{4}\\right)}{4} & 0 & 0 & 0\\\\0 & 0 & \\rho & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{\\rho \\left(x_{1} + x_{2} + x_{3} + x_{4}\\right)}{4} & \\frac{\\rho \\left(y_{1} + y_{2} + y_{3} + y_{4}\\right)}{4} & \\frac{\\rho \\left(z_{1} + z_{2} + z_{3} + z_{4}\\right)}{4}\\\\\\frac{\\rho \\left(x_{1} + x_{2} + x_{3} + x_{4}\\right)}{4} & 0 & 0 & \\frac{\\rho \\left(x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2}\\right)}{4} & \\frac{\\rho \\left(x_{1} y_{1} + x_{2} y_{2} + x_{3} y_{3} + x_{4} y_{4}\\right)}{4} & \\frac{\\rho \\left(x_{1} z_{1} + x_{2} z_{2} + x_{3} z_{3} + x_{4} z_{4}\\right)}{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{\\rho \\left(y_{1} + y_{2} + y_{3} + y_{4}\\right)}{4} & 0 & 0 & \\frac{\\rho \\left(x_{1} y_{1} + x_{2} y_{2} + x_{3} y_{3} + x_{4} y_{4}\\right)}{4} & \\frac{\\rho \\left(y_{1}^{2} + y_{2}^{2} + y_{3}^{2} + y_{4}^{2}\\right)}{4} & \\frac{\\rho \\left(y_{1} z_{1} + y_{2} z_{2} + y_{3} z_{3} + y_{4} z_{4}\\right)}{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\\\frac{\\rho \\left(z_{1} + z_{2} + z_{3} + z_{4}\\right)}{4} & 0 & 0 & \\frac{\\rho \\left(x_{1} z_{1} + x_{2} z_{2} + x_{3} z_{3} + x_{4} z_{4}\\right)}{4} & \\frac{\\rho \\left(y_{1} z_{1} + y_{2} z_{2} + y_{3} z_{3} + y_{4} z_{4}\\right)}{4} & \\frac{\\rho \\left(z_{1}^{2} + z_{2}^{2} + z_{3}^{2} + z_{4}^{2}\\right)}{4} & 0 & 0 & 0 & 0 & 0 & 0\\\\0 & \\frac{\\rho \\left(x_{1} + x_{2} + x_{3} + x_{4}\\right)}{4} & 0 & 0 & 0 & 0 & \\frac{\\rho \\left(x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2}\\right)}{4} & \\frac{\\rho \\left(x_{1} y_{1} + x_{2} y_{2} + x_{3} y_{3} + x_{4} y_{4}\\right)}{4} & \\frac{\\rho \\left(x_{1} z_{1} + x_{2} z_{2} + x_{3} z_{3} + x_{4} z_{4}\\right)}{4} & 0 & 0 & 0\\\\0 & \\frac{\\rho \\left(y_{1} + y_{2} + y_{3} + y_{4}\\right)}{4} & 0 & 0 & 0 & 0 & \\frac{\\rho \\left(x_{1} y_{1} + x_{2} y_{2} + x_{3} y_{3} + x_{4} y_{4}\\right)}{4} & \\frac{\\rho \\left(y_{1}^{2} + y_{2}^{2} + y_{3}^{2} + y_{4}^{2}\\right)}{4} & \\frac{\\rho \\left(y_{1} z_{1} + y_{2} z_{2} + y_{3} z_{3} + y_{4} z_{4}\\right)}{4} & 0 & 0 & 0\\\\0 & \\frac{\\rho \\left(z_{1} + z_{2} + z_{3} + z_{4}\\right)}{4} & 0 & 0 & 0 & 0 & \\frac{\\rho \\left(x_{1} z_{1} + x_{2} z_{2} + x_{3} z_{3} + x_{4} z_{4}\\right)}{4} & \\frac{\\rho \\left(y_{1} z_{1} + y_{2} z_{2} + y_{3} z_{3} + y_{4} z_{4}\\right)}{4} & \\frac{\\rho \\left(z_{1}^{2} + z_{2}^{2} + z_{3}^{2} + z_{4}^{2}\\right)}{4} & 0 & 0 & 0\\\\0 & 0 & \\frac{\\rho \\left(x_{1} + x_{2} + x_{3} + x_{4}\\right)}{4} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{\\rho \\left(x_{1}^{2} + x_{2}^{2} + x_{3}^{2} + x_{4}^{2}\\right)}{4} & \\frac{\\rho \\left(x_{1} y_{1} + x_{2} y_{2} + x_{3} y_{3} + x_{4} y_{4}\\right)}{4} & \\frac{\\rho \\left(x_{1} z_{1} + x_{2} z_{2} + x_{3} z_{3} + x_{4} z_{4}\\right)}{4}\\\\0 & 0 & \\frac{\\rho \\left(y_{1} + y_{2} + y_{3} + y_{4}\\right)}{4} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{\\rho \\left(x_{1} y_{1} + x_{2} y_{2} + x_{3} y_{3} + x_{4} y_{4}\\right)}{4} & \\frac{\\rho \\left(y_{1}^{2} + y_{2}^{2} + y_{3}^{2} + y_{4}^{2}\\right)}{4} & \\frac{\\rho \\left(y_{1} z_{1} + y_{2} z_{2} + y_{3} z_{3} + y_{4} z_{4}\\right)}{4}\\\\0 & 0 & \\frac{\\rho \\left(z_{1} + z_{2} + z_{3} + z_{4}\\right)}{4} & 0 & 0 & 0 & 0 & 0 & 0 & \\frac{\\rho \\left(x_{1} z_{1} + x_{2} z_{2} + x_{3} z_{3} + x_{4} z_{4}\\right)}{4} & \\frac{\\rho \\left(y_{1} z_{1} + y_{2} z_{2} + y_{3} z_{3} + y_{4} z_{4}\\right)}{4} & \\frac{\\rho \\left(z_{1}^{2} + z_{2}^{2} + z_{3}^{2} + z_{4}^{2}\\right)}{4}\\end{array}\\right]$" + ], + "text/plain": [ + "Matrix([\n", + "[ \\rho, 0, 0, \\rho*(x1 + x2 + x3 + x4)/4, \\rho*(y1 + y2 + y3 + y4)/4, \\rho*(z1 + z2 + z3 + z4)/4, 0, 0, 0, 0, 0, 0],\n", + "[ 0, \\rho, 0, 0, 0, 0, \\rho*(x1 + x2 + x3 + x4)/4, \\rho*(y1 + y2 + y3 + y4)/4, \\rho*(z1 + z2 + z3 + z4)/4, 0, 0, 0],\n", + "[ 0, 0, \\rho, 0, 0, 0, 0, 0, 0, \\rho*(x1 + x2 + x3 + x4)/4, \\rho*(y1 + y2 + y3 + y4)/4, \\rho*(z1 + z2 + z3 + z4)/4],\n", + "[\\rho*(x1 + x2 + x3 + x4)/4, 0, 0, \\rho*(x1**2 + x2**2 + x3**2 + x4**2)/4, \\rho*(x1*y1 + x2*y2 + x3*y3 + x4*y4)/4, \\rho*(x1*z1 + x2*z2 + x3*z3 + x4*z4)/4, 0, 0, 0, 0, 0, 0],\n", + "[\\rho*(y1 + y2 + y3 + y4)/4, 0, 0, \\rho*(x1*y1 + x2*y2 + x3*y3 + x4*y4)/4, \\rho*(y1**2 + y2**2 + y3**2 + y4**2)/4, \\rho*(y1*z1 + y2*z2 + y3*z3 + y4*z4)/4, 0, 0, 0, 0, 0, 0],\n", + "[\\rho*(z1 + z2 + z3 + z4)/4, 0, 0, \\rho*(x1*z1 + x2*z2 + x3*z3 + x4*z4)/4, \\rho*(y1*z1 + y2*z2 + y3*z3 + y4*z4)/4, \\rho*(z1**2 + z2**2 + z3**2 + z4**2)/4, 0, 0, 0, 0, 0, 0],\n", + "[ 0, \\rho*(x1 + x2 + x3 + x4)/4, 0, 0, 0, 0, \\rho*(x1**2 + x2**2 + x3**2 + x4**2)/4, \\rho*(x1*y1 + x2*y2 + x3*y3 + x4*y4)/4, \\rho*(x1*z1 + x2*z2 + x3*z3 + x4*z4)/4, 0, 0, 0],\n", + "[ 0, \\rho*(y1 + y2 + y3 + y4)/4, 0, 0, 0, 0, \\rho*(x1*y1 + x2*y2 + x3*y3 + x4*y4)/4, \\rho*(y1**2 + y2**2 + y3**2 + y4**2)/4, \\rho*(y1*z1 + y2*z2 + y3*z3 + y4*z4)/4, 0, 0, 0],\n", + "[ 0, \\rho*(z1 + z2 + z3 + z4)/4, 0, 0, 0, 0, \\rho*(x1*z1 + x2*z2 + x3*z3 + x4*z4)/4, \\rho*(y1*z1 + y2*z2 + y3*z3 + y4*z4)/4, \\rho*(z1**2 + z2**2 + z3**2 + z4**2)/4, 0, 0, 0],\n", + "[ 0, 0, \\rho*(x1 + x2 + x3 + x4)/4, 0, 0, 0, 0, 0, 0, \\rho*(x1**2 + x2**2 + x3**2 + x4**2)/4, \\rho*(x1*y1 + x2*y2 + x3*y3 + x4*y4)/4, \\rho*(x1*z1 + x2*z2 + x3*z3 + x4*z4)/4],\n", + "[ 0, 0, \\rho*(y1 + y2 + y3 + y4)/4, 0, 0, 0, 0, 0, 0, \\rho*(x1*y1 + x2*y2 + x3*y3 + x4*y4)/4, \\rho*(y1**2 + y2**2 + y3**2 + y4**2)/4, \\rho*(y1*z1 + y2*z2 + y3*z3 + y4*z4)/4],\n", + "[ 0, 0, \\rho*(z1 + z2 + z3 + z4)/4, 0, 0, 0, 0, 0, 0, \\rho*(x1*z1 + x2*z2 + x3*z3 + x4*z4)/4, \\rho*(y1*z1 + y2*z2 + y3*z3 + y4*z4)/4, \\rho*(z1**2 + z2**2 + z3**2 + z4**2)/4]])" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "display(sympy.Symbol(r\"\\rho\") * sympy.Matrix(J.T @ J) / x.shape[0])" + ] + }, { "cell_type": "code", "execution_count": null, diff --git a/src/ipc/dynamics/affine/affine_body.hpp b/src/ipc/dynamics/affine/affine_body.hpp index 0f005876d..9f002d757 100644 --- a/src/ipc/dynamics/affine/affine_body.hpp +++ b/src/ipc/dynamics/affine/affine_body.hpp @@ -18,6 +18,34 @@ struct AffineBody { { } + Eigen::SparseMatrix J(const Eigen::MatrixXd& rest_positions) const + { + std::vector> triplets; + + for (int i = 0; i < rest_positions.rows(); i++) { + for (int j = 0; j < rest_positions.cols(); j++) { + triplets.emplace_back(rest_positions.rows() * j + i, j, 1); + } + } + + // I ⊗ x̄ + for (int i = 0; i < rest_positions.rows(); i++) { + for (int j = 0; j < rest_positions.cols(); j++) { + for (int k = 0; k < A.cols(); k++) { + triplets.emplace_back( + i + k * rest_positions.rows(), + j + k * rest_positions.cols() + p.size(), + rest_positions(i, j)); + } + } + } + + Eigen::SparseMatrix J( + rest_positions.size(), A.size() + p.size()); + J.setFromTriplets(triplets.begin(), triplets.end()); + return J; + } + Eigen::MatrixXd transform_vertices(const Eigen::MatrixXd& rest_positions) const { @@ -25,6 +53,12 @@ struct AffineBody { // transpose because x is row-ordered return (rest_positions * A.transpose()).rowwise() + p.transpose(); } + + Eigen::SparseMatrix + transform_vertices_gradient(const Eigen::MatrixXd& rest_positions) const + { + return J(rest_positions); + } }; } // namespace ipc::affine \ No newline at end of file From 5c73e2727aaa840d291357bab36130daa1a6dc35 Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Sun, 10 Nov 2024 21:59:09 -0500 Subject: [PATCH 04/24] Fix comment --- src/ipc/dynamics/affine/orthogonality_potential.cpp | 2 +- src/ipc/dynamics/rigid/rigid_body.hpp | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/src/ipc/dynamics/affine/orthogonality_potential.cpp b/src/ipc/dynamics/affine/orthogonality_potential.cpp index 6a9d60ad5..9dddeafa5 100644 --- a/src/ipc/dynamics/affine/orthogonality_potential.cpp +++ b/src/ipc/dynamics/affine/orthogonality_potential.cpp @@ -1,8 +1,8 @@ #include "orthogonality_potential.hpp" -#include #include #include +#include namespace ipc::affine { diff --git a/src/ipc/dynamics/rigid/rigid_body.hpp b/src/ipc/dynamics/rigid/rigid_body.hpp index 6dafd5cab..2c272a6d4 100644 --- a/src/ipc/dynamics/rigid/rigid_body.hpp +++ b/src/ipc/dynamics/rigid/rigid_body.hpp @@ -5,7 +5,7 @@ namespace ipc::rigid { struct RigidBody { - VectorMax3d rotation_vector; // Affine matrix + VectorMax3d rotation_vector; // Rotation vector VectorMax3d position; // Translation vector RigidBody() = default; From 47c282b6b780bf410c1ad52f6e6048a9746fa309 Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Thu, 12 Jun 2025 22:09:11 -0400 Subject: [PATCH 05/24] [WIP] Implement rigid body dynamics framework - Added InertialTerm class for computing energy, gradient, and Hessian of rigid bodies. - Implemented mass properties computation for 2D and 3D meshes, including point clouds. - Created pose representation with rotation vector and matrix conversions. - Developed RigidBodies class to manage multiple rigid bodies from mesh data. - Implemented ImplicitEuler time integrator for updating positions and velocities. - Added unit tests for mass properties and pose transformations using Catch2 framework. --- src/ipc/distance/edge_edge_mollifier.cpp | 2 +- src/ipc/dynamics/rigid/CMakeLists.txt | 9 + src/ipc/dynamics/rigid/inertial_term.cpp | 239 +++++++++++++++++ src/ipc/dynamics/rigid/inertial_term.hpp | 87 +++++++ src/ipc/dynamics/rigid/mass.cpp | 244 ++++++++++++++++++ src/ipc/dynamics/rigid/mass.hpp | 32 +++ src/ipc/dynamics/rigid/pose.cpp | 142 ++++++++++ src/ipc/dynamics/rigid/pose.hpp | 101 ++++++++ src/ipc/dynamics/rigid/rigid_bodies.cpp | 80 ++++++ src/ipc/dynamics/rigid/rigid_bodies.hpp | 37 +++ src/ipc/dynamics/rigid/rigid_body.cpp | 224 +++++++++++++--- src/ipc/dynamics/rigid/rigid_body.hpp | 34 ++- src/ipc/dynamics/rigid/time_integrator.hpp | 87 +++++++ src/ipc/utils/sinc.cpp | 12 +- src/ipc/utils/sinc.hpp | 8 +- tests/src/tests/dynamics/CMakeLists.txt | 3 +- tests/src/tests/dynamics/rigid/CMakeLists.txt | 11 + tests/src/tests/dynamics/rigid/test_mass.cpp | 42 +++ tests/src/tests/dynamics/rigid/test_pose.cpp | 89 +++++++ tests/src/tests/utils/test_sinc.cpp | 12 +- 20 files changed, 1437 insertions(+), 58 deletions(-) create mode 100644 src/ipc/dynamics/rigid/inertial_term.cpp create mode 100644 src/ipc/dynamics/rigid/inertial_term.hpp create mode 100644 src/ipc/dynamics/rigid/mass.cpp create mode 100644 src/ipc/dynamics/rigid/mass.hpp create mode 100644 src/ipc/dynamics/rigid/pose.cpp create mode 100644 src/ipc/dynamics/rigid/pose.hpp create mode 100644 src/ipc/dynamics/rigid/rigid_bodies.cpp create mode 100644 src/ipc/dynamics/rigid/rigid_bodies.hpp create mode 100644 src/ipc/dynamics/rigid/time_integrator.hpp create mode 100644 tests/src/tests/dynamics/rigid/CMakeLists.txt create mode 100644 tests/src/tests/dynamics/rigid/test_mass.cpp create mode 100644 tests/src/tests/dynamics/rigid/test_pose.cpp diff --git a/src/ipc/distance/edge_edge_mollifier.cpp b/src/ipc/distance/edge_edge_mollifier.cpp index 5be0b25aa..c106f1dc5 100644 --- a/src/ipc/distance/edge_edge_mollifier.cpp +++ b/src/ipc/distance/edge_edge_mollifier.cpp @@ -53,7 +53,7 @@ double edge_edge_mollifier_gradient(const double x, const double eps_x) { if (x < eps_x) { const double one_div_eps_x = 1 / eps_x; - return 2 * one_div_eps_x * (-one_div_eps_x * x + 1); + return 2 * one_div_eps_x * fma(-one_div_eps_x, x, 1); } else { return 0; } diff --git a/src/ipc/dynamics/rigid/CMakeLists.txt b/src/ipc/dynamics/rigid/CMakeLists.txt index 910d603c6..89445e5b3 100644 --- a/src/ipc/dynamics/rigid/CMakeLists.txt +++ b/src/ipc/dynamics/rigid/CMakeLists.txt @@ -1,6 +1,15 @@ set(SOURCES + inertial_term.cpp + inertial_term.hpp + mass.cpp + mass.hpp + pose.cpp + pose.hpp + rigid_bodies.cpp + rigid_bodies.hpp rigid_body.cpp rigid_body.hpp + time_integrator.hpp ) source_group(TREE "${CMAKE_CURRENT_SOURCE_DIR}" PREFIX "Source Files" FILES ${SOURCES}) diff --git a/src/ipc/dynamics/rigid/inertial_term.cpp b/src/ipc/dynamics/rigid/inertial_term.cpp new file mode 100644 index 000000000..f46f06e87 --- /dev/null +++ b/src/ipc/dynamics/rigid/inertial_term.cpp @@ -0,0 +1,239 @@ +#include "inertial_term.hpp" + +#include +#include + +namespace ipc::rigid { + +namespace { + inline Eigen::Matrix3d + cross_product_matrix(Eigen::ConstRef x) + { + Eigen::Matrix3d X; + X << 0, -x.z(), x.y(), // + x.z(), 0, -x.x(), // + -x.y(), x.x(), 0; + return X; + } +} // namespace + +void InertialTerm::update(const RigidBodies& bodies) +{ + // Update the predicted poses based on the current time integrator state + predicted_poses = time_integrator->predicted_pose(); + + // Gravity in the y-direction + const double dt_sq = time_integrator->dt * time_integrator->dt; + + tbb::parallel_for( + tbb::blocked_range(0, predicted_poses.size()), + [&](const tbb::blocked_range& r) { + for (size_t i = r.begin(); i < r.end(); ++i) { + // Add gravity to the predicted pose + // TODO: Make this configurable + predicted_poses[i].position.y() += dt_sq * -9.81; + + const auto& force = bodies[i].external_force().position; + const auto& torque = bodies[i].external_force().rotation; + + // Add external forces to the predicted pose + if (!force.isZero()) { + predicted_poses[i].position += + dt_sq * force / bodies[i].mass(); + } + + // Add external torques to the predicted pose + if (!torque.isZero()) { + if (torque.size() == 3) { + const RotationMatrix& Q = + time_integrator->pose(i).rotation; + // Transform the world space torque into body space + const Eigen::Matrix3d Tau = + Q.transpose() * cross_product_matrix(torque); + predicted_poses[i].rotation += + dt_sq * bodies[i].J().inverse() * Tau; + } else { + assert(torque.size() == 1); + predicted_poses[i].rotation(0) += dt_sq * torque(0) + / bodies[i].moment_of_inertia()(0); + } + } + } + }); +} + +// ---- Cumulative functions --------------------------------------------------- + +double InertialTerm::operator()( + const RigidBodies& bodies, Eigen::ConstRef x) +{ + const int ndof = x.size() / bodies.num_bodies(); + + double energy = 0.0; + for (size_t i = 0; i < bodies.num_bodies(); ++i) { + energy += operator()( + bodies[i], x.segment(i * ndof, ndof), predicted_poses[i].position, + predicted_poses[i].rotation); + } + return energy; +} + +Eigen::VectorXd InertialTerm::gradient( + const RigidBodies& bodies, Eigen::ConstRef x) +{ + const int ndof = x.size() / bodies.num_bodies(); + + Eigen::VectorXd grad = Eigen::VectorXd::Zero(x.size()); + for (size_t i = 0; i < bodies.num_bodies(); ++i) { + grad.segment(i * ndof, ndof) = gradient( + bodies[i], x.segment(i * ndof, ndof), predicted_poses[i].position, + predicted_poses[i].rotation); + } + return grad; +} + +Eigen::MatrixXd InertialTerm::hessian( + const RigidBodies& bodies, Eigen::ConstRef x) +{ + const int ndof = x.size() / bodies.num_bodies(); + + Eigen::MatrixXd hess(x.size(), x.size()); + for (size_t i = 0; i < bodies.num_bodies(); ++i) { + hess.block(i * ndof, i * ndof, ndof, ndof) = hessian( + bodies[i], x.segment(i * ndof, ndof), predicted_poses[i].position, + predicted_poses[i].rotation); + } + return hess; +} + +// ---- Per-body functions ----------------------------------------------------- + +double InertialTerm::operator()( + const RigidBody& body, + Eigen::ConstRef x, + Eigen::ConstRef q_hat, + Eigen::ConstRef Q_hat) const +{ + double energy = 0.0; + + // Linear inertia + // if (!body.is_dof_fixed.head(pose.pos_ndof()).all()) + { + // ½m‖q - q̂‖² + energy += + 0.5 * body.mass() * (x.head(q_hat.size()) - q_hat).squaredNorm(); + } + + // Rotational energy + // if (!body.is_dof_fixed.tail(pose.rot_ndof()).all()) + { + if (q_hat.size() == 3) { + const Eigen::Matrix3d Q = rotation_vector_to_matrix(x.tail<3>()); + + // ½tr((Q - Q̂) J (Q - Q̂)ᵀ) + const RotationMatrix dQ = Q - Q_hat; + energy += 0.5 * (dQ * body.J() * dQ.transpose()).trace(); + } else { + assert(q_hat.size() == 2); + assert(x.size() == 3); + assert(Q_hat.size() == 1); + // ½ I (θ-θ̂)² + const double dtheta = x(2) - Q_hat(0, 0); + energy += 0.5 * body.moment_of_inertia()(0) * dtheta * dtheta; + } + } + + return energy; +} + +VectorMax6d InertialTerm::gradient( + const RigidBody& body, + Eigen::ConstRef x, + Eigen::ConstRef q_hat, + Eigen::ConstRef Q_hat) const +{ + VectorMax6d grad = VectorMax6d::Zero(x.size()); + + // Linear inertia + // if (!body.is_dof_fixed.head(pose.pos_ndof()).all()) + { + // m (q - q̂) + grad.head(q_hat.size()) = body.mass() * (x.head(q_hat.size()) - q_hat); + } + + // Rotational energy + // if (!body.is_dof_fixed.tail(pose.rot_ndof()).all()) + { + if (q_hat.size() == 3) { + const Eigen::Matrix3d Q = rotation_vector_to_matrix(x.tail<3>()); + + // ∂f​/∂xₖ = ∑ᵢ∑ⱼ ∂E/∂Qᵢⱼ ∂Qᵢⱼ/∂xₖ + const Eigen::Matrix dQ_dx = + rotation_vector_to_matrix_jacobian(x.tail<3>()); + const Eigen::Vector dE_dQ = + ((Q - Q_hat) * body.J()).reshaped(); + grad.tail<3>() = dQ_dx * dE_dQ; + } else { + assert(q_hat.size() == 2); + assert(x.size() == 3); + assert(Q_hat.size() == 1); + // I (θ - θ̂) + grad(2) = body.moment_of_inertia()(0) * (x(2) - Q_hat(0, 0)); + } + } + + return grad; +} + +MatrixMax6d InertialTerm::hessian( + const RigidBody& body, + Eigen::ConstRef x, + Eigen::ConstRef q_hat, + Eigen::ConstRef Q_hat) const +{ + MatrixMax6d hess = MatrixMax6d::Zero(x.size(), x.size()); + + // Linear inertia + // if (!body.is_dof_fixed.head(pose.pos_ndof()).all()) + { + // m (q - q̂) + hess.topLeftCorner(q_hat.size(), q_hat.size()).diagonal().array() = + body.mass(); + } + + // Rotational energy + // if (!body.is_dof_fixed.tail(pose.rot_ndof()).all()) + { + if (q_hat.size() == 3) { + const Eigen::Matrix3d Q = rotation_vector_to_matrix(x.tail<3>()); + const Eigen::Matrix dQ_dx = + rotation_vector_to_matrix_jacobian(x.tail<3>()); + const Eigen::Matrix d2Q_dx2 = + rotation_vector_to_matrix_hessian(x.tail<3>()); + + const Eigen::Vector dE_dQ = + ((Q - Q_hat) * body.J()).reshaped(); + + // ∂²E/∂Q² = J ⊗ I + Eigen::Matrix d2E_dQ2 = + Eigen::Matrix::Zero(); + d2E_dQ2.diagonal().segment<3>(0).array() = body.J()(0, 0); + d2E_dQ2.diagonal().segment<3>(3).array() = body.J()(1, 1); + d2E_dQ2.diagonal().segment<3>(6).array() = body.J()(2, 2); + + // (3x3) = (3×9)(9×9)(9x3) + mat((9x9)(9x1)) + hess.bottomRightCorner<3, 3>() = dQ_dx * d2E_dQ2 * dQ_dx.transpose() + + (d2Q_dx2 * dE_dQ).reshaped(3, 3); + } else { + assert(q_hat.size() == 2); + assert(x.size() == 3); + assert(Q_hat.size() == 1); + // I (θ - θ̂) + hess(2, 2) = body.moment_of_inertia()(0); + } + } + + return hess; +} + +} // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/inertial_term.hpp b/src/ipc/dynamics/rigid/inertial_term.hpp new file mode 100644 index 000000000..d75df53d4 --- /dev/null +++ b/src/ipc/dynamics/rigid/inertial_term.hpp @@ -0,0 +1,87 @@ +#pragma once + +#include +#include +#include + +namespace ipc::rigid { + +/// @brief Class representing the term ½m‖q - q̂‖² + ½tr((Q - Q̂) J (Q - Q̂)ᵀ) +class InertialTerm { +public: + InertialTerm(const std::shared_ptr& _time_integrator) + : time_integrator(_time_integrator) + { + } + + /// @brief Update the predicted poses of the rigid bodies. + /// @param bodies The collection of rigid bodies. + void update(const RigidBodies& bodies); + + // ---- Cumulative functions ----------------------------------------------- + + /// @brief Compute the total energy for all rigid bodies. + /// @param bodies The collection of rigid bodies. + /// @param x The DOFs of the rigid bodies, where the first 3 entries are the positions and the last 3 entries are the rotations. + /// @return The total energy of the rigid bodies. + double + operator()(const RigidBodies& bodies, Eigen::ConstRef x); + + /// @brief Compute the gradient of the total energy for all rigid bodies. + /// @param bodies The collection of rigid bodies. + /// @param x The DOFs of the rigid bodies, where the first 3 entries are the positions and the last 3 entries are the rotations. + /// @return The gradient of the total energy of the rigid bodies. + Eigen::VectorXd + gradient(const RigidBodies& bodies, Eigen::ConstRef x); + + /// @brief Compute the Hessian of the total energy for all rigid bodies. + /// @param bodies The collection of rigid bodies. + /// @param x The DOFs of the rigid bodies, where the first 3 entries are the positions and the last 3 entries are the rotations. + /// @return The Hessian of the total energy of the rigid bodies. + Eigen::MatrixXd + hessian(const RigidBodies& bodies, Eigen::ConstRef x); + + // ---- Per-body functions ------------------------------------------------- + + /// @brief Compute the energy of a rigid body at a given pose. + /// @param body The rigid body. + /// @param pose The pose of the rigid body. + /// @return The energy of the rigid body at the given pose. + double operator()( + const RigidBody& body, + Eigen::ConstRef x, + Eigen::ConstRef q_hat, + Eigen::ConstRef Q_hat) const; + + /// @brief Compute the gradient of the energy of a rigid body at a given pose. + /// @param body The rigid body. + /// @param x The pose of the rigid body. + /// @param q_hat The predicted rotation of the rigid body. + /// @param Q_hat The predicted rotation matrix of the rigid body. + /// @return The gradient of the energy of the rigid body at the given pose. + VectorMax6d gradient( + const RigidBody& body, + Eigen::ConstRef x, + Eigen::ConstRef q_hat, + Eigen::ConstRef Q_hat) const; + + /// @brief Compute the Hessian of the energy of a rigid body at a given pose. + /// @param body The rigid body. + /// @param x The pose of the rigid body. + /// @param q_hat The predicted rotation of the rigid body. + /// @param Q_hat The predicted rotation matrix of the rigid body. + /// @return The Hessian of the energy of the rigid body at the given pose. + MatrixMax6d hessian( + const RigidBody& body, + Eigen::ConstRef x, + Eigen::ConstRef q_hat, + Eigen::ConstRef Q_hat) const; + +private: + const std::shared_ptr time_integrator; + + /// Cached predicted poses for the rigid body + std::vector predicted_poses; +}; + +} // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/mass.cpp b/src/ipc/dynamics/rigid/mass.cpp new file mode 100644 index 000000000..c76b60ed6 --- /dev/null +++ b/src/ipc/dynamics/rigid/mass.cpp @@ -0,0 +1,244 @@ +#include "mass.hpp" + +#include + +#include + +namespace ipc::rigid { + +namespace { + + void compute_mass_properties_2D( + const Eigen::MatrixXd& vertices, + const Eigen::MatrixXi& edges, + double& total_mass, + VectorMax3d& center, + MatrixMax3d& inertia) + { + Eigen::SparseMatrix mass_matrix; + construct_mass_matrix(vertices, edges, mass_matrix); + total_mass = mass_matrix.sum(); + + if (total_mass == 0) { + center.setZero(vertices.cols()); + } else { + center = (mass_matrix * vertices).colwise().sum() / total_mass; + } + + // ∑ mᵢ rᵢ ⋅ rᵢ + inertia.resize(1, 1); + inertia(0) = (mass_matrix * vertices.rowwise().squaredNorm()).sum(); + } + + // Based on ChTriangleMeshConnected.cpp::ComputeMassProperties from Chrono: + // Copyright (c) 2016, Project Chrono Development Team + // All rights reserved. + // https://github.com/projectchrono/chrono/blob/main/LICENSE + // + // This requires the mesh to be closed, watertight, with proper triangle + // orientation. + bool compute_mass_properties_3D( + const Eigen::MatrixXd& vertices, + const Eigen::MatrixXi& faces, + double& total_mass, + VectorMax3d& center, + MatrixMax3d& inertia) + { + assert(vertices.cols() == 3); + assert(faces.rows() > 0 && faces.cols() == 3); + + // order: 1, x, y, z, x^2, y^2, z^2, xy, yz, zx + std::array integral = { 0.0 }; + + for (int i = 0; i < faces.rows(); i++) { + // Get vertices of triangle i. + const Eigen::Vector3d& v0 = vertices.row(faces(i, 0)); + const Eigen::Vector3d& v1 = vertices.row(faces(i, 1)); + const Eigen::Vector3d& v2 = vertices.row(faces(i, 2)); + + // Get cross product of edges and normal vector. + const Eigen::Vector3d& V1mV0 = v1 - v0; + const Eigen::Vector3d& V2mV0 = v2 - v0; + const Eigen::Vector3d& N = V1mV0.cross(V2mV0); + + // Compute integral terms. + double tmp0, tmp1, tmp2; + double f1x, f2x, f3x, g0x, g1x, g2x; + tmp0 = v0.x() + v1.x(); + f1x = tmp0 + v2.x(); + tmp1 = v0.x() * v0.x(); + tmp2 = tmp1 + v1.x() * tmp0; + f2x = tmp2 + v2.x() * f1x; + f3x = v0.x() * tmp1 + v1.x() * tmp2 + v2.x() * f2x; + g0x = f2x + v0.x() * (f1x + v0.x()); + g1x = f2x + v1.x() * (f1x + v1.x()); + g2x = f2x + v2.x() * (f1x + v2.x()); + + double f1y, f2y, f3y, g0y, g1y, g2y; + tmp0 = v0.y() + v1.y(); + f1y = tmp0 + v2.y(); + tmp1 = v0.y() * v0.y(); + tmp2 = tmp1 + v1.y() * tmp0; + f2y = tmp2 + v2.y() * f1y; + f3y = v0.y() * tmp1 + v1.y() * tmp2 + v2.y() * f2y; + g0y = f2y + v0.y() * (f1y + v0.y()); + g1y = f2y + v1.y() * (f1y + v1.y()); + g2y = f2y + v2.y() * (f1y + v2.y()); + + double f1z, f2z, f3z, g0z, g1z, g2z; + tmp0 = v0.z() + v1.z(); + f1z = tmp0 + v2.z(); + tmp1 = v0.z() * v0.z(); + tmp2 = tmp1 + v1.z() * tmp0; + f2z = tmp2 + v2.z() * f1z; + f3z = v0.z() * tmp1 + v1.z() * tmp2 + v2.z() * f2z; + g0z = f2z + v0.z() * (f1z + v0.z()); + g1z = f2z + v1.z() * (f1z + v1.z()); + g2z = f2z + v2.z() * (f1z + v2.z()); + + // Update integrals. + integral[0] += N.x() * f1x; + integral[1] += N.x() * f2x; + integral[2] += N.y() * f2y; + integral[3] += N.z() * f2z; + integral[4] += N.x() * f3x; + integral[5] += N.y() * f3y; + integral[6] += N.z() * f3z; + integral[7] += N.x() * (v0.y() * g0x + v1.y() * g1x + v2.y() * g2x); + integral[8] += N.y() * (v0.z() * g0y + v1.z() * g1y + v2.z() * g2y); + integral[9] += N.z() * (v0.x() * g0z + v1.x() * g1z + v2.x() * g2z); + } + + integral[0] /= 6; + integral[1] /= 24; + integral[2] /= 24; + integral[3] /= 24; + integral[4] /= 60; + integral[5] /= 60; + integral[6] /= 60; + integral[7] /= 120; + integral[8] /= 120; + integral[9] /= 120; + + // total_mass + total_mass = integral[0]; + if (total_mass <= 0 || !std::isfinite(total_mass)) { + // 3D mass computation only works for closed meshes! + return false; + } + assert(total_mass > 0); + + // center of mass + center = + Eigen::Vector3d(integral[1], integral[2], integral[3]) / total_mass; + + // inertia relative to world origin + inertia.resize(3, 3); + inertia(0, 0) = integral[5] + integral[6]; + inertia(0, 1) = -integral[7]; + inertia(0, 2) = -integral[9]; + inertia(1, 0) = inertia(0, 1); + inertia(1, 1) = integral[4] + integral[6]; + inertia(1, 2) = -integral[8]; + inertia(2, 0) = inertia(0, 2); + inertia(2, 1) = inertia(1, 2); + inertia(2, 2) = integral[4] + integral[5]; + + // inertia relative to center of mass + inertia(0, 0) -= + total_mass * (center.y() * center.y() + center.z() * center.z()); + inertia(0, 1) += total_mass * center.x() * center.y(); + inertia(0, 2) += total_mass * center.z() * center.x(); + inertia(1, 0) = inertia(0, 1); + inertia(1, 1) -= + total_mass * (center.z() * center.z() + center.x() * center.x()); + inertia(1, 2) += total_mass * center.y() * center.z(); + inertia(2, 0) = inertia(0, 2); + inertia(2, 1) = inertia(1, 2); + inertia(2, 2) -= + total_mass * (center.x() * center.x() + center.y() * center.y()); + + return true; + } + + void compute_mass_properties_point_cloud( + const Eigen::MatrixXd& vertices, + double& total_mass, + VectorMax3d& center, + MatrixMax3d& inertia) + { + assert(vertices.size() > 0); + total_mass = vertices.rows(); // Point cloud has unit mass per point + center = vertices.colwise().mean(); + inertia = Eigen::Matrix3d::Zero(); + // https://i.ytimg.com/vi/9jOrDufoO50/hqdefault.jpg + for (long i = 0; i < vertices.rows(); i++) { + const Eigen::Vector3d v = vertices.row(i); + const Eigen::Vector3d v_sqr = v.array().pow(2); + inertia(0, 0) += v_sqr.y() + v_sqr.z(); + inertia(1, 1) += v_sqr.x() + v_sqr.z(); + inertia(2, 2) += v_sqr.x() + v_sqr.y(); + inertia(0, 1) += -v.x() * v.y(); + inertia(0, 2) += -v.x() * v.z(); + inertia(1, 2) += -v.y() * v.z(); + } + inertia(1, 0) = inertia(0, 1); + inertia(2, 0) = inertia(0, 2); + inertia(2, 1) = inertia(1, 2); + } + +} // namespace + +void compute_mass_properties( + const Eigen::MatrixXd& vertices, + const Eigen::MatrixXi& facets, + double& total_mass, + VectorMax3d& center, + MatrixMax3d& inertia) +{ + if (vertices.cols() == 2) { + compute_mass_properties_2D( + vertices, facets, total_mass, center, inertia); + } + if (facets.size() == 0 || facets.cols() != 3) { + compute_mass_properties_point_cloud( + vertices, total_mass, center, inertia); + } else if (!compute_mass_properties_3D( + vertices, facets, total_mass, center, inertia)) { + compute_mass_properties_point_cloud( + vertices, total_mass, center, inertia); + } +} + +// Construct the sparse mass matrix for the given mesh (V, F). +void construct_mass_matrix( + const Eigen::MatrixXd& vertices, + const Eigen::MatrixXi& facets, + Eigen::SparseMatrix& mass_matrix) +{ + if (vertices.cols() == 2 || facets.cols() == 2) { + assert(facets.cols() == 2); + Eigen::VectorXd vertex_masses = Eigen::VectorXd::Zero(vertices.rows()); + for (long i = 0; i < facets.rows(); i++) { + const double edge_length = + (vertices.row(facets(i, 1)) - vertices.row(facets(i, 0))) + .norm(); + // Add Voronoi areas to the vertex weight + vertex_masses(facets(i, 0)) += edge_length / 2; + vertex_masses(facets(i, 1)) += edge_length / 2; + } + mass_matrix.resize(vertices.rows(), vertices.rows()); + mass_matrix.diagonal() = vertex_masses; + } else if (facets.cols() == 3) { + assert(vertices.cols() == 3); // Only use triangles in 3D + igl::massmatrix( + vertices, facets, igl::MassMatrixType::MASSMATRIX_TYPE_VORONOI, + mass_matrix); + } else { + // Probably a point cloud + mass_matrix.resize(vertices.rows(), vertices.rows()); + mass_matrix.setIdentity(); + } +} + +} // namespace ipc::rigid diff --git a/src/ipc/dynamics/rigid/mass.hpp b/src/ipc/dynamics/rigid/mass.hpp new file mode 100644 index 000000000..e022276f3 --- /dev/null +++ b/src/ipc/dynamics/rigid/mass.hpp @@ -0,0 +1,32 @@ +#pragma once + +#include + +#include +#include + +namespace ipc::rigid { + +/// @brief Compute the total mass, center of mass, and moment of inertia +/// @param vertices Vertices of the mesh +/// @param facets Facets (2D: edges; 3D: triangles) of the mesh +/// @param total_mass Total mass of the mesh +/// @param center_of_mass Center of mass of the mesh +/// @param moment_of_inertia Moment of inertia of the mesh +void compute_mass_properties( + const Eigen::MatrixXd& vertices, + const Eigen::MatrixXi& facets, + double& total_mass, + VectorMax3d& center_of_mass, + MatrixMax3d& moment_of_inertia); + +/// @brief Construct the sparse mass matrix for the given mesh (V, E). +/// @param vertices Vertices of the mesh +/// @param facets Facets (2D: edges; 3D: triangles) of the mesh +/// @param mass_matrix Sparse mass matrix of the mesh +void construct_mass_matrix( + const Eigen::MatrixXd& vertices, + const Eigen::MatrixXi& facets, + Eigen::SparseMatrix& mass_matrix); + +} // namespace ipc::rigid diff --git a/src/ipc/dynamics/rigid/pose.cpp b/src/ipc/dynamics/rigid/pose.cpp new file mode 100644 index 000000000..1df8b30ba --- /dev/null +++ b/src/ipc/dynamics/rigid/pose.cpp @@ -0,0 +1,142 @@ +#include "pose.hpp" + +#include + +namespace ipc::rigid { + +namespace { + inline Eigen::Matrix3d + cross_product_matrix(Eigen::ConstRef x) + { + Eigen::Matrix3d X; + X << 0, -x.z(), x.y(), // + x.z(), 0, -x.x(), // + -x.y(), x.x(), 0; + return X; + } +} // namespace + +Eigen::Matrix3d +rotation_vector_to_matrix(Eigen::ConstRef theta) +{ + const double sinc_angle = sinc_norm_x(theta); + const double sinc_half_angle = sinc_norm_x((theta / 2).eval()); + const Eigen::Matrix3d K = cross_product_matrix(theta); + const Eigen::Matrix3d K2 = K * K; + Eigen::Matrix3d R = + sinc_angle * K + 0.5 * sinc_half_angle * sinc_half_angle * K2; + R.diagonal().array() += 1.0; + return R; +} + +Eigen::Matrix +rotation_vector_to_matrix_jacobian(Eigen::ConstRef theta) +{ + assert(theta.size() == 3); // Only valid for 3D rotation vectors + + const double s = sinc_norm_x(theta); + const double sh = sinc_norm_x(theta / 2); + const double sh_sq = sh * sh; + const Eigen::Matrix3d K = cross_product_matrix(theta); + + const Eigen::Vector3d ds = sinc_norm_x_grad(theta); + const Eigen::Vector3d dsh = sinc_norm_x_grad(theta / 2); + + std::array dK; + dK[0] << 0, 0, 0, 0, 0, -1, 0, 1, 0; + dK[1] << 0, 0, 1, 0, 0, 0, -1, 0, 0; + dK[2] << 0, -1, 0, 1, 0, 0, 0, 0, 0; + + Eigen::Matrix3d s_plus_sh_sq_K = sh_sq * K; + s_plus_sh_sq_K.diagonal().array() += s; + + const Eigen::Matrix3d sh_K2 = sh * K * K; + + Eigen::Matrix dR; + for (int i = 0; i < 3; ++i) { + dR.row(i) = + (ds(i) * K + s_plus_sh_sq_K * dK[i] + dsh(i) * sh_K2).reshaped(); + } + + return dR; +} + +Eigen::Matrix +rotation_vector_to_matrix_hessian(Eigen::ConstRef theta) +{ + assert(theta.size() == 3); // Only valid for 3D rotation vectors + + const double sh = sinc_norm_x(theta / 2); + const double sh_sq = sh * sh; + const Eigen::Matrix3d K = cross_product_matrix(theta); + + const Eigen::Vector3d ds = sinc_norm_x_grad(theta); + const Eigen::Vector3d dsh = sinc_norm_x_grad(theta / 2); + const Eigen::Matrix3d d2s = sinc_norm_x_hess(theta); + const Eigen::Matrix3d d2sh = sinc_norm_x_hess(theta / 2); + + std::array dK; + dK[0] << 0, 0, 0, 0, 0, -1, 0, 1, 0; + dK[1] << 0, 0, 1, 0, 0, 0, -1, 0, 0; + dK[2] << 0, -1, 0, 1, 0, 0, 0, 0, 0; + + // NOTE: ∂²K/∂θ² = 0 + + const Eigen::Matrix3d sh_K2 = sh * K * K; + + Eigen::Matrix d2R; + for (int i = 0; i < 3; ++i) { + const Eigen::Matrix3d two_sh_K_dKi = 2 * sh * K * dK[i]; + + for (int j = 0; j < 3; ++j) { + d2R.row(i * 3 + j) = + (d2s(i, j) * K + ds(i) * dK[j] + ds(j) * dK[i] + + dsh(j) * two_sh_K_dKi + sh_sq * dK[j] * dK[i] + + d2sh(i, j) * sh_K2 + 2 * dsh(i) * K * dK[j]) + .reshaped(); + } + } + return d2R; +} + +Eigen::Vector3d rotation_matrix_to_vector(Eigen::Matrix3d R) +{ + Eigen::Vector3d r; + assert(R.trace() >= -1 && R.trace() <= 3); // Ensure acos is valid + double theta = acos((R.trace() - 1) / 2.0); // θ ∈ [0, π) + + // R = I + sin(θ)K + (1 - cos(θ))K² where K is the cross-product matrix of + // r/θ + if (theta < 1e-6) { + // θ ≈ 0 ⟹ R ≈ I + θK + // No need to divide by sin(θ)≈θ since the off-diagonals are ±rᵢθ + r.x() = (R(2, 1) - R(1, 2)) / 2; + r.y() = (R(0, 2) - R(2, 0)) / 2; + r.z() = (R(1, 0) - R(0, 1)) / 2; + // Θ is already part of the off-diagonal elements, so no need to scale + } else if (theta > M_PI - 1e-6) { + // θ ≈ π ⟹ R ≈ I - (θ - π)K + 2K² + // Ensure positive for sqrt + assert(R(0, 0) > -1); + r.x() = sqrt((R(0, 0) + 1) / 2); + // Determine the other components based on the first component + // R₀,₁ = 2r₀r₁+(θ-π)r₂, R₀,₂ = 2r₀r₂-(θ-π)r₁, R₁,₂ = 2r₁r₂+(θ-π)r₀ + r.y() = R(0, 1) / (2 * r.x()); + r.z() = R(0, 2) / (2 * r.x()); + r.normalize(); // Normalize just in case + r.array() *= theta; // Scale by the angle + } else { + r.x() = (R(2, 1) - R(1, 2)) / (2 * sin(theta)); + r.y() = (R(0, 2) - R(2, 0)) / (2 * sin(theta)); + r.z() = (R(1, 0) - R(0, 1)) / (2 * sin(theta)); + r.normalize(); // Normalize just in case + r *= theta; // Scale by the angle + } + + return r; +} + +template struct Pose; +template struct Pose; + +} // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/pose.hpp b/src/ipc/dynamics/rigid/pose.hpp new file mode 100644 index 000000000..97464935b --- /dev/null +++ b/src/ipc/dynamics/rigid/pose.hpp @@ -0,0 +1,101 @@ +#pragma once + +#include + +namespace ipc::rigid { + +using RotationVector = VectorMax3d; +using RotationMatrix = MatrixMax3d; + +/// @brief Convert from a 3D rotation vector to a rotation matrix. +/// @param theta The rotation vector +/// @return The rotation matrix corresponding to the rotation vector +Eigen::Matrix3d +rotation_vector_to_matrix(Eigen::ConstRef theta); + +/// @brief Compute the Jacobian of the rotation matrix with respect to the rotation vector. +/// @param theta The rotation vector +/// @return The Jacobian matrix +Eigen::Matrix +rotation_vector_to_matrix_jacobian(Eigen::ConstRef theta); + +/// @brief Compute the Hessian of the rotation matrix with respect to the rotation vector. +/// +/// This is a 9x9 matrix where each row corresponds to the second derivative of +/// each element of the rotation matrix with respect to each component of the +/// rotation vector. +/// +/// @param theta The rotation vector +/// @return The Hessian matrix +Eigen::Matrix +rotation_vector_to_matrix_hessian(Eigen::ConstRef theta); + +/// @brief Convert from a 3D rotation matrix to a rotation vector. +/// @param R The rotation matrix +/// @return The rotation vector corresponding to the rotation matrix +Eigen::Vector3d rotation_matrix_to_vector(Eigen::ConstRef R); + +// ---------------------------------------------------------------------------- + +template struct Pose { + // Position of the rigid body + VectorMax3d position; + // Rotation of the rigid body (rotation vector for 3D, angle for 1D) + RotationType rotation; + + RotationMatrix rotation_matrix() const + { + if constexpr (std::is_same_v) { + return rotation_vector_to_matrix(rotation); + } else { + return rotation; + } + } +}; + +struct AffinePose { + // Position of the rigid body + VectorMax3d position; + // Rotation of the rigid body (rotation vector for 3D, angle for 1D) + MatrixMax3d rotation; + + /// @brief Construct a rotation vector from the rotation matrix. + /// @return The rotation vector corresponding to the rotation matrix + VectorMax3d rotation_vector() const + { + assert(rotation.rows() == rotation.cols()); + assert(rotation.rows() == 2 || rotation.rows() == 3); + assert(rotation.isUnitary(1e-9)); // Ensure it's a rotation matrix + if (rotation.rows() == 2) { + // For 2D, return the angle + VectorMax3d angle(1); + // rotation(1, 0) = sin(θ), rotation(0, 0) = cos(θ) + // Thus, θ = atan2(sin(θ), cos(θ)) + angle(0) = std::atan2(rotation(1, 0), rotation(0, 0)); + return angle; + } else { + // For 3D, return the rotation vector + // Eigen::AngleAxisd r = + // Eigen::AngleAxisd(Eigen::Matrix3d(rotation)); return r.angle() * + // r.axis(); + return rotation_matrix_to_vector(rotation); + } + } + + /// @brief Set the rotation matrix from a rotation vector or angle. + /// @param theta The rotation vector (3D) or angle (2D). + void set_rotation_vector(Eigen::ConstRef theta) + { + assert(theta.size() == 1 || theta.size() == 3); + if (theta.size() == 1) { + // For 2D, set the rotation matrix directly + rotation << std::cos(theta(0)), -std::sin(theta(0)), + std::sin(theta(0)), std::cos(theta(0)); + } else { + // For 3D, convert the rotation vector to a rotation matrix + rotation = rotation_vector_to_matrix(theta); + } + } +}; + +} // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/rigid_bodies.cpp b/src/ipc/dynamics/rigid/rigid_bodies.cpp new file mode 100644 index 000000000..d86a9f316 --- /dev/null +++ b/src/ipc/dynamics/rigid/rigid_bodies.cpp @@ -0,0 +1,80 @@ +#include "rigid_bodies.hpp" + +namespace ipc::rigid { + +RigidBodies RigidBodies::build_from_meshes( + const std::vector& rest_positions, + const std::vector& edges, + const std::vector& faces) +{ + assert(rest_positions.size() == edges.size()); + assert(rest_positions.size() == faces.size()); + + size_t num_vertices = 0, num_edges = 0, num_faces = 0; + std::vector body_vertex_starts(rest_positions.size() + 1); + std::vector body_edge_starts(edges.size() + 1); + std::vector body_face_starts(faces.size() + 1); + body_vertex_starts[0] = body_edge_starts[0] = body_face_starts[0] = 0; + + for (size_t i = 0; i < rest_positions.size(); ++i) { + body_vertex_starts[i + 1] = (num_vertices += rest_positions[i].rows()); + body_edge_starts[i + 1] = (num_edges += edges[i].rows()); + body_face_starts[i + 1] = (num_faces += faces[i].rows()); + } + + Eigen::MatrixXd concat_rest_positions( + num_vertices, rest_positions[0].cols()); + Eigen::MatrixXi concat_edges(num_edges, 2); + Eigen::MatrixXi concat_faces(num_faces, 3); + + for (size_t i = 0; i < rest_positions.size(); ++i) { + concat_rest_positions.middleRows( + body_vertex_starts[i], rest_positions[i].rows()) = + rest_positions[i]; + concat_edges.middleRows(body_edge_starts[i], edges[i].rows()) = + edges[i].array() + body_vertex_starts[i]; + concat_faces.middleRows(body_face_starts[i], faces[i].rows()) = + faces[i].array() + body_vertex_starts[i]; + } + + return RigidBodies( + concat_rest_positions, concat_edges, concat_faces, body_vertex_starts, + body_edge_starts, body_face_starts); +} + +RigidBodies::RigidBodies( + Eigen::ConstRef _rest_positions, + Eigen::ConstRef _edges, + Eigen::ConstRef _faces, + std::vector _body_vertex_starts, + std::vector _body_edge_starts, + std::vector _body_face_starts) + : CollisionMesh(_rest_positions, _edges, _faces) + , body_vertex_starts(std::move(_body_vertex_starts)) + , body_edge_starts(std::move(_body_edge_starts)) + , body_face_starts(std::move(_body_face_starts)) +{ + assert(body_vertex_starts.size() == body_edge_starts.size()); + assert(body_edge_starts.size() == body_face_starts.size()); + assert(body_vertex_starts.back() == num_vertices()); + assert(body_edge_starts.back() == num_edges()); + assert(body_face_starts.back() == num_faces()); + + bodies.reserve(body_vertex_starts.size() - 1); + Pose<> initial_pose; + for (size_t i = 0; i < body_vertex_starts.size() - 1; ++i) { + bodies.emplace_back( + m_rest_positions.middleRows( + body_vertex_starts[i], + body_vertex_starts[i + 1] - body_vertex_starts[i]), + edges().middleRows( + body_edge_starts[i], + body_edge_starts[i + 1] - body_edge_starts[i]), + faces().middleRows( + body_face_starts[i], + body_face_starts[i + 1] - body_face_starts[i]), + initial_pose); + } +} + +} // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/rigid_bodies.hpp b/src/ipc/dynamics/rigid/rigid_bodies.hpp new file mode 100644 index 000000000..fae80f417 --- /dev/null +++ b/src/ipc/dynamics/rigid/rigid_bodies.hpp @@ -0,0 +1,37 @@ +#pragma once + +#include + +namespace ipc::rigid { + +class RigidBodies : public CollisionMesh { + RigidBodies() = delete; + +public: + RigidBodies( + Eigen::ConstRef rest_positions, + Eigen::ConstRef edges, + Eigen::ConstRef faces, + std::vector body_vertex_starts, + std::vector body_edge_starts, + std::vector body_face_starts); + + static RigidBodies build_from_meshes( + const std::vector& rest_positions, + const std::vector& edges, + const std::vector& faces); + + size_t num_bodies() const { return bodies.size(); } + + const RigidBody& operator[](size_t i) const { return bodies[i]; } + +private: + std::vector bodies; + + // Start indices of vertices for each body + std::vector body_vertex_starts; + std::vector body_edge_starts; + std::vector body_face_starts; +}; + +} // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/rigid_body.cpp b/src/ipc/dynamics/rigid/rigid_body.cpp index cc7dcb921..3ebcfa55d 100644 --- a/src/ipc/dynamics/rigid/rigid_body.cpp +++ b/src/ipc/dynamics/rigid/rigid_body.cpp @@ -1,47 +1,213 @@ #include "rigid_body.hpp" +#include #include namespace ipc::rigid { namespace { - inline Eigen::Matrix3d cross_product_matrix(const Eigen::Vector3d& x) + void center_vertices( + Eigen::Ref vertices, + Eigen::ConstRef edges, + Eigen::ConstRef faces, + Pose<>& pose) { - Eigen::Matrix3d X; - X << 0, -x.z(), x.y(), // - x.z(), 0, -x.x(), // - -x.y(), x.x(), 0; - return X; + // compute the center of mass several times to get more accurate + for (int i = 0; i < 10; i++) { + double mass; + VectorMax3d com; + MatrixMax3d inertia; + compute_mass_properties( + vertices, + (vertices.cols() == 2 || faces.size() == 0) ? edges : faces, + mass, com, inertia); + vertices.rowwise() -= com.transpose(); + pose.position += com; + if (com.squaredNorm() < 1e-8) { + break; + } + } + } + + inline Eigen::DiagonalMatrix compute_J(const VectorMax3d& I) + { + if (I.size() == 1) { + return I.asDiagonal(); + } else { + assert(I.size() == 3); + return Eigen::DiagonalMatrix( + 0.5 * (-I.x() + I.y() + I.z()), // + 0.5 * (I.x() - I.y() + I.z()), // + 0.5 * (I.x() + I.y() - I.z())); + } } } // namespace -Eigen::MatrixXd -RigidBody::transform_vertices(const Eigen::MatrixXd& rest_positions) const +RigidBody::RigidBody( + Eigen::Ref vertices, + Eigen::ConstRef edges, + Eigen::ConstRef faces, + Pose<>& initial_pose) { - // Compute: R(θ) x̄ + p - // transpose because x is row-ordered - const int dim = rest_positions.cols(); - - assert( - (dim == 2 && rotation_vector.size() == 1) - || (dim == 3 && rotation_vector.size() == 3)); - - // Convert the rotation vector to a rotation matrix - MatrixMax3d R(dim, dim); - if (dim == 2) { - const double theta = rotation_vector(0); - R << sin(theta), -cos(theta), cos(theta), sin(theta); + const double density = 1.0; // Default density + + assert(vertices.size() > 0); + assert(edges.size() == 0 || edges.cols() == 2); + assert(faces.size() == 0 || faces.cols() == 3); + + const int dim = vertices.cols(); + assert(dim == 2 || dim == 3); + + // 1. Center the vertices, so the mass properties are computed correctly + center_vertices(vertices, edges, faces, initial_pose); + + // 2. Compute the mass properties + VectorMax3d center_of_mass; + MatrixMax3d inertia_tensor; + compute_mass_properties( + vertices, (dim == 2 || faces.size() == 0) ? edges : faces, m_mass, + center_of_mass, inertia_tensor); + + // 3. The mass above is actually volume, so we need to scale it by the + // density to get the mass. + m_mass *= density; + + // 4. Convert the inertia tensor to the principal axes moments of inertia + MatrixMax3d R0; + if (dim == 3) { + // This computation is taken from ProjectChrono: https://bit.ly/2RpbTl1 + // The eigen values of the inertia tensor are the principal moments + // of inertia, which are the diagonal elements of the diagonalized + // inertia tensor. The eigenvectors are the principal axes of the + // inertia tensor, which are the columns of the rotation matrix R₀. + Eigen::SelfAdjointEigenSolver solver; + + // Remove small values from the inertia tensor to avoid numerical + // issues in the eigen decomposition + const double threshold = 1e-16 * inertia_tensor.maxCoeff(); + inertia_tensor = (inertia_tensor.array().abs() < threshold) + .select(0.0, inertia_tensor); + + solver.compute(inertia_tensor); + assert(solver.info() == Eigen::Success); + + // Multiply by density to get the units of moment of inertia + m_moment_of_inertia = density * solver.eigenvalues(); + if ((m_moment_of_inertia.array() < 0).any()) { + logger().warn( + "Negative moments of inertia ({}), inverting.", + m_moment_of_inertia); + // This typically only happens with negative ε inertias + m_moment_of_inertia = m_moment_of_inertia.array().abs(); + } + + // The rotation from the principal inertial frame to the input world + // frame. + R0 = solver.eigenvectors(); + + // Ensure that we have an orientation preserving transform + if (R0.determinant() < 0.0) { + R0.col(0) *= -1.0; + } + assert(R0.isUnitary(1e-9)); + + // TODO: Enable this code + // int num_rot_dof_fixed = + // is_dof_fixed.tail(PoseD::dim_to_rot_ndof(dim())).count(); + // if (num_rot_dof_fixed == 2) { + // // Convert moment of inertia to world coordinates + // // https://physics.stackexchange.com/a/268812 + // moment_of_inertia = -I.diagonal().array() + I.diagonal().sum(); + // R0.setIdentity(); + // } else if (num_rot_dof_fixed == 1) { + // spdlog::warn( + // "Rigid body dynamics with two rotational DoF has " + // "not been tested thoroughly."); + // } + + // TODO: this code below need to be updated + + // Remove the initial rotation from the rest vertices + vertices = vertices * R0; + + // Store the initial rotation in the pose (R = RᵢR₀) + Eigen::AngleAxisd r = Eigen::AngleAxisd( + Eigen::Matrix3d(initial_pose.rotation_matrix() * R0)); + initial_pose.rotation = r.angle() * r.axis(); + + // TODO: + // ω = R₀ᵀω₀ (ω₀ expressed in body coordinates) + // this->velocity.rotation = R0.transpose() * this->velocity.rotation; + // Eigen::Matrix3d Q_t0 = this->pose.construct_rotation_matrix(); + // this->Qdot = Q_t0 * Hat(this->velocity.rotation); + + // τ = R₀ᵀτ₀ (τ₀ expressed in body coordinates) + // NOTE: this transformation will be done later + // this->force.rotation = R0.transpose() * this->force.rotation; } else { - assert(dim == 3); - const double sinc_angle = sinc_normx(rotation_vector); - const double sinc_half_angle = sinc_normx((rotation_vector / 2).eval()); - const Eigen::Matrix3d K = cross_product_matrix(rotation_vector); - const Eigen::Matrix3d K2 = K * K; - R = sinc_angle * K + 0.5 * sinc_half_angle * sinc_half_angle * K2; - R.diagonal().array() += 1.0; + // For 2D, the inertia tensor is a scalar, and the rotation vector + // is a single value. + m_moment_of_inertia = density * inertia_tensor.diagonal(); + // The input orientation is already in the inertial frame + R0 = Eigen::Matrix::Identity(); } - return (rest_positions * R.transpose()).rowwise() + position.transpose(); + m_J = compute_J(m_moment_of_inertia); + + // Zero out the velocity and forces of fixed dof + // this->velocity.zero_dof(is_dof_fixed, R0); + // this->force.zero_dof(is_dof_fixed, R0); + + // Compute and construct some useful constants + // mass_matrix.resize(ndof()); + // mass_matrix.diagonal().head(pos_ndof()).setConstant(mass); + // mass_matrix.diagonal().tail(rot_ndof()) = moment_of_inertia; + + // r_max = this->vertices.rowwise().norm().maxCoeff(); + + // average_edge_length = 0; + // for (long i = 0; i < edges.rows(); i++) { + // average_edge_length += + // (this->vertices.row(edges(i, 0)) - this->vertices.row(edges(i, + // 1))) + // .norm(); + // } + // if (edges.rows() > 0) { + // average_edge_length /= edges.rows(); + // } + // assert(std::isfinite(average_edge_length)); + + // init_bvh(); } +// Eigen::MatrixXd +// RigidBody::transform_vertices(const Eigen::MatrixXd& rest_positions) const +// { +// // Compute: R(θ) x̄ + p +// // transpose because x is row-ordered +// const int dim = rest_positions.cols(); + +// assert( +// (dim == 2 && rotation_vector.size() == 1) +// || (dim == 3 && rotation_vector.size() == 3)); + +// // Convert the rotation vector to a rotation matrix +// MatrixMax3d R(dim, dim); +// if (dim == 2) { +// const double theta = rotation_vector(0); +// R << sin(theta), -cos(theta), cos(theta), sin(theta); +// } else { +// assert(dim == 3); +// const double sinc_angle = sinc_norm_x(rotation_vector); +// const double sinc_half_angle = +// sinc_norm_x((rotation_vector / 2).eval()); +// const Eigen::Matrix3d K = cross_product_matrix(rotation_vector); +// const Eigen::Matrix3d K2 = K * K; +// R = sinc_angle * K + 0.5 * sinc_half_angle * sinc_half_angle * K2; +// R.diagonal().array() += 1.0; +// } + +// return (rest_positions * R.transpose()).rowwise() + position.transpose(); +// } + } // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/rigid_body.hpp b/src/ipc/dynamics/rigid/rigid_body.hpp index 2c272a6d4..02d6ca241 100644 --- a/src/ipc/dynamics/rigid/rigid_body.hpp +++ b/src/ipc/dynamics/rigid/rigid_body.hpp @@ -1,23 +1,35 @@ #pragma once +#include +#include #include namespace ipc::rigid { -struct RigidBody { - VectorMax3d rotation_vector; // Rotation vector - VectorMax3d position; // Translation vector +class RigidBody { +public: + RigidBody( + Eigen::Ref vertices, + Eigen::ConstRef edges, + Eigen::ConstRef faces, + Pose<>& initial_pose); - RigidBody() = default; + double mass() const { return m_mass; } + const VectorMax3d& moment_of_inertia() const { return m_moment_of_inertia; } + const Eigen::Matrix3d& J() const { return m_J; } + const Pose<>& external_force() const { return m_external_force; } - RigidBody(const VectorMax3d& r, const VectorMax3d& p) - : rotation_vector(r) - , position(p) - { - } +private: + /// @brief Total mass of the rigid body + double m_mass; - Eigen::MatrixXd - transform_vertices(const Eigen::MatrixXd& rest_positions) const; + /// @brief Moment of inertia measured with respect to the principal axes + VectorMax3d m_moment_of_inertia; + + Eigen::Matrix3d m_J; + + /// @brief External force and torque applied to the rigid body + Pose<> m_external_force; }; } // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/time_integrator.hpp b/src/ipc/dynamics/rigid/time_integrator.hpp new file mode 100644 index 000000000..a3517f8dc --- /dev/null +++ b/src/ipc/dynamics/rigid/time_integrator.hpp @@ -0,0 +1,87 @@ +#pragma once + +#include + +#include +#include + +namespace ipc::rigid { + +class ImplicitEuler { +public: + Eigen::VectorXd x_prev; + Eigen::VectorXd v_prev; + Eigen::VectorXd a_prev; + double dt; + size_t num_bodies; + size_t pos_ndof; + size_t rot_ndof; + + ImplicitEuler( + Eigen::ConstRef _x, + Eigen::ConstRef _v, + Eigen::ConstRef _a, + const double _dt, + const size_t _num_bodies) + : x_prev(_x) + , v_prev(_v) + , a_prev(_a) + , dt(_dt) + , num_bodies(_num_bodies) + { + assert(x_prev.size() == v_prev.size()); + assert(v_prev.size() == a_prev.size()); + + pos_ndof = 3, rot_ndof = 9; // Default to 3D case + if (x_prev.size() != num_bodies * (pos_ndof + rot_ndof)) { + pos_ndof = 2, rot_ndof = 1; // 2D case + } + assert(x_prev.size() == num_bodies * (pos_ndof + rot_ndof)); + } + + void update(Eigen::ConstRef x) + { + assert(x.size() == x_prev.size()); + const Eigen::VectorXd v = (x - x_prev) / dt; + a_prev = (v - v_prev) / dt; + v_prev = v; + x_prev = x; + } + + std::vector predicted_pose() const + { + const Eigen::VectorXd x_hat = x_prev + dt * v_prev; + + std::vector predicted(num_bodies); + tbb::parallel_for( + tbb::blocked_range(0, num_bodies), + [&](const tbb::blocked_range& r) { + for (size_t i = r.begin(); i < r.end(); ++i) { + predicted[i] = pose(x_hat, i); + } + }); + + return predicted; + } + + AffinePose pose(size_t i) const { return pose(x_prev, i); } + + AffinePose pose(Eigen::ConstRef x, size_t i) const + { + AffinePose pose; + + pose.position = x.segment(i * (pos_ndof + rot_ndof), pos_ndof); + if (rot_ndof == 1) { + pose.rotation.resize(1, 1); + pose.rotation(0, 0) = x(i * (pos_ndof + rot_ndof) + pos_ndof); + } else { + pose.rotation = + x.segment(i * (pos_ndof + rot_ndof) + pos_ndof, rot_ndof) + .reshaped(3, 3); + } + + return pose; + } +}; + +} // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/utils/sinc.cpp b/src/ipc/utils/sinc.cpp index b44f90b26..b837fdaab 100644 --- a/src/ipc/utils/sinc.cpp +++ b/src/ipc/utils/sinc.cpp @@ -55,7 +55,7 @@ namespace { } } // namespace -double sinc(const double& x) +double sinc(const double x) { if (abs(x) >= taylor_n_bound) { return sin(x) / x; @@ -134,16 +134,16 @@ filib::Interval sinc(const filib::Interval& x) return intsec(y, bounds); } -VectorMax3d sinc_normx_grad(const VectorMax3d& x) +VectorMax3d sinc_norm_x_grad(Eigen::ConstRef x) { return dsinc_over_x(x.norm()) * x; } -MatrixMax3d sinc_normx_hess(const VectorMax3d& x) +MatrixMax3d sinc_norm_x_hess(Eigen::ConstRef x) { - double normx = x.norm(); - return ddsinc_over_x2_minus_dsinc_over_x3(normx) * x * x.transpose() - + dsinc_over_x(normx) * MatrixMax3d::Identity(x.size(), x.size()); + double norm_x = x.norm(); + return ddsinc_over_x2_minus_dsinc_over_x3(norm_x) * x * x.transpose() + + dsinc_over_x(norm_x) * MatrixMax3d::Identity(x.size(), x.size()); } } // namespace ipc diff --git a/src/ipc/utils/sinc.hpp b/src/ipc/utils/sinc.hpp index 61cf86ebb..cde862a29 100644 --- a/src/ipc/utils/sinc.hpp +++ b/src/ipc/utils/sinc.hpp @@ -7,7 +7,7 @@ namespace ipc { /// @brief Compute the sinc function: \f$ \frac{\sin(x)}{x} \f$ /// @param x The value for which to compute the sinc function /// @return The value of sinc(x) -double sinc(const double& x); +double sinc(const double x); #ifdef IPC_TOOLKIT_WITH_FILIB @@ -22,7 +22,7 @@ filib::Interval sinc(const filib::Interval& x); /// @tparam T The type of the elements of the vector /// @param x The vector for which to compute the sinc of the norm /// @return The value of \f$\operatorname{sinc}(\|x\|)\f$ -template T sinc_normx(const VectorMax3& x) +template T sinc_norm_x(Eigen::ConstRef> x) { if constexpr (std::is_same_v) { return sinc(x.norm()); @@ -34,11 +34,11 @@ template T sinc_normx(const VectorMax3& x) /// @brief Compute the gradient of the sinc of the norm of a vector /// @param x The vector for which to compute the gradient of the sinc of the norm /// @return The gradient of the sinc of the norm of the vector -VectorMax3d sinc_normx_grad(const VectorMax3d& x); +VectorMax3d sinc_norm_x_grad(Eigen::ConstRef x); /// @brief Compute the Hessian of the sinc of the norm of a vector /// @param x The vector for which to compute the Hessian of the sinc of the norm /// @return The Hessian of the sinc of the norm of the vector -MatrixMax3d sinc_normx_hess(const VectorMax3d& x); +MatrixMax3d sinc_norm_x_hess(Eigen::ConstRef x); } // namespace ipc \ No newline at end of file diff --git a/tests/src/tests/dynamics/CMakeLists.txt b/tests/src/tests/dynamics/CMakeLists.txt index fd6c3e17c..e43145b22 100644 --- a/tests/src/tests/dynamics/CMakeLists.txt +++ b/tests/src/tests/dynamics/CMakeLists.txt @@ -2,4 +2,5 @@ # Subfolders ################################################################################ -add_subdirectory(affine) \ No newline at end of file +add_subdirectory(affine) +add_subdirectory(rigid) \ No newline at end of file diff --git a/tests/src/tests/dynamics/rigid/CMakeLists.txt b/tests/src/tests/dynamics/rigid/CMakeLists.txt new file mode 100644 index 000000000..a10e42a7d --- /dev/null +++ b/tests/src/tests/dynamics/rigid/CMakeLists.txt @@ -0,0 +1,11 @@ +set(SOURCES + test_mass.cpp + test_pose.cpp +) + +source_group(TREE "${CMAKE_CURRENT_SOURCE_DIR}" PREFIX "Source Files" FILES ${SOURCES}) +target_sources(ipc_toolkit_tests PRIVATE ${SOURCES}) + +################################################################################ +# Subfolders +################################################################################ \ No newline at end of file diff --git a/tests/src/tests/dynamics/rigid/test_mass.cpp b/tests/src/tests/dynamics/rigid/test_mass.cpp new file mode 100644 index 000000000..775e6a1c4 --- /dev/null +++ b/tests/src/tests/dynamics/rigid/test_mass.cpp @@ -0,0 +1,42 @@ +// Test the mass utilities. + +#include +#include +#include + +#include + +#include + +using namespace ipc; +using namespace ipc::rigid; + +TEST_CASE("Mass properties", "[rigid][mass]") +{ + Eigen::MatrixXd V; + Eigen::MatrixXi E, F; + REQUIRE(tests::load_mesh("cube.ply", V, E, F)); + + const double L = 0.5, W = 1.0, H = 2.0; + + V.col(0).array() *= L; + V.col(1).array() *= W; + V.col(2).array() *= H; + + double total_mass; + VectorMax3d center; + MatrixMax3d inertia; + compute_mass_properties(V, F, total_mass, center, inertia); + + const double m = L * W * H; // unit mass per voxel + const double Ixx = m * (W * W + H * H) / 12.0; + const double Iyy = m * (L * L + H * H) / 12.0; + const double Izz = m * (L * L + W * W) / 12.0; + Eigen::Matrix3d expected_inertia = + Eigen::DiagonalMatrix(Ixx, Iyy, Izz); + + CAPTURE(total_mass, center, inertia); + REQUIRE(total_mass == Catch::Approx(m).margin(1e-6)); + REQUIRE(center.isApprox(Eigen::Vector3d(0.0, 0.0, 0.0), 1e-6)); + REQUIRE(inertia.isApprox(expected_inertia, 1e-6)); +} \ No newline at end of file diff --git a/tests/src/tests/dynamics/rigid/test_pose.cpp b/tests/src/tests/dynamics/rigid/test_pose.cpp new file mode 100644 index 000000000..69a2fbabf --- /dev/null +++ b/tests/src/tests/dynamics/rigid/test_pose.cpp @@ -0,0 +1,89 @@ +#include + +#include + +#include +#include + +using namespace ipc::rigid; + +TEST_CASE("SE(3) ↦ SO(3)", "[rigid][pose]") +{ + double angle; + Eigen::Vector3d axis; + + SECTION("zero") + { + angle = 0; + axis = Eigen::Vector3d::Random(); + } + SECTION("small angle") + { + angle = GENERATE(take(100, random(0.0, 1e-6))); + axis = Eigen::Vector3d::Random(); + } + SECTION("random") + { + angle = GENERATE(take(100, random(0.0, 2 * igl::PI))); + axis = Eigen::Vector3d::Random(); + } + axis.normalize(); + + const Eigen::Matrix3d R_expected = + Eigen::AngleAxisd(angle, axis).toRotationMatrix(); + + const Eigen::Vector3d theta = angle * axis; + const Eigen::Matrix3d R_actual = rotation_vector_to_matrix(theta); + + CHECK((R_actual - R_expected).norm() == Catch::Approx(0).margin(1e-12)); +} + +TEST_CASE("∇²(SE(3) ↦ SO(3))", "[!benchmark][rigid][pose]") +{ + Eigen::Vector3d theta = Eigen::Vector3d::Random(); + + BENCHMARK("Compute R") { return rotation_vector_to_matrix(theta); }; + + BENCHMARK("Compute ∇R") + { + return rotation_vector_to_matrix_jacobian(theta); + }; + + BENCHMARK("Compute ∇²R") + { + return rotation_vector_to_matrix_hessian(theta); + }; +} + +#if false +TEST_CASE("Interval SE(3) ↦ SO(3)", "[!benchmark][physics][pose]") +{ + using namespace ipc::rigid; + double angle; + Eigen::Vector3d axis; + + SECTION("zero") + { + angle = 0; + axis = Eigen::Vector3d::Random(); + } + SECTION("random") + { + angle = GENERATE(take(1, random(0.0, 2 * igl::PI))); + axis = Eigen::Vector3d::Random(); + } + axis.normalize(); + + Pose p = Pose::Zero(3); + p.rotation = angle * axis; + BENCHMARK("Double SE(3) ↦ SO(3)") + { + Eigen::Matrix3d R = p.construct_rotation_matrix(); + }; + Pose pI = p.cast(); + BENCHMARK("Interval SE(3) ↦ SO(3)") + { + Matrix3I R = pI.construct_rotation_matrix(); + }; +} +#endif diff --git a/tests/src/tests/utils/test_sinc.cpp b/tests/src/tests/utils/test_sinc.cpp index 8a3e7c622..56cca5afa 100644 --- a/tests/src/tests/utils/test_sinc.cpp +++ b/tests/src/tests/utils/test_sinc.cpp @@ -88,7 +88,7 @@ TEST_CASE("Interval sinc with looser bounds", "[sinc][interval]") } } -TEST_CASE("Interval sinc_normx", "[sinc][interval]") +TEST_CASE("Interval sinc_norm_x", "[sinc][interval]") { VectorMax3 x = VectorMax3::Zero(3); filib::Interval expected_y; @@ -114,7 +114,7 @@ TEST_CASE("Interval sinc_normx", "[sinc][interval]") expected_y = filib::Interval(0, 1); } - filib::Interval y = sinc_normx(x); + filib::Interval y = sinc_norm_x(x); CAPTURE(y.INF, y.SUP, expected_y.INF, expected_y.SUP); CHECK(expected_y.INF == Catch::Approx(y.INF).margin(1e-8)); CHECK(expected_y.SUP == Catch::Approx(y.SUP).margin(1e-8)); @@ -129,9 +129,9 @@ TEST_CASE("∇sinc(||x||)", "[sinc][vector][diff]") x(index) = sign * val; Eigen::VectorXd fgrad(3); - fd::finite_gradient(x, sinc_normx, fgrad); + fd::finite_gradient(x, sinc_norm_x, fgrad); - Eigen::Vector3d grad = sinc_normx_grad(x); + Eigen::Vector3d grad = sinc_norm_x_grad(x); CHECK(fd::compare_gradient(grad, fgrad)); } @@ -144,8 +144,8 @@ TEST_CASE("∇²sinc(||x||)", "[sinc][vector][diff]") x(index) = sign * val; Eigen::MatrixXd fhess(3, 3); - fd::finite_hessian(x, sinc_normx, fhess); + fd::finite_hessian(x, sinc_norm_x, fhess); - Eigen::Matrix3d hess = sinc_normx_hess(x); + Eigen::Matrix3d hess = sinc_norm_x_hess(x); CHECK(fd::compare_hessian(hess, fhess)); } \ No newline at end of file From caf4d50d248e5b585d83681e026cbd4be33b83aa Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Sat, 14 Jun 2025 13:19:34 -0400 Subject: [PATCH 06/24] Fix rotation_vector_to_matrix derivatives --- src/ipc/dynamics/rigid/inertial_term.cpp | 10 +- src/ipc/dynamics/rigid/pose.cpp | 104 +++++++++++----- src/ipc/dynamics/rigid/pose.hpp | 2 +- tests/src/tests/dynamics/rigid/test_pose.cpp | 120 ++++++++++++++++++- 4 files changed, 196 insertions(+), 40 deletions(-) diff --git a/src/ipc/dynamics/rigid/inertial_term.cpp b/src/ipc/dynamics/rigid/inertial_term.cpp index f46f06e87..3492dbcf7 100644 --- a/src/ipc/dynamics/rigid/inertial_term.cpp +++ b/src/ipc/dynamics/rigid/inertial_term.cpp @@ -168,11 +168,11 @@ VectorMax6d InertialTerm::gradient( const Eigen::Matrix3d Q = rotation_vector_to_matrix(x.tail<3>()); // ∂f​/∂xₖ = ∑ᵢ∑ⱼ ∂E/∂Qᵢⱼ ∂Qᵢⱼ/∂xₖ - const Eigen::Matrix dQ_dx = + const Eigen::Matrix dQ_dx = rotation_vector_to_matrix_jacobian(x.tail<3>()); const Eigen::Vector dE_dQ = ((Q - Q_hat) * body.J()).reshaped(); - grad.tail<3>() = dQ_dx * dE_dQ; + grad.tail<3>() = dQ_dx.transpose() * dE_dQ; } else { assert(q_hat.size() == 2); assert(x.size() == 3); @@ -206,7 +206,7 @@ MatrixMax6d InertialTerm::hessian( { if (q_hat.size() == 3) { const Eigen::Matrix3d Q = rotation_vector_to_matrix(x.tail<3>()); - const Eigen::Matrix dQ_dx = + const Eigen::Matrix dQ_dx = rotation_vector_to_matrix_jacobian(x.tail<3>()); const Eigen::Matrix d2Q_dx2 = rotation_vector_to_matrix_hessian(x.tail<3>()); @@ -222,8 +222,8 @@ MatrixMax6d InertialTerm::hessian( d2E_dQ2.diagonal().segment<3>(6).array() = body.J()(2, 2); // (3x3) = (3×9)(9×9)(9x3) + mat((9x9)(9x1)) - hess.bottomRightCorner<3, 3>() = dQ_dx * d2E_dQ2 * dQ_dx.transpose() - + (d2Q_dx2 * dE_dQ).reshaped(3, 3); + hess.bottomRightCorner<3, 3>() = dQ_dx.transpose() * d2E_dQ2 * dQ_dx + + (d2Q_dx2.transpose() * dE_dQ).reshaped(3, 3); } else { assert(q_hat.size() == 2); assert(x.size() == 3); diff --git a/src/ipc/dynamics/rigid/pose.cpp b/src/ipc/dynamics/rigid/pose.cpp index 1df8b30ba..d1e90cdc0 100644 --- a/src/ipc/dynamics/rigid/pose.cpp +++ b/src/ipc/dynamics/rigid/pose.cpp @@ -29,33 +29,37 @@ rotation_vector_to_matrix(Eigen::ConstRef theta) return R; } -Eigen::Matrix +Eigen::Matrix rotation_vector_to_matrix_jacobian(Eigen::ConstRef theta) { assert(theta.size() == 3); // Only valid for 3D rotation vectors const double s = sinc_norm_x(theta); - const double sh = sinc_norm_x(theta / 2); + const double sh = sinc_norm_x((theta / 2).eval()); const double sh_sq = sh * sh; const Eigen::Matrix3d K = cross_product_matrix(theta); const Eigen::Vector3d ds = sinc_norm_x_grad(theta); - const Eigen::Vector3d dsh = sinc_norm_x_grad(theta / 2); + const Eigen::Vector3d dsh = 0.5 * sinc_norm_x_grad((theta / 2).eval()); std::array dK; dK[0] << 0, 0, 0, 0, 0, -1, 0, 1, 0; dK[1] << 0, 0, 1, 0, 0, 0, -1, 0, 0; dK[2] << 0, -1, 0, 1, 0, 0, 0, 0, 0; - Eigen::Matrix3d s_plus_sh_sq_K = sh_sq * K; - s_plus_sh_sq_K.diagonal().array() += s; + std::array s_dK; + s_dK[0] << 0, 0, 0, 0, 0, -s, 0, s, 0; + s_dK[1] << 0, 0, s, 0, 0, 0, -s, 0, 0; + s_dK[2] << 0, -s, 0, s, 0, 0, 0, 0, 0; const Eigen::Matrix3d sh_K2 = sh * K * K; - Eigen::Matrix dR; + Eigen::Matrix dR; for (int i = 0; i < 3; ++i) { - dR.row(i) = - (ds(i) * K + s_plus_sh_sq_K * dK[i] + dsh(i) * sh_K2).reshaped(); + const Eigen::Matrix3d K_dKi = K * dK[i]; + dR.col(i) = (ds(i) * K + s_dK[i] + dsh(i) * sh_K2 + + (0.5 * sh_sq) * (K_dKi + K_dKi.transpose())) + .reshaped(); } return dR; @@ -71,9 +75,9 @@ rotation_vector_to_matrix_hessian(Eigen::ConstRef theta) const Eigen::Matrix3d K = cross_product_matrix(theta); const Eigen::Vector3d ds = sinc_norm_x_grad(theta); - const Eigen::Vector3d dsh = sinc_norm_x_grad(theta / 2); + const Eigen::Vector3d dsh = 0.5 * sinc_norm_x_grad(theta / 2); const Eigen::Matrix3d d2s = sinc_norm_x_hess(theta); - const Eigen::Matrix3d d2sh = sinc_norm_x_hess(theta / 2); + const Eigen::Matrix3d d2sh = 0.25 * sinc_norm_x_hess(theta / 2); std::array dK; dK[0] << 0, 0, 0, 0, 0, -1, 0, 1, 0; @@ -82,39 +86,66 @@ rotation_vector_to_matrix_hessian(Eigen::ConstRef theta) // NOTE: ∂²K/∂θ² = 0 - const Eigen::Matrix3d sh_K2 = sh * K * K; + const Eigen::Matrix3d K2 = K * K; - Eigen::Matrix d2R; - for (int i = 0; i < 3; ++i) { - const Eigen::Matrix3d two_sh_K_dKi = 2 * sh * K * dK[i]; + std::array K_dK; + K_dK[0] = K * dK[0]; + K_dK[1] = K * dK[1]; + K_dK[2] = K * dK[2]; - for (int j = 0; j < 3; ++j) { - d2R.row(i * 3 + j) = + std::array K_dK_plus_K_dK_T; + K_dK_plus_K_dK_T[0] = K_dK[0] + K_dK[0].transpose(); + K_dK_plus_K_dK_T[1] = K_dK[1] + K_dK[1].transpose(); + K_dK_plus_K_dK_T[2] = K_dK[2] + K_dK[2].transpose(); + + // Flatten in column-major order + Eigen::Matrix d2R; + for (int j = 0; j < 3; ++j) { + const Eigen::Matrix3d K_dKj = K * dK[j]; + const Eigen::Matrix3d K_dKj_plus_K_dKj_T = K_dKj + K_dKj.transpose(); + for (int i = j; i < 3; ++i) { + const Eigen::Matrix3d dKj_dKi = dK[j] * dK[i]; + d2R.col(j * 3 + i) = (d2s(i, j) * K + ds(i) * dK[j] + ds(j) * dK[i] - + dsh(j) * two_sh_K_dKi + sh_sq * dK[j] * dK[i] - + d2sh(i, j) * sh_K2 + 2 * dsh(i) * K * dK[j]) + + (d2sh(i, j) * sh + dsh(i) * dsh(j)) * K2 + + (sh * dsh(i)) * K_dK_plus_K_dK_T[j] + + (sh * dsh(j)) * K_dK_plus_K_dK_T[i] + + (0.5 * sh_sq) * (dKj_dKi + dKj_dKi.transpose())) .reshaped(); + if (i != j) { + d2R.col(i * 3 + j) = d2R.col(j * 3 + i); // Symmetric + } } } return d2R; } -Eigen::Vector3d rotation_matrix_to_vector(Eigen::Matrix3d R) +Eigen::Vector3d rotation_matrix_to_vector(Eigen::ConstRef R) { +#if false + // Eigen does this conversion by going from SO(3) -> Quaternion -> 𝔰𝔬(3), + // but we can do it directly from SO(3) -> 𝔰𝔬(3). In random benchmarking, + // this is about 2x faster than the Eigen implementation. However, this + // might be less accurate for some edge cases as it requires a sin and acos + // where as Eigen's approach uses atan2 and sqrt. + + assert(R.isUnitary(1e-9)); // Ensure it's a rotation matrix + Eigen::Vector3d r; - assert(R.trace() >= -1 && R.trace() <= 3); // Ensure acos is valid - double theta = acos((R.trace() - 1) / 2.0); // θ ∈ [0, π) + // θ ∈ [0, π) + double theta = acos((std::clamp(R.trace(), -1.0, 3.0) - 1) / 2.0); + assert(std::isfinite(theta)); // R = I + sin(θ)K + (1 - cos(θ))K² where K is the cross-product matrix of // r/θ - if (theta < 1e-6) { + if (theta <= 1e-5) { // θ ≈ 0 ⟹ R ≈ I + θK // No need to divide by sin(θ)≈θ since the off-diagonals are ±rᵢθ r.x() = (R(2, 1) - R(1, 2)) / 2; r.y() = (R(0, 2) - R(2, 0)) / 2; r.z() = (R(1, 0) - R(0, 1)) / 2; // Θ is already part of the off-diagonal elements, so no need to scale - } else if (theta > M_PI - 1e-6) { + } else if (theta >= M_PI - 1e-5) { // θ ≈ π ⟹ R ≈ I - (θ - π)K + 2K² // Ensure positive for sqrt assert(R(0, 0) > -1); @@ -123,17 +154,32 @@ Eigen::Vector3d rotation_matrix_to_vector(Eigen::Matrix3d R) // R₀,₁ = 2r₀r₁+(θ-π)r₂, R₀,₂ = 2r₀r₂-(θ-π)r₁, R₁,₂ = 2r₁r₂+(θ-π)r₀ r.y() = R(0, 1) / (2 * r.x()); r.z() = R(0, 2) / (2 * r.x()); - r.normalize(); // Normalize just in case + // r.normalize(); // Normalize just in case r.array() *= theta; // Scale by the angle } else { - r.x() = (R(2, 1) - R(1, 2)) / (2 * sin(theta)); - r.y() = (R(0, 2) - R(2, 0)) / (2 * sin(theta)); - r.z() = (R(1, 0) - R(0, 1)) / (2 * sin(theta)); - r.normalize(); // Normalize just in case - r *= theta; // Scale by the angle + const double sin_theta = sin(theta); + r.x() = (R(2, 1) - R(1, 2)) / (2 * sin_theta); + r.y() = (R(0, 2) - R(2, 0)) / (2 * sin_theta); + r.z() = (R(1, 0) - R(0, 1)) / (2 * sin_theta); + // r.normalize(); // Normalize just in case + r *= theta; // Scale by the angle } + assert(r.array().isFinite().all()); + +#ifndef NDEBUG + Eigen::AngleAxisd eigen(R); + assert( + (eigen.angle() * eigen.axis()).isApprox(r, 1e-4) + || (theta >= M_PI - 1e-5 // Eigen can flip the sign of angles close to π + && (-eigen.angle() * eigen.axis()).isApprox(r, 1e-4))); +#endif return r; +#else + // Use Eigen's built-in function for conversion + Eigen::AngleAxisd angle_axis(R); + return angle_axis.angle() * angle_axis.axis(); +#endif } template struct Pose; diff --git a/src/ipc/dynamics/rigid/pose.hpp b/src/ipc/dynamics/rigid/pose.hpp index 97464935b..9966c30ad 100644 --- a/src/ipc/dynamics/rigid/pose.hpp +++ b/src/ipc/dynamics/rigid/pose.hpp @@ -16,7 +16,7 @@ rotation_vector_to_matrix(Eigen::ConstRef theta); /// @brief Compute the Jacobian of the rotation matrix with respect to the rotation vector. /// @param theta The rotation vector /// @return The Jacobian matrix -Eigen::Matrix +Eigen::Matrix rotation_vector_to_matrix_jacobian(Eigen::ConstRef theta); /// @brief Compute the Hessian of the rotation matrix with respect to the rotation vector. diff --git a/tests/src/tests/dynamics/rigid/test_pose.cpp b/tests/src/tests/dynamics/rigid/test_pose.cpp index 69a2fbabf..4a150198f 100644 --- a/tests/src/tests/dynamics/rigid/test_pose.cpp +++ b/tests/src/tests/dynamics/rigid/test_pose.cpp @@ -4,10 +4,13 @@ #include #include +#include + +#include using namespace ipc::rigid; -TEST_CASE("SE(3) ↦ SO(3)", "[rigid][pose]") +TEST_CASE("𝔰𝔬(3) ↦ SO(3)", "[rigid][pose]") { double angle; Eigen::Vector3d axis; @@ -38,7 +41,7 @@ TEST_CASE("SE(3) ↦ SO(3)", "[rigid][pose]") CHECK((R_actual - R_expected).norm() == Catch::Approx(0).margin(1e-12)); } -TEST_CASE("∇²(SE(3) ↦ SO(3))", "[!benchmark][rigid][pose]") +TEST_CASE("∇²(𝔰𝔬(3) ↦ SO(3))", "[!benchmark][rigid][pose]") { Eigen::Vector3d theta = Eigen::Vector3d::Random(); @@ -56,7 +59,7 @@ TEST_CASE("∇²(SE(3) ↦ SO(3))", "[!benchmark][rigid][pose]") } #if false -TEST_CASE("Interval SE(3) ↦ SO(3)", "[!benchmark][physics][pose]") +TEST_CASE("Interval 𝔰𝔬(3) ↦ SO(3)", "[!benchmark][physics][pose]") { using namespace ipc::rigid; double angle; @@ -76,14 +79,121 @@ TEST_CASE("Interval SE(3) ↦ SO(3)", "[!benchmark][physics][pose]") Pose p = Pose::Zero(3); p.rotation = angle * axis; - BENCHMARK("Double SE(3) ↦ SO(3)") + BENCHMARK("Double 𝔰𝔬(3) ↦ SO(3)") { Eigen::Matrix3d R = p.construct_rotation_matrix(); }; Pose pI = p.cast(); - BENCHMARK("Interval SE(3) ↦ SO(3)") + BENCHMARK("Interval 𝔰𝔬(3) ↦ SO(3)") { Matrix3I R = pI.construct_rotation_matrix(); }; } #endif + +TEST_CASE("𝔰𝔬(3) ↦ SO(3) derivatives", "[rigid][pose]") +{ + double angle; + Eigen::Vector3d axis; + + SECTION("zero") + { + angle = 0; + axis = Eigen::Vector3d::Random(); + } + SECTION("small angle") + { + angle = GENERATE(take(100, random(0.0, 1e-6))); + axis = Eigen::Vector3d::Random(); + } + SECTION("random") + { + angle = GENERATE(take(100, random(0.0, 2 * igl::PI))); + axis = Eigen::Vector3d::Random(); + } + axis.normalize(); + + Eigen::Vector3d theta = angle * axis; + + { + Eigen::Matrix J_analytic = + rotation_vector_to_matrix_jacobian(theta); + + auto f = [&](const Eigen::VectorXd& x) -> Eigen::VectorXd { + return rotation_vector_to_matrix(x).reshaped(); + }; + + Eigen::MatrixXd J_numerical; + fd::finite_jacobian(theta, f, J_numerical); + + CHECK(fd::compare_jacobian(J_analytic, J_numerical)); + + // std::cout << "J_analytic:\n" << J_analytic << "\n\n"; + // std::cout << "J_numerical:\n" << J_numerical << "\n\n"; + } + + { + Eigen::Matrix H_analytic = + rotation_vector_to_matrix_hessian(theta); + + auto f = [&](const Eigen::VectorXd& x) -> Eigen::MatrixXd { + return rotation_vector_to_matrix_jacobian(x); + }; + + Eigen::MatrixXd H_numerical; + fd::finite_jacobian(theta, f, H_numerical); + + CHECK(fd::compare_jacobian(H_analytic, H_numerical)); + + // std::cout << "H_analytic:\n" << H_analytic << "\n\n"; + // std::cout << "H_numerical:\n" << H_numerical << "\n\n"; + } +} + +TEST_CASE("SO(3) ↦ 𝔰𝔬(3)", "[rigid][pose]") +{ + double angle = GENERATE( + 0.0, 1e-8, 1e-6, igl::PI / 4, igl::PI / 2, igl::PI * 0.75, + igl::PI - 1e-4, igl::PI - 1e-6, igl::PI - 1e-8, igl::PI, igl::PI + 1e-8, + igl::PI + 1e-6, igl::PI + 1e-4, igl::PI * 1.5, igl::PI * 2); + Eigen::Vector3d axis = Eigen::Vector3d::Random().normalized(); + + Eigen::Vector3d theta_expected = angle * axis; + + Eigen::Matrix3d R = rotation_vector_to_matrix(theta_expected); + + Eigen::Vector3d theta = rotation_matrix_to_vector(R); + + Eigen::AngleAxisd angle_axis(R); + theta_expected = angle_axis.angle() * angle_axis.axis(); + + CHECK( + (theta.isApprox(theta_expected, 1e-4) + || theta.isApprox(angle * axis, 1e-4))); + + // std::cout << "input axis: " << axis.transpose() << "\n" + // << "input angle: " << angle << " (" << angle - igl::PI << ")" + // << "\n" + // << "expected axis: " << angle_axis.axis().transpose() << "\n" + // << "expected angle: " << angle_axis.angle() << "\n" + // << "axis: " << theta.normalized().transpose() << "\n" + // << "angle: " << theta.norm() << "\n" + // << "\n" + // << std::endl; +} + +TEST_CASE("Benchmark SO(3) ↦ 𝔰𝔬(3)", "[!benchmark][rigid][pose]") +{ + Eigen::Matrix3d R = Eigen::Matrix3d::Random(); + Eigen::JacobiSVD svd( + R, Eigen::ComputeFullU | Eigen::ComputeFullV); + R = svd.matrixU() * svd.matrixV().transpose(); // closest rotation matrix + + BENCHMARK("Mine") { return rotation_matrix_to_vector(R); }; + + BENCHMARK("Eigen") + { + Eigen::AngleAxisd angle_axis(R); + return angle_axis.angle() * angle_axis.axis(); + }; +} \ No newline at end of file From 59edd853e9bb38d7e9e760934bcd5c3325c7c7bc Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Tue, 17 Jun 2025 00:40:08 -0400 Subject: [PATCH 07/24] Test RigidBody class - Updated finite-diff package from version 1.0.1 to 1.0.3 in CMake configuration. - Remove template from Pose. - Modified RigidBody and related classes to use the updated Pose structure. - Added unit tests for RigidBody construction and transformations. --- cmake/recipes/finite_diff.cmake | 2 +- src/ipc/dynamics/rigid/inertial_term.cpp | 5 +- src/ipc/dynamics/rigid/pose.cpp | 3 - src/ipc/dynamics/rigid/pose.hpp | 55 ++++++++--- src/ipc/dynamics/rigid/rigid_bodies.cpp | 2 +- src/ipc/dynamics/rigid/rigid_body.cpp | 4 +- src/ipc/dynamics/rigid/rigid_body.hpp | 6 +- tests/src/tests/dynamics/rigid/CMakeLists.txt | 1 + .../tests/dynamics/rigid/test_rigid_body.cpp | 98 +++++++++++++++++++ 9 files changed, 150 insertions(+), 26 deletions(-) create mode 100644 tests/src/tests/dynamics/rigid/test_rigid_body.cpp diff --git a/cmake/recipes/finite_diff.cmake b/cmake/recipes/finite_diff.cmake index 35661aff8..bf2ee6ab6 100644 --- a/cmake/recipes/finite_diff.cmake +++ b/cmake/recipes/finite_diff.cmake @@ -7,7 +7,7 @@ endif() message(STATUS "Third-party: creating target 'finitediff::finitediff'") include(CPM) -CPMAddPackage("gh:zfergus/finite-diff@1.0.1") +CPMAddPackage("gh:zfergus/finite-diff@1.0.3") # Folder name for IDE set_target_properties(finitediff_finitediff PROPERTIES FOLDER "ThirdParty") \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/inertial_term.cpp b/src/ipc/dynamics/rigid/inertial_term.cpp index 3492dbcf7..f68e058b1 100644 --- a/src/ipc/dynamics/rigid/inertial_term.cpp +++ b/src/ipc/dynamics/rigid/inertial_term.cpp @@ -45,8 +45,7 @@ void InertialTerm::update(const RigidBodies& bodies) // Add external torques to the predicted pose if (!torque.isZero()) { if (torque.size() == 3) { - const RotationMatrix& Q = - time_integrator->pose(i).rotation; + const auto& Q = time_integrator->pose(i).rotation; // Transform the world space torque into body space const Eigen::Matrix3d Tau = Q.transpose() * cross_product_matrix(torque); @@ -131,7 +130,7 @@ double InertialTerm::operator()( const Eigen::Matrix3d Q = rotation_vector_to_matrix(x.tail<3>()); // ½tr((Q - Q̂) J (Q - Q̂)ᵀ) - const RotationMatrix dQ = Q - Q_hat; + const Eigen::Matrix3d dQ = Q - Q_hat; energy += 0.5 * (dQ * body.J() * dQ.transpose()).trace(); } else { assert(q_hat.size() == 2); diff --git a/src/ipc/dynamics/rigid/pose.cpp b/src/ipc/dynamics/rigid/pose.cpp index d1e90cdc0..55797b88a 100644 --- a/src/ipc/dynamics/rigid/pose.cpp +++ b/src/ipc/dynamics/rigid/pose.cpp @@ -182,7 +182,4 @@ Eigen::Vector3d rotation_matrix_to_vector(Eigen::ConstRef R) #endif } -template struct Pose; -template struct Pose; - } // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/pose.hpp b/src/ipc/dynamics/rigid/pose.hpp index 9966c30ad..20c7af958 100644 --- a/src/ipc/dynamics/rigid/pose.hpp +++ b/src/ipc/dynamics/rigid/pose.hpp @@ -4,9 +4,6 @@ namespace ipc::rigid { -using RotationVector = VectorMax3d; -using RotationMatrix = MatrixMax3d; - /// @brief Convert from a 3D rotation vector to a rotation matrix. /// @param theta The rotation vector /// @return The rotation matrix corresponding to the rotation vector @@ -37,19 +34,54 @@ Eigen::Vector3d rotation_matrix_to_vector(Eigen::ConstRef R); // ---------------------------------------------------------------------------- -template struct Pose { +struct Pose { // Position of the rigid body VectorMax3d position; // Rotation of the rigid body (rotation vector for 3D, angle for 1D) - RotationType rotation; + VectorMax3d rotation; + + Pose() = default; + + Pose( + Eigen::ConstRef _position, + Eigen::ConstRef _rotation) + : position(_position) + , rotation(_rotation) + { + } - RotationMatrix rotation_matrix() const + static Pose Zero(const int dim) { - if constexpr (std::is_same_v) { - return rotation_vector_to_matrix(rotation); + return Pose(VectorMax3d::Zero(dim), VectorMax3d::Zero(dim)); + } + + MatrixMax3d rotation_matrix() const + { + return rotation_vector_to_matrix(rotation); + } + + Eigen::MatrixXd transform_vertices(Eigen::ConstRef V) const + { + // Compute: R(θ) V + p + // transpose because x is row-ordered + return (V * rotation_matrix().transpose()).rowwise() + + position.transpose(); + } + + friend Pose operator*(const Pose& a, const Pose& b) + { + Pose c; + + c.position = a.position + b.position; + + if (c.position.size() == 2) { + c.rotation = a.rotation + b.rotation; } else { - return rotation; + MatrixMax3d R = a.rotation_matrix() * b.rotation_matrix(); + c.rotation = rotation_matrix_to_vector(R); } + + return c; } }; @@ -75,16 +107,13 @@ struct AffinePose { return angle; } else { // For 3D, return the rotation vector - // Eigen::AngleAxisd r = - // Eigen::AngleAxisd(Eigen::Matrix3d(rotation)); return r.angle() * - // r.axis(); return rotation_matrix_to_vector(rotation); } } /// @brief Set the rotation matrix from a rotation vector or angle. /// @param theta The rotation vector (3D) or angle (2D). - void set_rotation_vector(Eigen::ConstRef theta) + void set_rotation_vector(Eigen::ConstRef theta) { assert(theta.size() == 1 || theta.size() == 3); if (theta.size() == 1) { diff --git a/src/ipc/dynamics/rigid/rigid_bodies.cpp b/src/ipc/dynamics/rigid/rigid_bodies.cpp index d86a9f316..548a85b23 100644 --- a/src/ipc/dynamics/rigid/rigid_bodies.cpp +++ b/src/ipc/dynamics/rigid/rigid_bodies.cpp @@ -61,7 +61,7 @@ RigidBodies::RigidBodies( assert(body_face_starts.back() == num_faces()); bodies.reserve(body_vertex_starts.size() - 1); - Pose<> initial_pose; + Pose initial_pose = Pose::Zero(dim()); for (size_t i = 0; i < body_vertex_starts.size() - 1; ++i) { bodies.emplace_back( m_rest_positions.middleRows( diff --git a/src/ipc/dynamics/rigid/rigid_body.cpp b/src/ipc/dynamics/rigid/rigid_body.cpp index 3ebcfa55d..37e55f667 100644 --- a/src/ipc/dynamics/rigid/rigid_body.cpp +++ b/src/ipc/dynamics/rigid/rigid_body.cpp @@ -10,7 +10,7 @@ namespace { Eigen::Ref vertices, Eigen::ConstRef edges, Eigen::ConstRef faces, - Pose<>& pose) + Pose& pose) { // compute the center of mass several times to get more accurate for (int i = 0; i < 10; i++) { @@ -47,7 +47,7 @@ RigidBody::RigidBody( Eigen::Ref vertices, Eigen::ConstRef edges, Eigen::ConstRef faces, - Pose<>& initial_pose) + Pose& initial_pose) { const double density = 1.0; // Default density diff --git a/src/ipc/dynamics/rigid/rigid_body.hpp b/src/ipc/dynamics/rigid/rigid_body.hpp index 02d6ca241..409e06dff 100644 --- a/src/ipc/dynamics/rigid/rigid_body.hpp +++ b/src/ipc/dynamics/rigid/rigid_body.hpp @@ -12,12 +12,12 @@ class RigidBody { Eigen::Ref vertices, Eigen::ConstRef edges, Eigen::ConstRef faces, - Pose<>& initial_pose); + Pose& initial_pose); double mass() const { return m_mass; } const VectorMax3d& moment_of_inertia() const { return m_moment_of_inertia; } const Eigen::Matrix3d& J() const { return m_J; } - const Pose<>& external_force() const { return m_external_force; } + const Pose& external_force() const { return m_external_force; } private: /// @brief Total mass of the rigid body @@ -29,7 +29,7 @@ class RigidBody { Eigen::Matrix3d m_J; /// @brief External force and torque applied to the rigid body - Pose<> m_external_force; + Pose m_external_force; }; } // namespace ipc::rigid \ No newline at end of file diff --git a/tests/src/tests/dynamics/rigid/CMakeLists.txt b/tests/src/tests/dynamics/rigid/CMakeLists.txt index a10e42a7d..6be684c36 100644 --- a/tests/src/tests/dynamics/rigid/CMakeLists.txt +++ b/tests/src/tests/dynamics/rigid/CMakeLists.txt @@ -1,6 +1,7 @@ set(SOURCES test_mass.cpp test_pose.cpp + test_rigid_body.cpp ) source_group(TREE "${CMAKE_CURRENT_SOURCE_DIR}" PREFIX "Source Files" FILES ${SOURCES}) diff --git a/tests/src/tests/dynamics/rigid/test_rigid_body.cpp b/tests/src/tests/dynamics/rigid/test_rigid_body.cpp new file mode 100644 index 000000000..d1bf6fbda --- /dev/null +++ b/tests/src/tests/dynamics/rigid/test_rigid_body.cpp @@ -0,0 +1,98 @@ +// Test the mass utilities. + +#include +#include +#include + +#include + +#include + +#include + +using namespace ipc; +using namespace ipc::rigid; + +TEST_CASE("Rigid body construction", "[rigid]") +{ + Eigen::MatrixXd V; + Eigen::MatrixXi E, F; + REQUIRE(tests::load_mesh("cube.ply", V, E, F)); + + const double L = 0.5, W = 1.0, H = 2.0; + V.col(0).array() *= L; + V.col(1).array() *= W; + V.col(2).array() *= H; + + Pose input_pose = Pose::Zero(3); + Pose initial_pose = Pose::Zero(3); + + SECTION("No modification") { } + SECTION("Input pose") + { + input_pose.position = Eigen::Vector3d(1.0, 2.0, 3.0); + input_pose.rotation = Eigen::Vector3d(0.1, 0.2, 0.3); + } + SECTION("Initial pose") + { + initial_pose.position = Eigen::Vector3d(1.0, 2.0, 3.0); + initial_pose.rotation = Eigen::Vector3d(0.1, 0.2, 0.3); + } + SECTION("Input and initial pose") + { + input_pose.position = Eigen::Vector3d(1.0, 2.0, 3.0); + input_pose.rotation = Eigen::Vector3d(0.1, 0.2, 0.3); + initial_pose.position = Eigen::Vector3d(4.0, 5.0, 6.0); + initial_pose.rotation = Eigen::Vector3d(0.4, 0.5, 0.6); + } + + Eigen::MatrixXd modified_V = input_pose.transform_vertices(V); + + const double m = L * W * H; // unit mass per voxel + const double Ixx = m * (W * W + H * H) / 12.0; + const double Iyy = m * (L * L + H * H) / 12.0; + const double Izz = m * (L * L + W * W) / 12.0; + Eigen::Vector3d I(Ixx, Iyy, Izz); + // Sort: + if (I(0) > I(1)) { + std::swap(I(0), I(1)); + } + if (I(1) > I(2)) { + std::swap(I(1), I(2)); + } + if (I(0) > I(1)) { + std::swap(I(0), I(1)); + } + + Pose modified_pose = initial_pose; + const RigidBody body(modified_V, E, F, modified_pose); + REQUIRE(modified_V.rows() == V.rows()); + REQUIRE(modified_V.cols() == V.cols()); + + { + CAPTURE(body.moment_of_inertia().transpose(), I.transpose()); + REQUIRE(body.mass() == Catch::Approx(m).margin(1e-8)); + REQUIRE(body.moment_of_inertia().isApprox(I)); + } + + // The modified position should be the initial position plus the input + // position + { + CAPTURE( + input_pose.position.transpose(), initial_pose.position.transpose(), + modified_pose.position.transpose()); + REQUIRE(modified_pose.position.isApprox( + input_pose.position + initial_pose.position)); + } + + // The modified rotation should be the initial rotation times the input + // rotation + { + const Eigen::MatrixXd _V = modified_pose.transform_vertices(modified_V); + + const Eigen::MatrixXd expected_V = + (initial_pose * input_pose).transform_vertices(V); + + CHECK(_V.isApprox(expected_V, 1e-8)); + } +} \ No newline at end of file From 5cbe3d469c70c981f8e2931fc08ee8b31eb47f9b Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Wed, 18 Jun 2025 01:34:18 -0400 Subject: [PATCH 08/24] Test InertialTerm --- src/ipc/dynamics/rigid/inertial_term.cpp | 50 ++++-- src/ipc/dynamics/rigid/inertial_term.hpp | 22 ++- tests/src/tests/dynamics/rigid/CMakeLists.txt | 1 + .../dynamics/rigid/test_inertial_term.cpp | 158 ++++++++++++++++++ 4 files changed, 212 insertions(+), 19 deletions(-) create mode 100644 tests/src/tests/dynamics/rigid/test_inertial_term.cpp diff --git a/src/ipc/dynamics/rigid/inertial_term.cpp b/src/ipc/dynamics/rigid/inertial_term.cpp index f68e058b1..ca1cb7771 100644 --- a/src/ipc/dynamics/rigid/inertial_term.cpp +++ b/src/ipc/dynamics/rigid/inertial_term.cpp @@ -20,25 +20,25 @@ namespace { void InertialTerm::update(const RigidBodies& bodies) { // Update the predicted poses based on the current time integrator state - predicted_poses = time_integrator->predicted_pose(); + m_predicted_poses = time_integrator->predicted_pose(); // Gravity in the y-direction const double dt_sq = time_integrator->dt * time_integrator->dt; tbb::parallel_for( - tbb::blocked_range(0, predicted_poses.size()), + tbb::blocked_range(0, m_predicted_poses.size()), [&](const tbb::blocked_range& r) { for (size_t i = r.begin(); i < r.end(); ++i) { // Add gravity to the predicted pose // TODO: Make this configurable - predicted_poses[i].position.y() += dt_sq * -9.81; + m_predicted_poses[i].position.y() += dt_sq * -9.81; const auto& force = bodies[i].external_force().position; const auto& torque = bodies[i].external_force().rotation; // Add external forces to the predicted pose if (!force.isZero()) { - predicted_poses[i].position += + m_predicted_poses[i].position += dt_sq * force / bodies[i].mass(); } @@ -49,11 +49,11 @@ void InertialTerm::update(const RigidBodies& bodies) // Transform the world space torque into body space const Eigen::Matrix3d Tau = Q.transpose() * cross_product_matrix(torque); - predicted_poses[i].rotation += + m_predicted_poses[i].rotation += dt_sq * bodies[i].J().inverse() * Tau; } else { assert(torque.size() == 1); - predicted_poses[i].rotation(0) += dt_sq * torque(0) + m_predicted_poses[i].rotation(0) += dt_sq * torque(0) / bodies[i].moment_of_inertia()(0); } } @@ -66,13 +66,15 @@ void InertialTerm::update(const RigidBodies& bodies) double InertialTerm::operator()( const RigidBodies& bodies, Eigen::ConstRef x) { + assert(predicted_poses().size() == bodies.num_bodies()); + const int ndof = x.size() / bodies.num_bodies(); double energy = 0.0; for (size_t i = 0; i < bodies.num_bodies(); ++i) { energy += operator()( - bodies[i], x.segment(i * ndof, ndof), predicted_poses[i].position, - predicted_poses[i].rotation); + bodies[i], x.segment(i * ndof, ndof), predicted_poses()[i].position, + predicted_poses()[i].rotation); } return energy; } @@ -80,27 +82,33 @@ double InertialTerm::operator()( Eigen::VectorXd InertialTerm::gradient( const RigidBodies& bodies, Eigen::ConstRef x) { + assert(predicted_poses().size() == bodies.num_bodies()); + const int ndof = x.size() / bodies.num_bodies(); Eigen::VectorXd grad = Eigen::VectorXd::Zero(x.size()); for (size_t i = 0; i < bodies.num_bodies(); ++i) { grad.segment(i * ndof, ndof) = gradient( - bodies[i], x.segment(i * ndof, ndof), predicted_poses[i].position, - predicted_poses[i].rotation); + bodies[i], x.segment(i * ndof, ndof), predicted_poses()[i].position, + predicted_poses()[i].rotation); } return grad; } Eigen::MatrixXd InertialTerm::hessian( - const RigidBodies& bodies, Eigen::ConstRef x) + const RigidBodies& bodies, + Eigen::ConstRef x, + const PSDProjectionMethod project_hessian_to_psd) { + assert(predicted_poses().size() == bodies.num_bodies()); + const int ndof = x.size() / bodies.num_bodies(); Eigen::MatrixXd hess(x.size(), x.size()); for (size_t i = 0; i < bodies.num_bodies(); ++i) { hess.block(i * ndof, i * ndof, ndof, ndof) = hessian( - bodies[i], x.segment(i * ndof, ndof), predicted_poses[i].position, - predicted_poses[i].rotation); + bodies[i], x.segment(i * ndof, ndof), predicted_poses()[i].position, + predicted_poses()[i].rotation, project_hessian_to_psd); } return hess; } @@ -188,7 +196,8 @@ MatrixMax6d InertialTerm::hessian( const RigidBody& body, Eigen::ConstRef x, Eigen::ConstRef q_hat, - Eigen::ConstRef Q_hat) const + Eigen::ConstRef Q_hat, + const PSDProjectionMethod project_hessian_to_psd) const { MatrixMax6d hess = MatrixMax6d::Zero(x.size(), x.size()); @@ -198,6 +207,9 @@ MatrixMax6d InertialTerm::hessian( // m (q - q̂) hess.topLeftCorner(q_hat.size(), q_hat.size()).diagonal().array() = body.mass(); + + // NOTE: No need to project to PSD here, as the Hessian is already + // positive semi-definite (diagonal matrix with positive entries). } // Rotational energy @@ -221,14 +233,22 @@ MatrixMax6d InertialTerm::hessian( d2E_dQ2.diagonal().segment<3>(6).array() = body.J()(2, 2); // (3x3) = (3×9)(9×9)(9x3) + mat((9x9)(9x1)) - hess.bottomRightCorner<3, 3>() = dQ_dx.transpose() * d2E_dQ2 * dQ_dx + Eigen::Matrix3d hess_rotation = dQ_dx.transpose() * d2E_dQ2 * dQ_dx + (d2Q_dx2.transpose() * dE_dQ).reshaped(3, 3); + + hess.bottomRightCorner<3, 3>() = + project_to_psd(hess_rotation, project_hessian_to_psd); + } else { assert(q_hat.size() == 2); assert(x.size() == 3); assert(Q_hat.size() == 1); // I (θ - θ̂) hess(2, 2) = body.moment_of_inertia()(0); + + // NOTE: No need to project to PSD here, as the Hessian is already + // positive semi-definite (single positive value). + assert(body.moment_of_inertia()(0) > 0.0); } } diff --git a/src/ipc/dynamics/rigid/inertial_term.hpp b/src/ipc/dynamics/rigid/inertial_term.hpp index d75df53d4..326e3859a 100644 --- a/src/ipc/dynamics/rigid/inertial_term.hpp +++ b/src/ipc/dynamics/rigid/inertial_term.hpp @@ -38,8 +38,11 @@ class InertialTerm { /// @param bodies The collection of rigid bodies. /// @param x The DOFs of the rigid bodies, where the first 3 entries are the positions and the last 3 entries are the rotations. /// @return The Hessian of the total energy of the rigid bodies. - Eigen::MatrixXd - hessian(const RigidBodies& bodies, Eigen::ConstRef x); + Eigen::MatrixXd hessian( + const RigidBodies& bodies, + Eigen::ConstRef x, + const PSDProjectionMethod project_hessian_to_psd = + PSDProjectionMethod::NONE); // ---- Per-body functions ------------------------------------------------- @@ -75,13 +78,24 @@ class InertialTerm { const RigidBody& body, Eigen::ConstRef x, Eigen::ConstRef q_hat, - Eigen::ConstRef Q_hat) const; + Eigen::ConstRef Q_hat, + const PSDProjectionMethod project_hessian_to_psd = + PSDProjectionMethod::NONE) const; + + // ---- Predicted poses ---------------------------------------------------- + + /// @brief Get the predicted poses of the rigid bodies. + /// @return A vector of predicted poses for each rigid body. + const std::vector& predicted_poses() const + { + return m_predicted_poses; + } private: const std::shared_ptr time_integrator; /// Cached predicted poses for the rigid body - std::vector predicted_poses; + std::vector m_predicted_poses; }; } // namespace ipc::rigid \ No newline at end of file diff --git a/tests/src/tests/dynamics/rigid/CMakeLists.txt b/tests/src/tests/dynamics/rigid/CMakeLists.txt index 6be684c36..1a7ecae80 100644 --- a/tests/src/tests/dynamics/rigid/CMakeLists.txt +++ b/tests/src/tests/dynamics/rigid/CMakeLists.txt @@ -1,4 +1,5 @@ set(SOURCES + test_inertial_term.cpp test_mass.cpp test_pose.cpp test_rigid_body.cpp diff --git a/tests/src/tests/dynamics/rigid/test_inertial_term.cpp b/tests/src/tests/dynamics/rigid/test_inertial_term.cpp new file mode 100644 index 000000000..39abaf66b --- /dev/null +++ b/tests/src/tests/dynamics/rigid/test_inertial_term.cpp @@ -0,0 +1,158 @@ +// src/ipc/dynamics/rigid/test_inertial_term.hpp +#include + +#include + +#include + +#include +#include +#include + +#include + +using namespace ipc; +using namespace ipc::rigid; + +namespace { + +// Helper function to generate a RigidBody +RigidBodies rigid_bodies() +{ + Eigen::MatrixXd V; + Eigen::MatrixXi E, F; + REQUIRE(tests::load_mesh("cube.ply", V, E, F)); + + const double L = 0.5, W = 1.0, H = 2.0; + V.col(0).array() *= L; + V.col(1).array() *= W; + V.col(2).array() *= H; + + return RigidBodies::build_from_meshes({ V }, { E }, { F }); +} + +std::shared_ptr time_integrator(const RigidBodies& bodies) +{ + Eigen::VectorXd x = Eigen::VectorXd::Zero(12 * bodies.num_bodies()); + for (int i = 0; i < bodies.num_bodies(); ++i) { + x.segment<9>(i * 12 + 3) = Eigen::Matrix3d::Identity().reshaped(); + } + const Eigen::VectorXd v = Eigen::VectorXd::Random(12 * bodies.num_bodies()); + const Eigen::VectorXd a = Eigen::VectorXd::Random(12 * bodies.num_bodies()); + const double dt = 0.01; // Arbitrary time step + + return std::make_shared( + x, v, a, dt, bodies.num_bodies()); +} + +} // namespace + +TEST_CASE( + "InertialTerm energy and derivative", + "[inertial_term][energy][gradient][hessian]") +{ + RigidBodies bodies = rigid_bodies(); + InertialTerm inertial_term(time_integrator(bodies)); + + VectorMax6d x = VectorMax6d::Random(6); + VectorMax3d q_hat = VectorMax3d::Random(3); + MatrixMax3d Q_hat = MatrixMax3d::Random(3, 3); + + double energy = inertial_term(bodies[0], x, q_hat, Q_hat); + + // Since we don't have a ground truth, we can only check if the energy is a + // valid number + CHECK(std::isfinite(energy)); + + VectorMax6d analytical_gradient; + MatrixMax6d analytical_hessian; + + { + analytical_gradient = + inertial_term.gradient(bodies[0], x, q_hat, Q_hat); + + // Numerical gradient calculation + auto f = [&](const Eigen::VectorXd& x_arg) { + return inertial_term( + bodies[0], x_arg, q_hat, + Q_hat); // Capture other variables by value + }; + Eigen::VectorXd numerical_gradient; + fd::finite_gradient(x, f, numerical_gradient); + + // std::cout << "Analytical Gradient:\n" << analytical_gradient << + // "\n\n"; std::cout << "Numerical Gradient:\n" << numerical_gradient << + // "\n\n"; + + CHECK(fd::compare_gradient(analytical_gradient, numerical_gradient)); + } + + { + analytical_hessian = inertial_term.hessian(bodies[0], x, q_hat, Q_hat); + + // Numerical hessian calculation + auto f = [&](const Eigen::VectorXd& x_arg) { + return inertial_term.gradient(bodies[0], x_arg, q_hat, Q_hat); + }; + Eigen::MatrixXd numerical_hessian; + fd::finite_jacobian(x, f, numerical_hessian); + + // std::cout << "Analytical Hessian:\n" << analytical_hessian << "\n\n"; + // std::cout << "Numerical Hessian:\n" << numerical_hessian << "\n\n"; + + // Compare analytical and numerical Hessians + CHECK(fd::compare_jacobian(analytical_hessian, numerical_hessian)); + } + + // Newton direction + { + Eigen::VectorXd newton_direction = + -analytical_hessian.ldlt().solve(analytical_gradient); + // std::cout << "Newton Direction:\n" << newton_direction << "\n\n"; + + if (newton_direction.dot(analytical_gradient) < 0.0) { + CHECK(true); + } else { + analytical_hessian = inertial_term.hessian( + bodies[0], x, q_hat, Q_hat, PSDProjectionMethod::ABS); + + newton_direction = + -analytical_hessian.ldlt().solve(analytical_gradient); + + // std::cout << "Newton Direction:\n" << newton_direction << "\n\n"; + + CHECK(newton_direction.dot(analytical_gradient) < 0.0); + } + } +} + +TEST_CASE( + "InertialTerm total energy and derivatives", + "[inertial_term][total_energy][total_gradient][total_hessian]") +{ + RigidBodies bodies = rigid_bodies(); + InertialTerm inertial_term(time_integrator(bodies)); + inertial_term.update(bodies); + + VectorMax6d x = VectorMax6d::Random(6); + + CHECK( + inertial_term(bodies, x) + == inertial_term( + bodies[0], x, inertial_term.predicted_poses()[0].position, + inertial_term.predicted_poses()[0].rotation)); + + CHECK( + fd::compare_gradient( + inertial_term.gradient(bodies, x), + inertial_term.gradient( + bodies[0], x, inertial_term.predicted_poses()[0].position, + inertial_term.predicted_poses()[0].rotation))); + + CHECK( + inertial_term.hessian(bodies, x, PSDProjectionMethod::ABS) + == inertial_term.hessian( + bodies[0], x, inertial_term.predicted_poses()[0].position, + inertial_term.predicted_poses()[0].rotation, + PSDProjectionMethod::ABS)); +} \ No newline at end of file From dbad1ba4b383faad639ebec014b9b859b852f3e1 Mon Sep 17 00:00:00 2001 From: zachferguson Date: Wed, 18 Jun 2025 14:00:39 -0400 Subject: [PATCH 09/24] Add density parameter to mass calculations; store R0 in RB --- src/ipc/dynamics/rigid/inertial_term.cpp | 6 +- src/ipc/dynamics/rigid/mass.cpp | 61 +++++++++++---- src/ipc/dynamics/rigid/mass.hpp | 1 + src/ipc/dynamics/rigid/rigid_bodies.cpp | 15 ++-- src/ipc/dynamics/rigid/rigid_bodies.hpp | 10 ++- src/ipc/dynamics/rigid/rigid_body.cpp | 78 ++++++------------- src/ipc/dynamics/rigid/rigid_body.hpp | 13 +++- .../dynamics/rigid/test_inertial_term.cpp | 6 +- tests/src/tests/dynamics/rigid/test_mass.cpp | 6 +- .../tests/dynamics/rigid/test_rigid_body.cpp | 6 +- 10 files changed, 110 insertions(+), 92 deletions(-) diff --git a/src/ipc/dynamics/rigid/inertial_term.cpp b/src/ipc/dynamics/rigid/inertial_term.cpp index ca1cb7771..dcc8b5fd5 100644 --- a/src/ipc/dynamics/rigid/inertial_term.cpp +++ b/src/ipc/dynamics/rigid/inertial_term.cpp @@ -228,9 +228,9 @@ MatrixMax6d InertialTerm::hessian( // ∂²E/∂Q² = J ⊗ I Eigen::Matrix d2E_dQ2 = Eigen::Matrix::Zero(); - d2E_dQ2.diagonal().segment<3>(0).array() = body.J()(0, 0); - d2E_dQ2.diagonal().segment<3>(3).array() = body.J()(1, 1); - d2E_dQ2.diagonal().segment<3>(6).array() = body.J()(2, 2); + d2E_dQ2.diagonal().segment<3>(0).array() = body.J().diagonal()(0); + d2E_dQ2.diagonal().segment<3>(3).array() = body.J().diagonal()(1); + d2E_dQ2.diagonal().segment<3>(6).array() = body.J().diagonal()(2); // (3x3) = (3×9)(9×9)(9x3) + mat((9x9)(9x1)) Eigen::Matrix3d hess_rotation = dQ_dx.transpose() * d2E_dQ2 * dQ_dx diff --git a/src/ipc/dynamics/rigid/mass.cpp b/src/ipc/dynamics/rigid/mass.cpp index c76b60ed6..096a38515 100644 --- a/src/ipc/dynamics/rigid/mass.cpp +++ b/src/ipc/dynamics/rigid/mass.cpp @@ -11,6 +11,7 @@ namespace { void compute_mass_properties_2D( const Eigen::MatrixXd& vertices, const Eigen::MatrixXi& edges, + const double density, double& total_mass, VectorMax3d& center, MatrixMax3d& inertia) @@ -28,6 +29,12 @@ namespace { // ∑ mᵢ rᵢ ⋅ rᵢ inertia.resize(1, 1); inertia(0) = (mass_matrix * vertices.rowwise().squaredNorm()).sum(); + + // Total mass above is the paremeter length of the edges, so we need to + // multiply by the density to get the total mass in the correct units. + total_mass *= density; + // Same for the inertia. + inertia *= density; } // Based on ChTriangleMeshConnected.cpp::ComputeMassProperties from Chrono: @@ -40,6 +47,7 @@ namespace { bool compute_mass_properties_3D( const Eigen::MatrixXd& vertices, const Eigen::MatrixXi& faces, + const double density, double& total_mass, VectorMax3d& center, MatrixMax3d& inertia) @@ -109,16 +117,20 @@ namespace { integral[9] += N.z() * (v0.x() * g0z + v1.x() * g1z + v2.x() * g2z); } - integral[0] /= 6; - integral[1] /= 24; - integral[2] /= 24; - integral[3] /= 24; - integral[4] /= 60; - integral[5] /= 60; - integral[6] /= 60; - integral[7] /= 120; - integral[8] /= 120; - integral[9] /= 120; + constexpr double inv_6 = 1.0 / 6.0; + constexpr double inv_24 = 1.0 / 24.0; + constexpr double inv_60 = 1.0 / 60.0; + constexpr double inv_120 = 1.0 / 120.0; + integral[0] *= inv_6; + integral[1] *= inv_24; + integral[2] *= inv_24; + integral[3] *= inv_24; + integral[4] *= inv_60; + integral[5] *= inv_60; + integral[6] *= inv_60; + integral[7] *= inv_120; + integral[8] *= inv_120; + integral[9] *= inv_120; // total_mass total_mass = integral[0]; @@ -158,11 +170,18 @@ namespace { inertia(2, 2) -= total_mass * (center.x() * center.x() + center.y() * center.y()); + // Total mass above is the volume of the mesh, so we need to multiply by + // the density to get the total mass in the correct units. + total_mass *= density; + // Same for the inertia. + inertia *= density; + return true; } void compute_mass_properties_point_cloud( const Eigen::MatrixXd& vertices, + const double density, double& total_mass, VectorMax3d& center, MatrixMax3d& inertia) @@ -185,6 +204,12 @@ namespace { inertia(1, 0) = inertia(0, 1); inertia(2, 0) = inertia(0, 2); inertia(2, 1) = inertia(1, 2); + + // Total mass above is the number of points, so we need to multiply by + // the density to get the total mass in the correct units. + total_mass *= density; + // Same for the inertia. + inertia *= density; } } // namespace @@ -192,21 +217,27 @@ namespace { void compute_mass_properties( const Eigen::MatrixXd& vertices, const Eigen::MatrixXi& facets, + const double density, double& total_mass, VectorMax3d& center, MatrixMax3d& inertia) { + assert(facets.cols() <= 3); if (vertices.cols() == 2) { compute_mass_properties_2D( - vertices, facets, total_mass, center, inertia); + vertices, facets, density, total_mass, center, inertia); } if (facets.size() == 0 || facets.cols() != 3) { compute_mass_properties_point_cloud( - vertices, total_mass, center, inertia); - } else if (!compute_mass_properties_3D( - vertices, facets, total_mass, center, inertia)) { + vertices, density, total_mass, center, inertia); + } else if ( + facets.rows() < 4 // Not enough faces to form a closed mesh + || !compute_mass_properties_3D( + vertices, facets, density, total_mass, center, inertia)) { + // If the mesh is not closed, we fall back to treating it as a point + // cloud. compute_mass_properties_point_cloud( - vertices, total_mass, center, inertia); + vertices, density, total_mass, center, inertia); } } diff --git a/src/ipc/dynamics/rigid/mass.hpp b/src/ipc/dynamics/rigid/mass.hpp index e022276f3..6e43f2f56 100644 --- a/src/ipc/dynamics/rigid/mass.hpp +++ b/src/ipc/dynamics/rigid/mass.hpp @@ -16,6 +16,7 @@ namespace ipc::rigid { void compute_mass_properties( const Eigen::MatrixXd& vertices, const Eigen::MatrixXi& facets, + const double density, double& total_mass, VectorMax3d& center_of_mass, MatrixMax3d& moment_of_inertia); diff --git a/src/ipc/dynamics/rigid/rigid_bodies.cpp b/src/ipc/dynamics/rigid/rigid_bodies.cpp index 548a85b23..e31e010cd 100644 --- a/src/ipc/dynamics/rigid/rigid_bodies.cpp +++ b/src/ipc/dynamics/rigid/rigid_bodies.cpp @@ -5,10 +5,12 @@ namespace ipc::rigid { RigidBodies RigidBodies::build_from_meshes( const std::vector& rest_positions, const std::vector& edges, - const std::vector& faces) + const std::vector& faces, + const std::vector& densities) { assert(rest_positions.size() == edges.size()); assert(rest_positions.size() == faces.size()); + assert(rest_positions.size() == densities.size()); size_t num_vertices = 0, num_edges = 0, num_faces = 0; std::vector body_vertex_starts(rest_positions.size() + 1); @@ -39,16 +41,17 @@ RigidBodies RigidBodies::build_from_meshes( return RigidBodies( concat_rest_positions, concat_edges, concat_faces, body_vertex_starts, - body_edge_starts, body_face_starts); + body_edge_starts, body_face_starts, densities); } RigidBodies::RigidBodies( Eigen::ConstRef _rest_positions, Eigen::ConstRef _edges, Eigen::ConstRef _faces, - std::vector _body_vertex_starts, - std::vector _body_edge_starts, - std::vector _body_face_starts) + const std::vector& _body_vertex_starts, + const std::vector& _body_edge_starts, + const std::vector& _body_face_starts, + const std::vector& densities) : CollisionMesh(_rest_positions, _edges, _faces) , body_vertex_starts(std::move(_body_vertex_starts)) , body_edge_starts(std::move(_body_edge_starts)) @@ -73,7 +76,7 @@ RigidBodies::RigidBodies( faces().middleRows( body_face_starts[i], body_face_starts[i + 1] - body_face_starts[i]), - initial_pose); + densities[i], initial_pose); } } diff --git a/src/ipc/dynamics/rigid/rigid_bodies.hpp b/src/ipc/dynamics/rigid/rigid_bodies.hpp index fae80f417..a5d3dce35 100644 --- a/src/ipc/dynamics/rigid/rigid_bodies.hpp +++ b/src/ipc/dynamics/rigid/rigid_bodies.hpp @@ -12,14 +12,16 @@ class RigidBodies : public CollisionMesh { Eigen::ConstRef rest_positions, Eigen::ConstRef edges, Eigen::ConstRef faces, - std::vector body_vertex_starts, - std::vector body_edge_starts, - std::vector body_face_starts); + const std::vector& body_vertex_starts, + const std::vector& body_edge_starts, + const std::vector& body_face_starts, + const std::vector& densities); static RigidBodies build_from_meshes( const std::vector& rest_positions, const std::vector& edges, - const std::vector& faces); + const std::vector& faces, + const std::vector& densities); size_t num_bodies() const { return bodies.size(); } diff --git a/src/ipc/dynamics/rigid/rigid_body.cpp b/src/ipc/dynamics/rigid/rigid_body.cpp index 37e55f667..a05394074 100644 --- a/src/ipc/dynamics/rigid/rigid_body.cpp +++ b/src/ipc/dynamics/rigid/rigid_body.cpp @@ -20,6 +20,7 @@ namespace { compute_mass_properties( vertices, (vertices.cols() == 2 || faces.size() == 0) ? edges : faces, + 1.0, // density (1.0 because we only want the center of mass) mass, com, inertia); vertices.rowwise() -= com.transpose(); pose.position += com; @@ -47,10 +48,9 @@ RigidBody::RigidBody( Eigen::Ref vertices, Eigen::ConstRef edges, Eigen::ConstRef faces, + const double density, Pose& initial_pose) { - const double density = 1.0; // Default density - assert(vertices.size() > 0); assert(edges.size() == 0 || edges.cols() == 2); assert(faces.size() == 0 || faces.cols() == 3); @@ -59,21 +59,18 @@ RigidBody::RigidBody( assert(dim == 2 || dim == 3); // 1. Center the vertices, so the mass properties are computed correctly + // TODO: This should not be necessary. Determine why the mass properties + // are not computed correctly without centering the vertices. center_vertices(vertices, edges, faces, initial_pose); // 2. Compute the mass properties VectorMax3d center_of_mass; MatrixMax3d inertia_tensor; compute_mass_properties( - vertices, (dim == 2 || faces.size() == 0) ? edges : faces, m_mass, - center_of_mass, inertia_tensor); - - // 3. The mass above is actually volume, so we need to scale it by the - // density to get the mass. - m_mass *= density; + vertices, (dim == 2 || faces.size() == 0) ? edges : faces, density, + m_mass, center_of_mass, inertia_tensor); - // 4. Convert the inertia tensor to the principal axes moments of inertia - MatrixMax3d R0; + // 3. Convert the inertia tensor to the principal axes moments of inertia if (dim == 3) { // This computation is taken from ProjectChrono: https://bit.ly/2RpbTl1 // The eigen values of the inertia tensor are the principal moments @@ -91,8 +88,9 @@ RigidBody::RigidBody( solver.compute(inertia_tensor); assert(solver.info() == Eigen::Success); - // Multiply by density to get the units of moment of inertia - m_moment_of_inertia = density * solver.eigenvalues(); + // The principal moments of inertia are the eigenvalues of the inertia + // tensor. + m_moment_of_inertia = solver.eigenvalues(); if ((m_moment_of_inertia.array() < 0).any()) { logger().warn( "Negative moments of inertia ({}), inverting.", @@ -103,13 +101,13 @@ RigidBody::RigidBody( // The rotation from the principal inertial frame to the input world // frame. - R0 = solver.eigenvectors(); + m_R0 = solver.eigenvectors(); // Ensure that we have an orientation preserving transform - if (R0.determinant() < 0.0) { - R0.col(0) *= -1.0; + if (m_R0.determinant() < 0.0) { + m_R0.col(0) *= -1.0; } - assert(R0.isUnitary(1e-9)); + assert(m_R0.isUnitary(1e-9)); // TODO: Enable this code // int num_rot_dof_fixed = @@ -118,26 +116,24 @@ RigidBody::RigidBody( // // Convert moment of inertia to world coordinates // // https://physics.stackexchange.com/a/268812 // moment_of_inertia = -I.diagonal().array() + I.diagonal().sum(); - // R0.setIdentity(); + // m_R0.setIdentity(); // } else if (num_rot_dof_fixed == 1) { // spdlog::warn( // "Rigid body dynamics with two rotational DoF has " // "not been tested thoroughly."); // } - // TODO: this code below need to be updated - // Remove the initial rotation from the rest vertices - vertices = vertices * R0; + vertices = vertices * m_R0; // Store the initial rotation in the pose (R = RᵢR₀) Eigen::AngleAxisd r = Eigen::AngleAxisd( - Eigen::Matrix3d(initial_pose.rotation_matrix() * R0)); + Eigen::Matrix3d(initial_pose.rotation_matrix() * m_R0)); initial_pose.rotation = r.angle() * r.axis(); // TODO: // ω = R₀ᵀω₀ (ω₀ expressed in body coordinates) - // this->velocity.rotation = R0.transpose() * this->velocity.rotation; + // this->velocity.rotation = m_R0.transpose() * this->velocity.rotation; // Eigen::Matrix3d Q_t0 = this->pose.construct_rotation_matrix(); // this->Qdot = Q_t0 * Hat(this->velocity.rotation); @@ -147,16 +143,16 @@ RigidBody::RigidBody( } else { // For 2D, the inertia tensor is a scalar, and the rotation vector // is a single value. - m_moment_of_inertia = density * inertia_tensor.diagonal(); + m_moment_of_inertia = inertia_tensor.diagonal(); // The input orientation is already in the inertial frame - R0 = Eigen::Matrix::Identity(); + m_R0 = Eigen::Matrix2d::Identity(); } m_J = compute_J(m_moment_of_inertia); // Zero out the velocity and forces of fixed dof - // this->velocity.zero_dof(is_dof_fixed, R0); - // this->force.zero_dof(is_dof_fixed, R0); + // this->velocity.zero_dof(is_dof_fixed, m_R0); + // this->force.zero_dof(is_dof_fixed, m_R0); // Compute and construct some useful constants // mass_matrix.resize(ndof()); @@ -180,34 +176,4 @@ RigidBody::RigidBody( // init_bvh(); } -// Eigen::MatrixXd -// RigidBody::transform_vertices(const Eigen::MatrixXd& rest_positions) const -// { -// // Compute: R(θ) x̄ + p -// // transpose because x is row-ordered -// const int dim = rest_positions.cols(); - -// assert( -// (dim == 2 && rotation_vector.size() == 1) -// || (dim == 3 && rotation_vector.size() == 3)); - -// // Convert the rotation vector to a rotation matrix -// MatrixMax3d R(dim, dim); -// if (dim == 2) { -// const double theta = rotation_vector(0); -// R << sin(theta), -cos(theta), cos(theta), sin(theta); -// } else { -// assert(dim == 3); -// const double sinc_angle = sinc_norm_x(rotation_vector); -// const double sinc_half_angle = -// sinc_norm_x((rotation_vector / 2).eval()); -// const Eigen::Matrix3d K = cross_product_matrix(rotation_vector); -// const Eigen::Matrix3d K2 = K * K; -// R = sinc_angle * K + 0.5 * sinc_half_angle * sinc_half_angle * K2; -// R.diagonal().array() += 1.0; -// } - -// return (rest_positions * R.transpose()).rowwise() + position.transpose(); -// } - } // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/rigid_body.hpp b/src/ipc/dynamics/rigid/rigid_body.hpp index 409e06dff..54e8c2184 100644 --- a/src/ipc/dynamics/rigid/rigid_body.hpp +++ b/src/ipc/dynamics/rigid/rigid_body.hpp @@ -12,11 +12,13 @@ class RigidBody { Eigen::Ref vertices, Eigen::ConstRef edges, Eigen::ConstRef faces, + const double density, Pose& initial_pose); double mass() const { return m_mass; } const VectorMax3d& moment_of_inertia() const { return m_moment_of_inertia; } - const Eigen::Matrix3d& J() const { return m_J; } + const Eigen::DiagonalMatrix& J() const { return m_J; } + const MatrixMax3d& R0() const { return m_R0; } const Pose& external_force() const { return m_external_force; } private: @@ -26,7 +28,14 @@ class RigidBody { /// @brief Moment of inertia measured with respect to the principal axes VectorMax3d m_moment_of_inertia; - Eigen::Matrix3d m_J; + Eigen::DiagonalMatrix m_J; + + /// @brief Rotation matrix from the principal axes to the world frame + /// This also stored in initial_pose.rotation upon construction. + /// This is useful for converting to and from input world coordinates. + /// @note Maybe this should be a rotation vector instead? + /// @note Maybe we should store position as well? + MatrixMax3d m_R0; /// @brief External force and torque applied to the rigid body Pose m_external_force; diff --git a/tests/src/tests/dynamics/rigid/test_inertial_term.cpp b/tests/src/tests/dynamics/rigid/test_inertial_term.cpp index 39abaf66b..c487fd4a6 100644 --- a/tests/src/tests/dynamics/rigid/test_inertial_term.cpp +++ b/tests/src/tests/dynamics/rigid/test_inertial_term.cpp @@ -28,7 +28,9 @@ RigidBodies rigid_bodies() V.col(1).array() *= W; V.col(2).array() *= H; - return RigidBodies::build_from_meshes({ V }, { E }, { F }); + const double density = GENERATE(1.0, 2.0, 3.0); + + return RigidBodies::build_from_meshes({ V }, { E }, { F }, { density }); } std::shared_ptr time_integrator(const RigidBodies& bodies) @@ -128,7 +130,7 @@ TEST_CASE( TEST_CASE( "InertialTerm total energy and derivatives", - "[inertial_term][total_energy][total_gradient][total_hessian]") + "[rigid][inertial_term][total_energy][total_gradient][total_hessian]") { RigidBodies bodies = rigid_bodies(); InertialTerm inertial_term(time_integrator(bodies)); diff --git a/tests/src/tests/dynamics/rigid/test_mass.cpp b/tests/src/tests/dynamics/rigid/test_mass.cpp index 775e6a1c4..9565d9fad 100644 --- a/tests/src/tests/dynamics/rigid/test_mass.cpp +++ b/tests/src/tests/dynamics/rigid/test_mass.cpp @@ -23,12 +23,14 @@ TEST_CASE("Mass properties", "[rigid][mass]") V.col(1).array() *= W; V.col(2).array() *= H; + const double density = GENERATE(1.0, 2.0, 3.0); + double total_mass; VectorMax3d center; MatrixMax3d inertia; - compute_mass_properties(V, F, total_mass, center, inertia); + compute_mass_properties(V, F, density, total_mass, center, inertia); - const double m = L * W * H; // unit mass per voxel + const double m = density * L * W * H; const double Ixx = m * (W * W + H * H) / 12.0; const double Iyy = m * (L * L + H * H) / 12.0; const double Izz = m * (L * L + W * W) / 12.0; diff --git a/tests/src/tests/dynamics/rigid/test_rigid_body.cpp b/tests/src/tests/dynamics/rigid/test_rigid_body.cpp index d1bf6fbda..f20f29fbd 100644 --- a/tests/src/tests/dynamics/rigid/test_rigid_body.cpp +++ b/tests/src/tests/dynamics/rigid/test_rigid_body.cpp @@ -24,6 +24,8 @@ TEST_CASE("Rigid body construction", "[rigid]") V.col(1).array() *= W; V.col(2).array() *= H; + const double density = GENERATE(1.0, 2.0, 3.0); + Pose input_pose = Pose::Zero(3); Pose initial_pose = Pose::Zero(3); @@ -48,7 +50,7 @@ TEST_CASE("Rigid body construction", "[rigid]") Eigen::MatrixXd modified_V = input_pose.transform_vertices(V); - const double m = L * W * H; // unit mass per voxel + const double m = density * L * W * H; // unit mass per voxel const double Ixx = m * (W * W + H * H) / 12.0; const double Iyy = m * (L * L + H * H) / 12.0; const double Izz = m * (L * L + W * W) / 12.0; @@ -65,7 +67,7 @@ TEST_CASE("Rigid body construction", "[rigid]") } Pose modified_pose = initial_pose; - const RigidBody body(modified_V, E, F, modified_pose); + const RigidBody body(modified_V, E, F, density, modified_pose); REQUIRE(modified_V.rows() == V.rows()); REQUIRE(modified_V.cols() == V.cols()); From 5d7512a562ca396ab429cf9b1167d0d5ad6d5305 Mon Sep 17 00:00:00 2001 From: zachferguson Date: Wed, 18 Jun 2025 17:57:02 -0400 Subject: [PATCH 10/24] Add (empty) simulator loop --- python/src/CMakeLists.txt | 1 + python/src/bindings.cpp | 3 + python/src/bindings.hpp | 1 + python/src/collision_mesh.cpp | 3 +- python/src/dynamics/CMakeLists.txt | 9 ++ python/src/dynamics/bindings.hpp | 1 + python/src/dynamics/rigid/CMakeLists.txt | 5 + python/src/dynamics/rigid/bindings.hpp | 6 ++ python/src/dynamics/rigid/simulator.cpp | 86 ++++++++++++++++ python/tests/rigid_example.py | 46 +++++++++ src/ipc/dynamics/rigid/CMakeLists.txt | 1 + src/ipc/dynamics/rigid/rigid_bodies.cpp | 18 +++- src/ipc/dynamics/rigid/rigid_bodies.hpp | 19 +++- src/ipc/dynamics/rigid/simulator.cpp | 97 +++++++++++++++++++ src/ipc/dynamics/rigid/simulator.hpp | 71 ++++++++++++++ .../dynamics/rigid/test_inertial_term.cpp | 6 +- 16 files changed, 364 insertions(+), 9 deletions(-) create mode 100644 python/src/dynamics/CMakeLists.txt create mode 100644 python/src/dynamics/bindings.hpp create mode 100644 python/src/dynamics/rigid/CMakeLists.txt create mode 100644 python/src/dynamics/rigid/bindings.hpp create mode 100644 python/src/dynamics/rigid/simulator.cpp create mode 100644 python/tests/rigid_example.py create mode 100644 src/ipc/dynamics/rigid/simulator.cpp create mode 100644 src/ipc/dynamics/rigid/simulator.hpp diff --git a/python/src/CMakeLists.txt b/python/src/CMakeLists.txt index 5e8499e29..c7644f8b3 100644 --- a/python/src/CMakeLists.txt +++ b/python/src/CMakeLists.txt @@ -17,6 +17,7 @@ add_subdirectory(candidates) add_subdirectory(ccd) add_subdirectory(collisions) add_subdirectory(distance) +add_subdirectory(dynamics) add_subdirectory(friction) add_subdirectory(implicits) add_subdirectory(potentials) diff --git a/python/src/bindings.cpp b/python/src/bindings.cpp index ac6d8eeb9..4e4db6356 100644 --- a/python/src/bindings.cpp +++ b/python/src/bindings.cpp @@ -112,4 +112,7 @@ PYBIND11_MODULE(ipctk, m) // root define_collision_mesh(m); define_ipc(m); + + // dynamics + define_rigid_simulator(m); } diff --git a/python/src/bindings.hpp b/python/src/bindings.hpp index 5edc63ee9..83075456b 100644 --- a/python/src/bindings.hpp +++ b/python/src/bindings.hpp @@ -7,6 +7,7 @@ #include #include #include +#include #include #include #include diff --git a/python/src/collision_mesh.cpp b/python/src/collision_mesh.cpp index 44e0e89c1..3ab58d7c9 100644 --- a/python/src/collision_mesh.cpp +++ b/python/src/collision_mesh.cpp @@ -132,7 +132,8 @@ void define_collision_mesh(py::module_& m) )ipc_Qu8mg5v7", py::arg("i"), py::arg("j")); - py::class_(m, "CollisionMesh") + py::class_>( + m, "CollisionMesh") .def( py::init< Eigen::ConstRef, diff --git a/python/src/dynamics/CMakeLists.txt b/python/src/dynamics/CMakeLists.txt new file mode 100644 index 000000000..3e0548d96 --- /dev/null +++ b/python/src/dynamics/CMakeLists.txt @@ -0,0 +1,9 @@ +# set(SOURCES) + +# target_sources(ipc_toolkit PRIVATE ${SOURCES}) + +################################################################################ +# Subfolders +################################################################################ + +add_subdirectory(rigid) \ No newline at end of file diff --git a/python/src/dynamics/bindings.hpp b/python/src/dynamics/bindings.hpp new file mode 100644 index 000000000..5e9a3caaf --- /dev/null +++ b/python/src/dynamics/bindings.hpp @@ -0,0 +1 @@ +#include \ No newline at end of file diff --git a/python/src/dynamics/rigid/CMakeLists.txt b/python/src/dynamics/rigid/CMakeLists.txt new file mode 100644 index 000000000..b1c691bee --- /dev/null +++ b/python/src/dynamics/rigid/CMakeLists.txt @@ -0,0 +1,5 @@ +set(SOURCES + simulator.cpp +) + +target_sources(ipctk PRIVATE ${SOURCES}) \ No newline at end of file diff --git a/python/src/dynamics/rigid/bindings.hpp b/python/src/dynamics/rigid/bindings.hpp new file mode 100644 index 000000000..0625f8986 --- /dev/null +++ b/python/src/dynamics/rigid/bindings.hpp @@ -0,0 +1,6 @@ +#pragma once + +#include +namespace py = pybind11; + +void define_rigid_simulator(py::module_& m); \ No newline at end of file diff --git a/python/src/dynamics/rigid/simulator.cpp b/python/src/dynamics/rigid/simulator.cpp new file mode 100644 index 000000000..885545e95 --- /dev/null +++ b/python/src/dynamics/rigid/simulator.cpp @@ -0,0 +1,86 @@ +#include + +#include +#include + +#include + +namespace py = pybind11; +using namespace ipc; +using namespace ipc::rigid; + +PYBIND11_MAKE_OPAQUE(std::vector) + +void define_rigid_simulator(py::module_& m) +{ + py::bind_vector>(m, "Poses") + .def("__repr__", [](const std::vector& poses) { + std::string repr = "Poses(["; + for (const auto& pose : poses) { + repr += fmt::format( + "Pose(position={}, rotation={}){}", pose.position, + pose.rotation, (&pose != &poses.back() ? ", " : "")); + } + repr += "])"; + return repr; + }); + + py::class_(m, "Pose") + .def(py::init<>()) + .def( + py::init(), + py::arg("position"), py::arg("rotation")) + .def("rotation_matrix", &Pose::rotation_matrix) + .def( + "transform_vertices", &Pose::transform_vertices, + py::arg("vertices")) + .def(py::self * py::self) + .def_readwrite("position", &Pose::position) + .def_readwrite("rotation", &Pose::rotation) + .def("__repr__", [](const Pose& p) { + return fmt::format( + "Pose(position={}, rotation={})", p.position, p.rotation); + }); + + py::class_, CollisionMesh>( + m, "RigidBodies") + .def( + py::init(&RigidBodies::build_from_meshes), + py::arg("rest_positions"), py::arg("edges"), py::arg("faces"), + py::arg("densities"), py::arg("initial_poses")) + .def( + "vertices", &RigidBodies::vertices, + R"ipc_Qu8mg5v7( + Compute the vertex positions from the poses of the rigid bodies. + + Parameters: + poses: The poses of the rigid bodies. + + Returns: + The vertex positions of the rigid bodies (#V × dim). + )ipc_Qu8mg5v7", + py::arg("poses")) + .def_property_readonly("num_bodies", &RigidBodies::num_bodies) + .def("__getitem__", &RigidBodies::operator[], py::arg("index")); + + py::class_(m, "Simulator") + .def( + py::init< + const std::shared_ptr, const std::vector&, + const double>(), + py::arg("bodies"), py::arg("initial_poses"), py::arg("dt")) + .def( + "run", &rigid::Simulator::run, py::arg("t_end"), + py::arg("callback")) + .def("step", &rigid::Simulator::step) + .def("reset", &rigid::Simulator::reset) + .def_property_readonly( + "poses_history", &rigid::Simulator::poses_history, + R"ipc_Qu8mg5v7( + Get the history of poses in the simulation. + + Returns: + A list of poses at each time step. + )ipc_Qu8mg5v7") + .def_property_readonly("t", &rigid::Simulator::t); +} diff --git a/python/tests/rigid_example.py b/python/tests/rigid_example.py new file mode 100644 index 000000000..9d7cc0970 --- /dev/null +++ b/python/tests/rigid_example.py @@ -0,0 +1,46 @@ +from find_ipctk import ipctk +import meshio +import polyscope as ps +import numpy as np + +import pathlib + +mesh = meshio.read(pathlib.Path(__file__).parents[2] / "tests/data/bunny.ply") + +initial_poses = ipctk.Poses([ + ipctk.Pose(position=np.zeros(3), rotation=np.zeros(3)) +]) + +bodies = ipctk.RigidBodies( + rest_positions=[mesh.points.astype("float64")], + edges=[ipctk.edges(mesh.cells_dict["triangle"])], + faces=[mesh.cells_dict["triangle"]], + densities=[1.0], + initial_poses=initial_poses +) + +ps.init() + +ps_mesh = ps.register_surface_mesh( + "bunny", + bodies.vertices(initial_poses), + bodies.faces +) + +sim = ipctk.Simulator( + bodies=bodies, + initial_poses=initial_poses, + dt=0.01 +) + + +def foo(): + sim.step() + ps_mesh.update_vertex_positions( + bodies.vertices(sim.poses_history[-1]) + ) + + +ps.set_user_callback(foo) + +ps.show() diff --git a/src/ipc/dynamics/rigid/CMakeLists.txt b/src/ipc/dynamics/rigid/CMakeLists.txt index 89445e5b3..a01f3638c 100644 --- a/src/ipc/dynamics/rigid/CMakeLists.txt +++ b/src/ipc/dynamics/rigid/CMakeLists.txt @@ -9,6 +9,7 @@ set(SOURCES rigid_bodies.hpp rigid_body.cpp rigid_body.hpp + simulator.cpp time_integrator.hpp ) diff --git a/src/ipc/dynamics/rigid/rigid_bodies.cpp b/src/ipc/dynamics/rigid/rigid_bodies.cpp index e31e010cd..1c525474d 100644 --- a/src/ipc/dynamics/rigid/rigid_bodies.cpp +++ b/src/ipc/dynamics/rigid/rigid_bodies.cpp @@ -1,12 +1,15 @@ #include "rigid_bodies.hpp" +#include + namespace ipc::rigid { RigidBodies RigidBodies::build_from_meshes( const std::vector& rest_positions, const std::vector& edges, const std::vector& faces, - const std::vector& densities) + const std::vector& densities, + std::vector& initial_poses) { assert(rest_positions.size() == edges.size()); assert(rest_positions.size() == faces.size()); @@ -41,7 +44,7 @@ RigidBodies RigidBodies::build_from_meshes( return RigidBodies( concat_rest_positions, concat_edges, concat_faces, body_vertex_starts, - body_edge_starts, body_face_starts, densities); + body_edge_starts, body_face_starts, densities, initial_poses); } RigidBodies::RigidBodies( @@ -51,7 +54,8 @@ RigidBodies::RigidBodies( const std::vector& _body_vertex_starts, const std::vector& _body_edge_starts, const std::vector& _body_face_starts, - const std::vector& densities) + const std::vector& densities, + std::vector& initial_poses) : CollisionMesh(_rest_positions, _edges, _faces) , body_vertex_starts(std::move(_body_vertex_starts)) , body_edge_starts(std::move(_body_edge_starts)) @@ -62,9 +66,9 @@ RigidBodies::RigidBodies( assert(body_vertex_starts.back() == num_vertices()); assert(body_edge_starts.back() == num_edges()); assert(body_face_starts.back() == num_faces()); + assert(initial_poses.size() == body_vertex_starts.size() - 1); bodies.reserve(body_vertex_starts.size() - 1); - Pose initial_pose = Pose::Zero(dim()); for (size_t i = 0; i < body_vertex_starts.size() - 1; ++i) { bodies.emplace_back( m_rest_positions.middleRows( @@ -76,7 +80,11 @@ RigidBodies::RigidBodies( faces().middleRows( body_face_starts[i], body_face_starts[i + 1] - body_face_starts[i]), - densities[i], initial_pose); + densities[i], initial_poses[i]); + logger().info( + "Initial pose: position={}, rotation={}", + initial_poses[i].position.transpose(), + initial_poses[i].rotation.transpose()); } } diff --git a/src/ipc/dynamics/rigid/rigid_bodies.hpp b/src/ipc/dynamics/rigid/rigid_bodies.hpp index a5d3dce35..a6de70b3f 100644 --- a/src/ipc/dynamics/rigid/rigid_bodies.hpp +++ b/src/ipc/dynamics/rigid/rigid_bodies.hpp @@ -15,13 +15,28 @@ class RigidBodies : public CollisionMesh { const std::vector& body_vertex_starts, const std::vector& body_edge_starts, const std::vector& body_face_starts, - const std::vector& densities); + const std::vector& densities, + std::vector& initial_poses); static RigidBodies build_from_meshes( const std::vector& rest_positions, const std::vector& edges, const std::vector& faces, - const std::vector& densities); + const std::vector& densities, + std::vector& initial_poses); + + Eigen::MatrixXd vertices(const std::vector& poses) const + { + Eigen::MatrixXd V(num_vertices(), dim()); + for (size_t i = 0; i < num_bodies(); ++i) { + const index_t start = body_vertex_starts[i]; + const index_t end = body_vertex_starts[i + 1]; + V.middleRows(start, end - start) = poses[i].transform_vertices( + rest_positions().middleRows( + body_vertex_starts[i], end - start)); + } + return V; + } size_t num_bodies() const { return bodies.size(); } diff --git a/src/ipc/dynamics/rigid/simulator.cpp b/src/ipc/dynamics/rigid/simulator.cpp new file mode 100644 index 000000000..2c7deaca6 --- /dev/null +++ b/src/ipc/dynamics/rigid/simulator.cpp @@ -0,0 +1,97 @@ +#include "simulator.hpp" + +#include +#include +#include + +namespace ipc::rigid { + +Simulator::Simulator( + const std::shared_ptr _bodies, + const std::vector& initial_poses, + const double dt) + : m_bodies(std::move(_bodies)) +{ + m_pose_history.push_back(initial_poses); + + Eigen::VectorXd x0 = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); + for (size_t i = 0; i < m_bodies->num_bodies(); ++i) { + x0.segment<3>(12 * i) = initial_poses[i].position; + x0.segment<9>(12 * i) = initial_poses[i].rotation_matrix().reshaped(); + } + Eigen::VectorXd v0 = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); + Eigen::VectorXd a0 = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); + + // Initialize the time integrator + m_time_integrator = + std::make_shared(x0, v0, a0, dt, m_bodies->num_bodies()); + + // Initialize the inertial term + m_inertial_term = std::make_shared(m_time_integrator); +} + +void Simulator::run( + // const double dt, + const double t_end, + const std::function callback) +{ + if (t_end <= m_t) { + logger().warn( + "simulation already complete: t={:g} t_end={:g}", m_t, t_end); + return; + } + + // m_time_integrator->dt = dt; + + while (m_t < t_end) { + step(); // increments time by dt + callback(); + } +} + +void Simulator::step() +{ + std::vector poses = m_pose_history.back(); + + // TODO: Solve the implicit time integration problem here + // poses = m_solver->solve(poses); + Pose delta(Eigen::Vector3d::Zero(), Eigen::Vector3d(0.05, 0, 0)); + for (int i = 0; i < m_bodies->num_bodies(); ++i) { + poses[i] = delta * poses[i]; + } + + m_pose_history.push_back(poses); + + Eigen::VectorXd x = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); + for (size_t i = 0; i < m_bodies->num_bodies(); ++i) { + x.segment<3>(12 * i) = poses[i].position; + x.segment<9>(12 * i) = poses[i].rotation_matrix().reshaped(); + } + + m_time_integrator->update(x); + + m_t += m_time_integrator->dt; +} + +void Simulator::reset() +{ + m_t = 0.0; + // Reset pose history to only contain the initial poses + m_pose_history.resize(1); + + Eigen::VectorXd x0 = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); + for (size_t i = 0; i < m_bodies->num_bodies(); ++i) { + x0.segment<3>(12 * i) = m_pose_history[0][i].position; + x0.segment<9>(12 * i) = + m_pose_history[0][i].rotation_matrix().reshaped(); + } + Eigen::VectorXd v0 = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); + Eigen::VectorXd a0 = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); + + m_time_integrator = std::make_shared( + x0, v0, a0, m_time_integrator->dt, m_bodies->num_bodies()); + + m_inertial_term = std::make_shared(m_time_integrator); +} + +} // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/simulator.hpp b/src/ipc/dynamics/rigid/simulator.hpp new file mode 100644 index 000000000..afa5f4361 --- /dev/null +++ b/src/ipc/dynamics/rigid/simulator.hpp @@ -0,0 +1,71 @@ +#pragma once + +#include + +#include +#include + +namespace ipc::rigid { + +class RigidBodies; +class ImplicitEuler; +class InertialTerm; + +class Simulator { +public: + /// @brief Create a simulation box + /// @param corners Corners of the simulation box + /// @param gravity Gravity vector + Simulator( + const std::shared_ptr _bodies, + const std::vector& initial_poses, + const double dt); + + /// @brief Run the simulation + /// @param t_end End time + /// @param dt Time step + /// @param callback + void run( + // const double dt, + const double t_end, + const std::function callback = []() { }); + + /// @brief Step the simulation + /// @param dt Time step + void step( + // double dt + ); + + /// @brief Reset the simulation to time t=0 + void reset(); + + // ----------------------------------------------------------------------- + // Accessors + // ----------------------------------------------------------------------- + + const std::vector>& poses_history() const + { + return m_pose_history; + } + + const std::shared_ptr& bodies() const { return m_bodies; } + + double t() const { return m_t; } + +protected: + /// @brief Bodies in the simulation + std::shared_ptr m_bodies; + + /// @brief Time integrator for the simulation + std::shared_ptr m_time_integrator; + + /// @brief Inertial term for the rigid body dynamics + std::shared_ptr m_inertial_term; + + std::vector> m_pose_history; + + /// @brief t Current simulation time + double m_t = 0.0; +}; + +} // namespace ipc::rigid \ No newline at end of file diff --git a/tests/src/tests/dynamics/rigid/test_inertial_term.cpp b/tests/src/tests/dynamics/rigid/test_inertial_term.cpp index c487fd4a6..77631b6f7 100644 --- a/tests/src/tests/dynamics/rigid/test_inertial_term.cpp +++ b/tests/src/tests/dynamics/rigid/test_inertial_term.cpp @@ -30,7 +30,11 @@ RigidBodies rigid_bodies() const double density = GENERATE(1.0, 2.0, 3.0); - return RigidBodies::build_from_meshes({ V }, { E }, { F }, { density }); + std::vector initial_poses; + initial_poses.push_back(Pose::Zero(3)); // Initial pose at the origin + + return RigidBodies::build_from_meshes( + { V }, { E }, { F }, { density }, initial_poses); } std::shared_ptr time_integrator(const RigidBodies& bodies) From 01070734cfc9b1773eefdbe5a38ca32ff66bbcfd Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Sat, 21 Jun 2025 01:34:38 -0400 Subject: [PATCH 11/24] Move body forces into separate class - Update CPM to 0.42.0 - Add TinyGLTF dependency - Rename save_obj to write_candidates_obj - Add write_gltf --- CMakeLists.txt | 18 +- cmake/recipes/CPM.cmake | 2 +- cmake/recipes/ccd_query_io.cmake | 9 +- cmake/recipes/libigl.cmake | 7 +- cmake/recipes/scalable_ccd.cmake | 7 +- cmake/recipes/tinygltf.cmake | 21 + python/example.ipynb | 91379 ---------------- python/examples/example.ipynb | 43279 ++++++++ python/examples/find_ipctk.py | 20 + .../rigid_example.py => examples/rigid.py} | 29 +- python/src/candidates/candidates.cpp | 2 +- src/ipc/CMakeLists.txt | 1 + src/ipc/candidates/candidates.cpp | 16 +- src/ipc/candidates/candidates.hpp | 2 +- src/ipc/dynamics/rigid/CMakeLists.txt | 2 + src/ipc/dynamics/rigid/body_forces.cpp | 179 + src/ipc/dynamics/rigid/body_forces.hpp | 99 + src/ipc/dynamics/rigid/inertial_term.cpp | 52 +- src/ipc/dynamics/rigid/pose.hpp | 8 + src/ipc/dynamics/rigid/rigid_bodies.hpp | 56 +- src/ipc/dynamics/rigid/rigid_body.hpp | 10 + src/ipc/dynamics/rigid/simulator.cpp | 72 +- src/ipc/dynamics/rigid/simulator.hpp | 12 +- src/ipc/io/CMakeLists.txt | 8 + .../write_candidates_obj.cpp} | 12 +- .../write_candidates_obj.hpp} | 6 +- src/ipc/io/write_gltf.cpp | 244 + src/ipc/io/write_gltf.hpp | 19 + src/ipc/utils/CMakeLists.txt | 2 - src/ipc/utils/eigen_ext.hpp | 9 + tests/src/tests/utils/test_utils.cpp | 14 +- 31 files changed, 44102 insertions(+), 91494 deletions(-) create mode 100644 cmake/recipes/tinygltf.cmake delete mode 100755 python/example.ipynb create mode 100755 python/examples/example.ipynb create mode 100644 python/examples/find_ipctk.py rename python/{tests/rigid_example.py => examples/rigid.py} (55%) create mode 100644 src/ipc/dynamics/rigid/body_forces.cpp create mode 100644 src/ipc/dynamics/rigid/body_forces.hpp create mode 100644 src/ipc/io/CMakeLists.txt rename src/ipc/{utils/save_obj.cpp => io/write_candidates_obj.cpp} (95%) rename src/ipc/{utils/save_obj.hpp => io/write_candidates_obj.hpp} (87%) create mode 100644 src/ipc/io/write_gltf.cpp create mode 100644 src/ipc/io/write_gltf.hpp diff --git a/CMakeLists.txt b/CMakeLists.txt index 325941e75..0d25e4411 100644 --- a/CMakeLists.txt +++ b/CMakeLists.txt @@ -168,13 +168,6 @@ target_link_libraries(ipc_toolkit PUBLIC tight_inclusion::tight_inclusion) include(scalable_ccd) target_link_libraries(ipc_toolkit PUBLIC scalable_ccd::scalable_ccd) -# CCD -if(IPC_TOOLKIT_WITH_INEXACT_CCD) - # Etienne Vouga's CTCD Library for the floating point root finding algorithm - include(evouga_ccd) - target_link_libraries(ipc_toolkit PUBLIC evouga::ccd) -endif() - # SimpleBVH include(simple_bvh) target_link_libraries(ipc_toolkit PUBLIC simple_bvh::simple_bvh) @@ -183,6 +176,17 @@ target_link_libraries(ipc_toolkit PUBLIC simple_bvh::simple_bvh) include(spdlog) target_link_libraries(ipc_toolkit PUBLIC spdlog::spdlog) +# TinyGLTF +include(tinygltf) +target_link_libraries(ipc_toolkit PRIVATE tinygltf::tinygltf) + +# CCD +if(IPC_TOOLKIT_WITH_INEXACT_CCD) + # Etienne Vouga's CTCD Library for the floating point root finding algorithm + include(evouga_ccd) + target_link_libraries(ipc_toolkit PUBLIC evouga::ccd) +endif() + # rational-cpp (requires GMP) if(IPC_TOOLKIT_WITH_RATIONAL_INTERSECTION) include(rational_cpp) diff --git a/cmake/recipes/CPM.cmake b/cmake/recipes/CPM.cmake index fb1846742..c7b9c090c 100644 --- a/cmake/recipes/CPM.cmake +++ b/cmake/recipes/CPM.cmake @@ -1,4 +1,4 @@ -set(CPM_DOWNLOAD_VERSION 0.40.2) +set(CPM_DOWNLOAD_VERSION 0.42.0) if(CPM_SOURCE_CACHE) set(CPM_DOWNLOAD_LOCATION "${CPM_SOURCE_CACHE}/cpm/CPM_${CPM_DOWNLOAD_VERSION}.cmake") diff --git a/cmake/recipes/ccd_query_io.cmake b/cmake/recipes/ccd_query_io.cmake index be26e87cc..ca1db9dc7 100644 --- a/cmake/recipes/ccd_query_io.cmake +++ b/cmake/recipes/ccd_query_io.cmake @@ -8,8 +8,9 @@ message(STATUS "Third-party: creating target 'ccd_io::ccd_io'") include(ipc_toolkit_tests_data) -set(CCD_IO_DOWNLOAD_SAMPLE_QUERIES ON CACHE BOOL "Download sample CCD queries" FORCE) -set(CCD_IO_SAMPLE_QUERIES_DIR "${IPC_TOOLKIT_TESTS_DATA_DIR}/ccd-queries/" CACHE PATH "Where should we download sample queries?") - include(CPM) -CPMAddPackage("gh:Continuous-Collision-Detection/CCD-Query-IO#36f6093af81a65acc27d9f05ad32d6b5729e8d15") \ No newline at end of file +CPMAddPackage( + URI "gh:Continuous-Collision-Detection/CCD-Query-IO#36f6093af81a65acc27d9f05ad32d6b5729e8d15" + OPTIONS "CCD_IO_DOWNLOAD_SAMPLE_QUERIES=ON" + "CCD_IO_SAMPLE_QUERIES_DIR=${IPC_TOOLKIT_TESTS_DATA_DIR}/ccd-queries/" +) \ No newline at end of file diff --git a/cmake/recipes/libigl.cmake b/cmake/recipes/libigl.cmake index 11046a192..28f25132c 100644 --- a/cmake/recipes/libigl.cmake +++ b/cmake/recipes/libigl.cmake @@ -6,12 +6,13 @@ endif() message(STATUS "Third-party: creating target 'igl::core'") -set(LIBIGL_PREDICATES ON CACHE BOOL "Use exact predicates" FORCE) - include(eigen) include(CPM) -CPMAddPackage("gh:libigl/libigl#89267b4a80b1904de3f6f2812a2053e5e9332b7e") +CPMAddPackage( + URI "gh:libigl/libigl#89267b4a80b1904de3f6f2812a2053e5e9332b7e" + OPTIONS "LIBIGL_PREDICATES=ON" +) # Folder name for IDE foreach(target_name IN ITEMS core predicates) diff --git a/cmake/recipes/scalable_ccd.cmake b/cmake/recipes/scalable_ccd.cmake index f8152b25a..52f5d6200 100644 --- a/cmake/recipes/scalable_ccd.cmake +++ b/cmake/recipes/scalable_ccd.cmake @@ -6,10 +6,11 @@ endif() message(STATUS "Third-party: creating target 'scalable_ccd::scalable_ccd'") -set(SCALABLE_CCD_WITH_CUDA ${IPC_TOOLKIT_WITH_CUDA} CACHE BOOL "Enable CUDA CCD" FORCE) - include(CPM) -CPMAddPackage("gh:continuous-collision-detection/scalable-ccd#2c82b9ca43fba30b85f7e9aa83283464b1bb7843") +CPMAddPackage( + URI "gh:continuous-collision-detection/scalable-ccd#2c82b9ca43fba30b85f7e9aa83283464b1bb7843" + OPTIONS "SCALABLE_CCD_WITH_CUDA=${IPC_TOOLKIT_WITH_CUDA}" +) # Folder name for IDE set_target_properties(scalable_ccd PROPERTIES FOLDER "ThirdParty") \ No newline at end of file diff --git a/cmake/recipes/tinygltf.cmake b/cmake/recipes/tinygltf.cmake new file mode 100644 index 000000000..d6b384ddf --- /dev/null +++ b/cmake/recipes/tinygltf.cmake @@ -0,0 +1,21 @@ +# TinyGLTF (https://github.com/syoyo/tinygltf) +# License: MIT +if(TARGET tinygltf::tinygltf) + return() +endif() + +message(STATUS "Third-party: creating target 'tinygltf::tinygltf'") + +include(CPM) +CPMAddPackage( + URI "gh:syoyo/tinygltf@2.9.6" + DOWNLOAD_ONLY TRUE +) + +add_library(tinygltf) +add_library(tinygltf::tinygltf ALIAS tinygltf) +target_sources(tinygltf PRIVATE ${tinygltf_SOURCE_DIR}/tiny_gltf.cc) +target_include_directories(tinygltf INTERFACE + $ + $ +) \ No newline at end of file diff --git a/python/example.ipynb b/python/example.ipynb deleted file mode 100755 index 1717f8b0b..000000000 --- a/python/example.ipynb +++ /dev/null @@ -1,91379 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "a59fb5aa", - "metadata": {}, - "source": [ - "# IPC Toolkit Python Examples" - ] - }, - { - "cell_type": "code", - "execution_count": 54, - "id": "e03f8e39", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy\n", - "import plotly.figure_factory as ff\n", - "import plotly.graph_objects as go\n", - "import meshio\n", - "\n", - "import sys\n", - "sys.path.append(\"../notebooks\") # noqa\n", - "\n", - "from find_ipctk import ipctk\n", - "from ipctk import *" - ] - }, - { - "cell_type": "markdown", - "id": "c408e62d", - "metadata": { - "heading_collapsed": true - }, - "source": [ - "## Distance" - ] - }, - { - "cell_type": "code", - "execution_count": 55, - "id": "60e6c8a0", - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "text/plain": [ - "0.03313444539727968" - ] - }, - "execution_count": 55, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "numpy.random.seed(0)\n", - "ea0, ea1, eb0, eb1 = 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numpy.empty(x.shape)\n", - "for i in range(x.shape[0]):\n", - " for j in range(x.shape[1]):\n", - " grad = point_edge_distance_gradient(\n", - " numpy.array([x[i, j], y[i, j]]), e0, e1)\n", - " u[i, j] = grad[0]\n", - " v[i, j] = grad[1]\n", - " d[i, j] = numpy.sqrt(point_edge_distance(\n", - " numpy.array([x[i, j], y[i, j]]), e0, e1))\n", - "\n", - "fig = ff.create_quiver(x, y, u, v, name=\"point_grad\")\n", - "fig.add_trace(go.Scatter(x=[e0[0], e1[0]], y=[e0[1], e1[1]], name=\"edge\"))\n", - "fig.update_layout(width=800, height=800)\n", - "fig.show()\n", - "fig = ff.create_quiver(x, y, u/(2 * d), v / (2 * d), name=\"point_grad\")\n", - "fig.add_trace(go.Scatter(x=[e0[0], e1[0]], y=[e0[1], e1[1]], name=\"edge\"))\n", - "fig.update_layout(width=800, height=800)\n", - "fig.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 59, - "id": "b50fae20", - "metadata": {}, - "outputs": [ - { - "data": { - "application/vnd.plotly.v1+json": { - "config": { - "plotlyServerURL": 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ea1, eb0, eb1))" - ] - }, - { - "cell_type": "code", - "execution_count": 63, - "id": "cd1aa64c", - "metadata": { - "hidden": true - }, - "outputs": [ - { - "data": { - "application/vnd.plotly.v1+json": { - "config": { - "plotlyServerURL": "https://plot.ly" - }, - "data": [ - { - "type": "scatter", - "x": [ - -1, - 1 - ], - "y": [ - -1, - 1 - ] - }, - { - "type": "contour", - "x": [ - -2, - -1.9595959595959596, - -1.9191919191919191, - -1.878787878787879, - -1.8383838383838385, - -1.797979797979798, - -1.7575757575757576, - -1.7171717171717171, - -1.6767676767676767, - -1.6363636363636362, - -1.595959595959596, - -1.5555555555555556, - -1.5151515151515151, - -1.4747474747474747, - -1.4343434343434343, - -1.393939393939394, - -1.3535353535353534, - -1.3131313131313131, - -1.2727272727272727, - -1.2323232323232323, - -1.1919191919191918, - -1.1515151515151514, - -1.1111111111111112, - -1.0707070707070705, - -1.0303030303030303, - -0.9898989898989898, - -0.9494949494949494, - 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numpy.vectorize(lambda x: barrier_second_derivative(x, dhat))(d)\n", - "fig = go.Figure(data=[go.Scatter(x=d, y=b, name=\"b(x)\"), go.Scatter(x=d, y=b_grad, name=r\"\\nabla b(x)\"), go.Scatter(x=d, y=b_hess, name=r\"\\nabla^2 b(x)\")])\n", - "fig.update_layout(yaxis_range=[-1000, 1000])\n", - "fig.show()" - ] - }, - { - "cell_type": "markdown", - "id": "aece0d06", - "metadata": {}, - "source": [ - "## Compute Barrier Potential" - ] - }, - { - "cell_type": "code", - "execution_count": 66, - "id": "7bcb52ee", - "metadata": {}, - "outputs": [], - "source": [ - "V = numpy.random.random((4, 3))\n", - "E = numpy.arange(10).reshape(-1, 2)\n", - "F = numpy.arange(9).reshape(-1, 3)\n", - "dhat = 1\n", - "B = BarrierPotential(dhat)" - ] - }, - { - "cell_type": "code", - "execution_count": 67, - "id": "cd18873b", - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "potential: 0.13736206524830097\n", - "gradient: [ 3.10836254 -0.44411327 1.02048799 -3.10836254 0.44411327 -1.02048799]\n", - "hessian: [[ 45.4591324 -7.03247155 16.15928481 -45.4591324 7.03247155\n", - " -16.15928481]\n", - " [ -7.03247155 -2.75657651 -2.30878884 7.03247155 2.75657651\n", - " 2.30878884]\n", - " [ 16.15928481 -2.30878884 1.54380415 -16.15928481 2.30878884\n", - " -1.54380415]\n", - " [-45.4591324 7.03247155 -16.15928481 45.4591324 -7.03247155\n", - " 16.15928481]\n", - " [ 7.03247155 2.75657651 2.30878884 -7.03247155 -2.75657651\n", - " -2.30878884]\n", - " [-16.15928481 2.30878884 -1.54380415 16.15928481 -2.30878884\n", - " 1.54380415]]\n", - "weight: 10.0\n" - ] - } - ], - "source": [ - "vvc = VertexVertexNormalCollision(0, 1)\n", - "vvc.weight = 10\n", - "print(\"potential:\", B(vvc, vvc.dof(V, E, F)))\n", - "print(\"gradient:\", B.gradient(vvc, vvc.dof(V, E, F)))\n", - "print(\"hessian:\", B.hessian(vvc, vvc.dof(V, E, F)))\n", - "print(\"weight:\", vvc.weight)" - ] - }, - { - "cell_type": "code", - "execution_count": 68, - "id": "f0dda628", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[EdgeVertexCandidate(0, 1),\n", - " EdgeVertexCandidate(1, 2),\n", - " EdgeVertexCandidate(2, 3),\n", - " EdgeVertexCandidate(3, 4),\n", - " EdgeVertexCandidate(4, 5),\n", - " EdgeVertexCandidate(5, 6),\n", - " EdgeVertexCandidate(6, 7),\n", - " EdgeVertexCandidate(7, 8),\n", - " EdgeVertexCandidate(8, 9),\n", - " EdgeVertexCandidate(9, 10),\n", - " EdgeVertexCandidate(10, 11),\n", - " EdgeVertexCandidate(11, 12),\n", - " EdgeVertexCandidate(12, 13),\n", - " EdgeVertexCandidate(13, 14),\n", - " EdgeVertexCandidate(14, 15),\n", - " EdgeVertexCandidate(15, 16),\n", - " EdgeVertexCandidate(16, 17),\n", - " EdgeVertexCandidate(17, 18),\n", - " EdgeVertexCandidate(18, 19),\n", - " EdgeVertexCandidate(19, 20)]" - ] - }, - "execution_count": 68, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "cs = Candidates()\n", - "num_candidates = 20\n", - "cs.ev_candidates = [EdgeVertexCandidate(i, i+1) for i in range(num_candidates)]\n", - "assert(len(cs) == num_candidates)\n", - "cs.ev_candidates" - ] - }, - { - "cell_type": "markdown", - "id": "c81b3d24", - "metadata": {}, - "source": [ - "## Real-World Example" - ] - }, - { - "cell_type": "code", - "execution_count": 69, - "id": "71545264", - "metadata": {}, - "outputs": [], - "source": [ - "in_mesh = meshio.read(\"../tests/data/bunny.ply\")\n", - "V = in_mesh.points\n", - "F = in_mesh.cells[0].data\n", - "E = edges(F)" - ] - }, - { - "cell_type": "code", - "execution_count": 70, - "id": "0b3e5dfe", - "metadata": {}, - "outputs": [], - "source": [ - "mesh = CollisionMesh(V, E, F)" - ] - }, - { - "cell_type": "code", - "execution_count": 71, - "id": "2a62c7e2", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "True" - ] - }, - "execution_count": 71, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "U = numpy.random.random((mesh.num_vertices, 3))\n", - "V1 = mesh.displace_vertices(0.01 * U)\n", - "has_intersections(mesh, V1)" - ] - }, - { - "cell_type": "code", - "execution_count": 72, - "id": "ad840404", - "metadata": {}, - "outputs": [], - "source": [ - "cs = NormalCollisions()\n", - "cs.build(mesh, V, 1e-2)\n", - "B = BarrierPotential(1e-2)" - ] - }, - { - "cell_type": "code", - "execution_count": 73, - "id": "4f73f2d1", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "570" - ] - }, - "execution_count": 73, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "len(cs)" - ] - }, - { - "cell_type": "code", - "execution_count": 74, - "id": "52169183", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "3.0948257658451044e-06" - ] - }, - "execution_count": 74, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "B(cs, mesh, V)" - ] - }, - { - "cell_type": "code", - "execution_count": 75, - "id": "046601e9", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "np.float64(0.00031142693797427427)" - ] - }, - "execution_count": 75, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "g = B.gradient(cs, mesh, V)\n", - "numpy.linalg.norm(g)" - ] - }, - { - "cell_type": "code", - "execution_count": 76, - "id": "1ebe2ac0", - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "np.float64(0.2680460874504241)" - ] - }, - "execution_count": 76, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "H = B.hessian(cs, mesh, V)\n", - "numpy.linalg.norm(H.todense())" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3.10.5 64-bit", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.11.9" - }, - "varInspector": { - "cols": { - "lenName": 16, - "lenType": 16, - "lenVar": 40 - }, - "kernels_config": { - "python": { - "delete_cmd_postfix": "", - "delete_cmd_prefix": "del ", - "library": "var_list.py", - "varRefreshCmd": "print(var_dic_list())" - }, - "r": { - "delete_cmd_postfix": ") ", - "delete_cmd_prefix": "rm(", - "library": "var_list.r", - "varRefreshCmd": "cat(var_dic_list()) " - } - }, - "types_to_exclude": [ - "module", - "function", - "builtin_function_or_method", - "instance", - "_Feature" - ], - "window_display": false - }, - "vscode": { - "interpreter": { - "hash": "e7370f93d1d0cde622a1f8e1c04877d8463912d04d973331ad4851f04de6915a" - } - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/python/examples/example.ipynb b/python/examples/example.ipynb new file mode 100755 index 000000000..c1e66aff2 --- /dev/null +++ b/python/examples/example.ipynb @@ -0,0 +1,43279 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "a59fb5aa", + "metadata": {}, + "source": [ + "# IPC Toolkit Python Examples" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e03f8e39", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy\n", + "import plotly.figure_factory as ff\n", + "import plotly.graph_objects as go\n", + "import meshio\n", + "\n", + "import sys\n", + "sys.path.append(\"../notebooks\") # noqa\n", + "\n", + "from find_ipctk import ipctk\n", + "from ipctk import *" + ] + }, + { + "cell_type": "markdown", + "id": "c408e62d", + "metadata": { + "heading_collapsed": true + }, + "source": [ + "## Distance" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "60e6c8a0", + "metadata": { + "hidden": true + }, + "outputs": [ + { + "data": { + "text/plain": [ + "0.03313444539727968" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "numpy.random.seed(0)\n", + "ea0, ea1, eb0, eb1 = (numpy.random.random(3) for i in range(4))\n", + "edge_edge_distance(ea0, ea1, eb0, eb1)" + ] + }, + { 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+ "dtype": "f8" + }, + "z": { + "bdata": 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grad[0]\n", + " v[i, j] = grad[1]\n", + " d[i, j] = numpy.sqrt(point_edge_distance(\n", + " numpy.array([x[i, j], y[i, j]]), e0, e1))\n", + "\n", + "fig = ff.create_quiver(x, y, u, v, name=\"point_grad\")\n", + "fig.add_trace(go.Scatter(x=[e0[0], e1[0]], y=[e0[1], e1[1]], name=\"edge\"))\n", + "fig.update_layout(width=800, height=800)\n", + "fig.show()\n", + "fig = ff.create_quiver(x, y, u/(2 * d), v / (2 * d), name=\"point_grad\")\n", + "fig.add_trace(go.Scatter(x=[e0[0], e1[0]], y=[e0[1], e1[1]], name=\"edge\"))\n", + "fig.update_layout(width=800, height=800)\n", + "fig.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "b50fae20", + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "mode": "lines", + "name": "point_hessian_x", + "type": "scatter", + "x": [ + -2, + -1.8, + null, + -1.8, + -1.6, + null, + -1.6, + -1.4000000000000001, + null, + 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height=800)\n", + "fig.show()\n", + "fig = ff.create_quiver(x, y, u/(2 * d), v / (2 * d), name=\"point_grad\")\n", + "fig.add_trace(go.Scatter(x=[p[0]], y=[p[1]], name=\"edge\"))\n", + "fig.update_layout(width=800, height=800)\n", + "fig.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "8b11f45a", + "metadata": { + "hidden": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.3298505342009098\n", + "[-0.46155054 -0.00707979 -0.2998706 -0.50158084 -0.00769382 -0.3258784\n", + " 0. 0. 0. 0.96313139 0.01477362 0.625749 ]\n", + "[[ 0.3819837 0.13132058 -0.20871499 0.72453323 0.14745627 -0.02578582\n", + " 0. 0. 0. -1.10651693 -0.27877685 0.23450081]\n", + " [ 0.13132058 0.23625808 0.35449442 -0.38282811 0.24868745 0.04379623\n", + " 0. 0. 0. 0.25150752 -0.48494553 -0.39829065]\n", + " [-0.20871499 0.35449442 -0.10411631 0.60844965 0.39805202 0.42952853\n", + " 0. 0. 0. -0.39973466 -0.75254644 -0.32541222]\n", + " [ 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numpy.random.random(3)\n", + "ea1 = numpy.random.random(3)\n", + "eb0 = numpy.random.random(3)\n", + "eb1 = numpy.random.random(3)\n", + "\n", + "print(edge_edge_distance(ea0, ea1, eb0, eb1))\n", + "print(edge_edge_distance_gradient(ea0, ea1, eb0, eb1))\n", + "print(edge_edge_distance_hessian(ea0, ea1, eb0, eb1))" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "cd1aa64c", + "metadata": { + "hidden": true + }, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "type": "scatter", + "x": [ + -1, + 1 + ], + "y": [ + -1, + 1 + ] + }, + { + "type": "contour", + "x": { + "bdata": 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"showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + } + } + } + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x = numpy.linspace(0, 2e-3)\n", + "y = numpy.vectorize(edge_edge_mollifier)(x, eps_x=1e-3)\n", + "fig = go.Figure(data=go.Scatter(x=x, y=y))\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "id": "b78ab5d7", + "metadata": { + "heading_collapsed": true + }, + "source": [ + "## IPC Barrier Function" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "97410995", + "metadata": { + "hidden": true + }, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "name": "b(x)", + "type": "scatter", + "x": { + "bdata": 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+ "dtype": "f8" + } + }, + { + "name": "\\nabla b(x)", + "type": "scatter", + "x": { + "bdata": 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+ "dtype": "f8" + } + }, + { + "name": "\\nabla^2 b(x)", + "type": "scatter", + "x": { + "bdata": 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"backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "yaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + }, + "zaxis": { + "backgroundcolor": "#E5ECF6", + "gridcolor": "white", + "gridwidth": 2, + "linecolor": "white", + "showbackground": true, + "ticks": "", + "zerolinecolor": "white" + } + }, + "shapedefaults": { + "line": { + "color": "#2a3f5f" + } + }, + "ternary": { + "aaxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "baxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + }, + "bgcolor": "#E5ECF6", + "caxis": { + "gridcolor": "white", + "linecolor": "white", + "ticks": "" + } + }, + "title": { + "x": 0.05 + }, + "xaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + }, + "yaxis": { + "automargin": true, + "gridcolor": "white", + "linecolor": "white", + "ticks": "", + "title": { + "standoff": 15 + }, + "zerolinecolor": "white", + "zerolinewidth": 2 + } + } + }, + "yaxis": { + "range": [ + -1000, + 1000 + ] + } + } + } + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "d = numpy.geomspace(1e-12, 0.2, 1000)\n", + "dhat = 0.1\n", + "b = numpy.vectorize(lambda x: barrier(x, dhat))(d)\n", + "b_grad = numpy.vectorize(lambda x: barrier_first_derivative(x, dhat))(d)\n", + "b_hess = numpy.vectorize(lambda x: barrier_second_derivative(x, dhat))(d)\n", + "fig = go.Figure(data=[go.Scatter(x=d, y=b, name=\"b(x)\"), go.Scatter(\n", + " x=d, y=b_grad, name=r\"\\nabla b(x)\"), go.Scatter(x=d, y=b_hess, name=r\"\\nabla^2 b(x)\")])\n", + "fig.update_layout(yaxis_range=[-1000, 1000])\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "id": "aece0d06", + "metadata": {}, + "source": [ + "## Compute Barrier Potential" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "7bcb52ee", + "metadata": {}, + "outputs": [], + "source": [ + "V = numpy.random.random((4, 3))\n", + "E = numpy.arange(10).reshape(-1, 2)\n", + "F = numpy.arange(9).reshape(-1, 3)\n", + "dhat = 1\n", + "B = BarrierPotential(dhat)" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "cd18873b", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "potential: 0.13736206524830097\n", + "gradient: [ 3.10836254 -0.44411327 1.02048799 -3.10836254 0.44411327 -1.02048799]\n", + "hessian: [[ 45.4591324 -7.03247155 16.15928481 -45.4591324 7.03247155\n", + " -16.15928481]\n", + " [ -7.03247155 -2.75657651 -2.30878884 7.03247155 2.75657651\n", + " 2.30878884]\n", + " [ 16.15928481 -2.30878884 1.54380415 -16.15928481 2.30878884\n", + " -1.54380415]\n", + " [-45.4591324 7.03247155 -16.15928481 45.4591324 -7.03247155\n", + " 16.15928481]\n", + " [ 7.03247155 2.75657651 2.30878884 -7.03247155 -2.75657651\n", + " -2.30878884]\n", + " [-16.15928481 2.30878884 -1.54380415 16.15928481 -2.30878884\n", + " 1.54380415]]\n", + "weight: 10.0\n" + ] + } + ], + "source": [ + "vvc = VertexVertexNormalCollision(0, 1)\n", + "vvc.weight = 10\n", + "print(\"potential:\", B(vvc, vvc.dof(V, E, F)))\n", + "print(\"gradient:\", B.gradient(vvc, vvc.dof(V, E, F)))\n", + "print(\"hessian:\", B.hessian(vvc, vvc.dof(V, E, F)))\n", + "print(\"weight:\", vvc.weight)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "f0dda628", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "[EdgeVertexCandidate(0, 1),\n", + " EdgeVertexCandidate(1, 2),\n", + " EdgeVertexCandidate(2, 3),\n", + " EdgeVertexCandidate(3, 4),\n", + " EdgeVertexCandidate(4, 5),\n", + " EdgeVertexCandidate(5, 6),\n", + " EdgeVertexCandidate(6, 7),\n", + " EdgeVertexCandidate(7, 8),\n", + " EdgeVertexCandidate(8, 9),\n", + " EdgeVertexCandidate(9, 10),\n", + " EdgeVertexCandidate(10, 11),\n", + " EdgeVertexCandidate(11, 12),\n", + " EdgeVertexCandidate(12, 13),\n", + " EdgeVertexCandidate(13, 14),\n", + " EdgeVertexCandidate(14, 15),\n", + " EdgeVertexCandidate(15, 16),\n", + " EdgeVertexCandidate(16, 17),\n", + " EdgeVertexCandidate(17, 18),\n", + " EdgeVertexCandidate(18, 19),\n", + " EdgeVertexCandidate(19, 20)]" + ] + }, + "execution_count": 20, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "cs = Candidates()\n", + "num_candidates = 20\n", + "cs.ev_candidates = [EdgeVertexCandidate(i, i+1) for i in range(num_candidates)]\n", + "assert (len(cs) == num_candidates)\n", + "cs.ev_candidates" + ] + }, + { + "cell_type": "markdown", + "id": "c81b3d24", + "metadata": {}, + "source": [ + "## Real-World Example" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "71545264", + "metadata": {}, + "outputs": [], + "source": [ + "in_mesh = meshio.read(\"../../tests/data/bunny.ply\")\n", + "V = in_mesh.points\n", + "F = in_mesh.cells[0].data\n", + "E = edges(F)" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "0b3e5dfe", + "metadata": {}, + "outputs": [], + "source": [ + "mesh = CollisionMesh(V, E, F)" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "2a62c7e2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "True" + ] + }, + "execution_count": 25, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "U = numpy.random.random((mesh.num_vertices, 3))\n", + "V1 = mesh.displace_vertices(0.01 * U)\n", + "has_intersections(mesh, V1)" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "ad840404", + "metadata": {}, + "outputs": [], + "source": [ + "cs = NormalCollisions()\n", + "cs.build(mesh, V, 1e-2)\n", + "B = BarrierPotential(1e-2)" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "4f73f2d1", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "570" + ] + }, + "execution_count": 27, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "len(cs)" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "52169183", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "3.094825765845104e-06" + ] + }, + "execution_count": 28, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "B(cs, mesh, V)" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "046601e9", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "np.float64(0.00031142693797427427)" + ] + }, + "execution_count": 29, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "g = B.gradient(cs, mesh, V)\n", + "numpy.linalg.norm(g)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "1ebe2ac0", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "np.float64(0.2680460874504241)" + ] + }, + "execution_count": 30, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "H = B.hessian(cs, mesh, V)\n", + "numpy.linalg.norm(H.todense())" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.13.4" + }, + "varInspector": { + "cols": { + "lenName": 16, + "lenType": 16, + "lenVar": 40 + }, + "kernels_config": { + "python": { + "delete_cmd_postfix": "", + "delete_cmd_prefix": "del ", + "library": "var_list.py", + "varRefreshCmd": "print(var_dic_list())" + }, + "r": { + "delete_cmd_postfix": ") ", + "delete_cmd_prefix": "rm(", + "library": "var_list.r", + "varRefreshCmd": "cat(var_dic_list()) " + } + }, + "types_to_exclude": [ + "module", + "function", + "builtin_function_or_method", + "instance", + "_Feature" + ], + "window_display": false + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/python/examples/find_ipctk.py b/python/examples/find_ipctk.py new file mode 100644 index 000000000..b3197cc04 --- /dev/null +++ b/python/examples/find_ipctk.py @@ -0,0 +1,20 @@ +try: + import ipctk # Try to import the built module +except ImportError: + import sys + import pathlib + repo_root = pathlib.Path(__file__).parents[2] + possible_paths = [ + pathlib.Path("python").resolve(), + repo_root / "build" / "python", + repo_root / "build" / "release" / "python", + repo_root / "build" / "debug" / "python", + ] + for path in possible_paths: + if path.exists() and len(list(path.glob("ipctk.*"))) > 0: + sys.path.append(str(path)) + break + else: + raise ImportError("Could not find the ipctk module") + print(f"Using found ipctk module at {path}") + import ipctk # Try again diff --git a/python/tests/rigid_example.py b/python/examples/rigid.py similarity index 55% rename from python/tests/rigid_example.py rename to python/examples/rigid.py index 9d7cc0970..a8da46311 100644 --- a/python/tests/rigid_example.py +++ b/python/examples/rigid.py @@ -1,11 +1,12 @@ from find_ipctk import ipctk import meshio import polyscope as ps +from polyscope import imgui import numpy as np import pathlib -mesh = meshio.read(pathlib.Path(__file__).parents[2] / "tests/data/bunny.ply") +mesh = meshio.read(pathlib.Path(__file__).parents[2] / "tests/data/cube.ply") initial_poses = ipctk.Poses([ ipctk.Pose(position=np.zeros(3), rotation=np.zeros(3)) @@ -19,8 +20,13 @@ initial_poses=initial_poses ) +for pose in initial_poses: + print(pose) + ps.init() +ps.set_give_focus_on_show(True) + ps_mesh = ps.register_surface_mesh( "bunny", bodies.vertices(initial_poses), @@ -33,12 +39,25 @@ dt=0.01 ) +playing = False + def foo(): - sim.step() - ps_mesh.update_vertex_positions( - bodies.vertices(sim.poses_history[-1]) - ) + global playing + if imgui.Button("Play" if not playing else "Pause"): + playing = not playing + imgui.SameLine() + if imgui.Button("Step") or playing: + sim.step() + ps_mesh.update_vertex_positions( + bodies.vertices(sim.poses_history[-1]) + ) + imgui.SameLine() + if imgui.Button("Reset"): + sim.reset() + ps_mesh.update_vertex_positions( + bodies.vertices(sim.poses_history[-1]) + ) ps.set_user_callback(foo) diff --git a/python/src/candidates/candidates.cpp b/python/src/candidates/candidates.cpp index 55e50f548..345aade92 100644 --- a/python/src/candidates/candidates.cpp +++ b/python/src/candidates/candidates.cpp @@ -131,7 +131,7 @@ void define_candidates(py::module_& m) py::arg("broad_phase") = make_default_broad_phase(), py::arg("narrow_phase_ccd") = DEFAULT_NARROW_PHASE_CCD) .def( - "save_obj", &Candidates::save_obj, py::arg("filename"), + "write_obj", &Candidates::write_obj, py::arg("filename"), py::arg("vertices"), py::arg("edges"), py::arg("faces")) .def_readwrite("vv_candidates", &Candidates::vv_candidates) .def_readwrite("ev_candidates", &Candidates::ev_candidates) diff --git a/src/ipc/CMakeLists.txt b/src/ipc/CMakeLists.txt index ab9cdaff4..d3579ccfe 100644 --- a/src/ipc/CMakeLists.txt +++ b/src/ipc/CMakeLists.txt @@ -21,6 +21,7 @@ add_subdirectory(distance) add_subdirectory(dynamics) add_subdirectory(friction) add_subdirectory(implicits) +add_subdirectory(io) add_subdirectory(potentials) add_subdirectory(tangent) add_subdirectory(utils) \ No newline at end of file diff --git a/src/ipc/candidates/candidates.cpp b/src/ipc/candidates/candidates.cpp index bdaffce9a..029de09fb 100644 --- a/src/ipc/candidates/candidates.cpp +++ b/src/ipc/candidates/candidates.cpp @@ -3,8 +3,8 @@ #include #include #include +#include #include -#include #include #include @@ -384,7 +384,7 @@ const CollisionStencil& Candidates::operator[](size_t i) const throw std::out_of_range("Candidate index is out of range!"); } -bool Candidates::save_obj( +bool Candidates::write_obj( const std::string& filename, Eigen::ConstRef vertices, Eigen::ConstRef edges, @@ -395,13 +395,17 @@ bool Candidates::save_obj( return false; } int v_offset = 0; - ipc::save_obj(obj, vertices, edges, faces, vv_candidates, v_offset); + ipc::write_candidates_obj( + obj, vertices, edges, faces, vv_candidates, v_offset); v_offset += vv_candidates.size() * 2; - ipc::save_obj(obj, vertices, edges, faces, ev_candidates, v_offset); + ipc::write_candidates_obj( + obj, vertices, edges, faces, ev_candidates, v_offset); v_offset += ev_candidates.size() * 3; - ipc::save_obj(obj, vertices, edges, faces, ee_candidates, v_offset); + ipc::write_candidates_obj( + obj, vertices, edges, faces, ee_candidates, v_offset); v_offset += ee_candidates.size() * 4; - ipc::save_obj(obj, vertices, faces, faces, fv_candidates, v_offset); + ipc::write_candidates_obj( + obj, vertices, faces, faces, fv_candidates, v_offset); return true; } diff --git a/src/ipc/candidates/candidates.hpp b/src/ipc/candidates/candidates.hpp index 76e863113..f3e31b807 100644 --- a/src/ipc/candidates/candidates.hpp +++ b/src/ipc/candidates/candidates.hpp @@ -112,7 +112,7 @@ class Candidates { const NarrowPhaseCCD& narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD) const; - bool save_obj( + bool write_obj( const std::string& filename, Eigen::ConstRef vertices, Eigen::ConstRef edges, diff --git a/src/ipc/dynamics/rigid/CMakeLists.txt b/src/ipc/dynamics/rigid/CMakeLists.txt index a01f3638c..00820d997 100644 --- a/src/ipc/dynamics/rigid/CMakeLists.txt +++ b/src/ipc/dynamics/rigid/CMakeLists.txt @@ -1,4 +1,6 @@ set(SOURCES + body_forces.cpp + body_forces.hpp inertial_term.cpp inertial_term.hpp mass.cpp diff --git a/src/ipc/dynamics/rigid/body_forces.cpp b/src/ipc/dynamics/rigid/body_forces.cpp new file mode 100644 index 000000000..7bb38e124 --- /dev/null +++ b/src/ipc/dynamics/rigid/body_forces.cpp @@ -0,0 +1,179 @@ +#include "body_forces.hpp" + +#include +#include + +#include + +namespace ipc::rigid { + +void BodyForces::update(const RigidBodies& bodies) +{ + const double dt_sq = time_integrator->dt * time_integrator->dt; + + forces.resize(bodies.num_bodies()); + torques.resize(bodies.num_bodies()); + + tbb::parallel_for( + tbb::blocked_range(0, bodies.num_bodies()), + [&](const tbb::blocked_range& r) { + for (size_t i = r.begin(); i < r.end(); ++i) { + forces[i] = -dt_sq + * (bodies[i].mass() * gravity() + + bodies[i].external_force().position); + + const auto& torque = bodies[i].external_force().rotation; + + // Add external torques to the predicted pose + if (torque.size() == 3) { + const auto& Q = time_integrator->pose(i).rotation; + // Transform the world space torque into body space + const Eigen::Matrix3d Tau = + Q.transpose() * cross_product_matrix(torque); + torques[i] = -dt_sq * Tau; + } else { + assert(torque.size() == 1); + torques[i].resize(1, 1); + torques[i](0, 0) = -dt_sq * torque(0); + } + } + }); +} + +// ---- Cumulative functions --------------------------------------------------- + +double BodyForces::operator()( + const RigidBodies& bodies, Eigen::ConstRef x) +{ + assert(predicted_poses().size() == bodies.num_bodies()); + + const int ndof = x.size() / bodies.num_bodies(); + + double energy = 0.0; + for (size_t i = 0; i < bodies.num_bodies(); ++i) { + energy += operator()( + bodies[i], x.segment(i * ndof, ndof), forces[i], torques[i]); + } + return energy; +} + +Eigen::VectorXd BodyForces::gradient( + const RigidBodies& bodies, Eigen::ConstRef x) +{ + assert(predicted_poses().size() == bodies.num_bodies()); + + const int ndof = x.size() / bodies.num_bodies(); + + Eigen::VectorXd grad = Eigen::VectorXd::Zero(x.size()); + for (size_t i = 0; i < bodies.num_bodies(); ++i) { + grad.segment(i * ndof, ndof) = gradient( + bodies[i], x.segment(i * ndof, ndof), forces[i], torques[i]); + } + return grad; +} + +Eigen::MatrixXd BodyForces::hessian( + const RigidBodies& bodies, + Eigen::ConstRef x, + const PSDProjectionMethod project_hessian_to_psd) +{ + assert(predicted_poses().size() == bodies.num_bodies()); + + const int ndof = x.size() / bodies.num_bodies(); + + Eigen::MatrixXd hess(x.size(), x.size()); + for (size_t i = 0; i < bodies.num_bodies(); ++i) { + hess.block(i * ndof, i * ndof, ndof, ndof) = hessian( + bodies[i], x.segment(i * ndof, ndof), forces[i], torques[i], + project_hessian_to_psd); + } + return hess; +} + +// ---- Per-body functions ----------------------------------------------------- + +double BodyForces::operator()( + const RigidBody& body, + Eigen::ConstRef x, + Eigen::ConstRef force, + Eigen::ConstRef torque) const +{ + double energy = 0.0; + + // if (!body.is_dof_fixed.head(pose.pos_ndof()).all()) + { + energy += x.head(forces.size()).dot(force); + } + + // Rotational energy + // if (!body.is_dof_fixed.tail(pose.rot_ndof()).all()) + { + if (torque.size() == 9) { + const Eigen::Matrix3d Q = rotation_vector_to_matrix(x.tail<3>()); + energy += (Q.transpose() * torque).trace(); + } else { + assert(torque.size() == 1); + energy += x(2) * torque(0, 0); + } + } + + return energy; +} + +VectorMax6d BodyForces::gradient( + const RigidBody& body, + Eigen::ConstRef x, + Eigen::ConstRef force, + Eigen::ConstRef torque) const +{ + VectorMax6d grad = VectorMax6d::Zero(x.size()); + + // if (!body.is_dof_fixed.head(pose.pos_ndof()).all()) + { + grad.head(gravity().size()) = force; + } + + // Rotational energy + // if (!body.is_dof_fixed.tail(pose.rot_ndof()).all()) + { + if (torque.size() == 9) { + const Eigen::Matrix dQ_dx = + rotation_vector_to_matrix_jacobian(x.tail<3>()); + grad.tail<3>() = dQ_dx.transpose() * torque.reshaped(); + } else { + assert(torque.size() == 1); + grad(2) = torque(0, 0); + } + } + + return grad; +} + +MatrixMax6d BodyForces::hessian( + const RigidBody& body, + Eigen::ConstRef x, + Eigen::ConstRef force, + Eigen::ConstRef torque, + const PSDProjectionMethod project_hessian_to_psd) const +{ + MatrixMax6d hess = MatrixMax6d::Zero(x.size(), x.size()); + + // Rotational energy + // if (!body.is_dof_fixed.tail(pose.rot_ndof()).all()) + { + if (torque.size() == 9) { + const Eigen::Matrix d2Q_dx2 = + rotation_vector_to_matrix_hessian(x.tail<3>()); + + const Eigen::Matrix3d hess_rotation = + (d2Q_dx2.transpose() * torque.reshaped()).reshaped(3, 3); + + hess.bottomRightCorner<3, 3>() = + project_to_psd(hess_rotation, project_hessian_to_psd); + } + } + + return hess; +} + +} // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/body_forces.hpp b/src/ipc/dynamics/rigid/body_forces.hpp new file mode 100644 index 000000000..487d781b1 --- /dev/null +++ b/src/ipc/dynamics/rigid/body_forces.hpp @@ -0,0 +1,99 @@ +#pragma once + +#include +#include +#include + +namespace ipc::rigid { + +/// @brief Class representing the term ½m‖q - q̂‖² + ½tr((Q - Q̂) J (Q - Q̂)ᵀ) +class BodyForces { +public: + BodyForces(const std::shared_ptr& _time_integrator) + : time_integrator(_time_integrator) + { + } + + /// @brief Update the predicted poses of the rigid bodies. + /// @param bodies The collection of rigid bodies. + void update(const RigidBodies& bodies); + + // ---- Cumulative functions ----------------------------------------------- + + /// @brief Compute the total energy for all rigid bodies. + /// @param bodies The collection of rigid bodies. + /// @param x The DOFs of the rigid bodies, where the first 3 entries are the positions and the last 3 entries are the rotations. + /// @return The total energy of the rigid bodies. + double + operator()(const RigidBodies& bodies, Eigen::ConstRef x); + + /// @brief Compute the gradient of the total energy for all rigid bodies. + /// @param bodies The collection of rigid bodies. + /// @param x The DOFs of the rigid bodies, where the first 3 entries are the positions and the last 3 entries are the rotations. + /// @return The gradient of the total energy of the rigid bodies. + Eigen::VectorXd + gradient(const RigidBodies& bodies, Eigen::ConstRef x); + + /// @brief Compute the Hessian of the total energy for all rigid bodies. + /// @param bodies The collection of rigid bodies. + /// @param x The DOFs of the rigid bodies, where the first 3 entries are the positions and the last 3 entries are the rotations. + /// @return The Hessian of the total energy of the rigid bodies. + Eigen::MatrixXd hessian( + const RigidBodies& bodies, + Eigen::ConstRef x, + const PSDProjectionMethod project_hessian_to_psd = + PSDProjectionMethod::NONE); + + // ---- Per-body functions ------------------------------------------------- + + /// @brief Compute the energy of a rigid body at a given pose. + /// @param body The rigid body. + /// @param pose The pose of the rigid body. + /// @return The energy of the rigid body at the given pose. + double operator()( + const RigidBody& body, + Eigen::ConstRef x, + Eigen::ConstRef q_hat, + Eigen::ConstRef Q_hat) const; + + /// @brief Compute the gradient of the energy of a rigid body at a given pose. + /// @param body The rigid body. + /// @param x The pose of the rigid body. + /// @param q_hat The predicted rotation of the rigid body. + /// @param Q_hat The predicted rotation matrix of the rigid body. + /// @return The gradient of the energy of the rigid body at the given pose. + VectorMax6d gradient( + const RigidBody& body, + Eigen::ConstRef x, + Eigen::ConstRef q_hat, + Eigen::ConstRef Q_hat) const; + + /// @brief Compute the Hessian of the energy of a rigid body at a given pose. + /// @param body The rigid body. + /// @param x The pose of the rigid body. + /// @param q_hat The predicted rotation of the rigid body. + /// @param Q_hat The predicted rotation matrix of the rigid body. + /// @return The Hessian of the energy of the rigid body at the given pose. + MatrixMax6d hessian( + const RigidBody& body, + Eigen::ConstRef x, + Eigen::ConstRef q_hat, + Eigen::ConstRef Q_hat, + const PSDProjectionMethod project_hessian_to_psd = + PSDProjectionMethod::NONE) const; + + // ---- Predicted poses ---------------------------------------------------- + + const VectorMax3d& gravity() const { return m_gravity; } + void set_gravity(const VectorMax3d& gravity) { m_gravity = gravity; } + +private: + const std::shared_ptr time_integrator; + + std::vector forces; + std::vector torques; + + VectorMax3d m_gravity = VectorMax3d::Zero(3); +}; + +} // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/inertial_term.cpp b/src/ipc/dynamics/rigid/inertial_term.cpp index dcc8b5fd5..7e6f998da 100644 --- a/src/ipc/dynamics/rigid/inertial_term.cpp +++ b/src/ipc/dynamics/rigid/inertial_term.cpp @@ -3,62 +3,14 @@ #include #include -namespace ipc::rigid { +#include -namespace { - inline Eigen::Matrix3d - cross_product_matrix(Eigen::ConstRef x) - { - Eigen::Matrix3d X; - X << 0, -x.z(), x.y(), // - x.z(), 0, -x.x(), // - -x.y(), x.x(), 0; - return X; - } -} // namespace +namespace ipc::rigid { void InertialTerm::update(const RigidBodies& bodies) { // Update the predicted poses based on the current time integrator state m_predicted_poses = time_integrator->predicted_pose(); - - // Gravity in the y-direction - const double dt_sq = time_integrator->dt * time_integrator->dt; - - tbb::parallel_for( - tbb::blocked_range(0, m_predicted_poses.size()), - [&](const tbb::blocked_range& r) { - for (size_t i = r.begin(); i < r.end(); ++i) { - // Add gravity to the predicted pose - // TODO: Make this configurable - m_predicted_poses[i].position.y() += dt_sq * -9.81; - - const auto& force = bodies[i].external_force().position; - const auto& torque = bodies[i].external_force().rotation; - - // Add external forces to the predicted pose - if (!force.isZero()) { - m_predicted_poses[i].position += - dt_sq * force / bodies[i].mass(); - } - - // Add external torques to the predicted pose - if (!torque.isZero()) { - if (torque.size() == 3) { - const auto& Q = time_integrator->pose(i).rotation; - // Transform the world space torque into body space - const Eigen::Matrix3d Tau = - Q.transpose() * cross_product_matrix(torque); - m_predicted_poses[i].rotation += - dt_sq * bodies[i].J().inverse() * Tau; - } else { - assert(torque.size() == 1); - m_predicted_poses[i].rotation(0) += dt_sq * torque(0) - / bodies[i].moment_of_inertia()(0); - } - } - } - }); } // ---- Cumulative functions --------------------------------------------------- diff --git a/src/ipc/dynamics/rigid/pose.hpp b/src/ipc/dynamics/rigid/pose.hpp index 20c7af958..6d21419a9 100644 --- a/src/ipc/dynamics/rigid/pose.hpp +++ b/src/ipc/dynamics/rigid/pose.hpp @@ -60,6 +60,14 @@ struct Pose { return rotation_vector_to_matrix(rotation); } + Eigen::Quaternion quaternion() const + { + assert(rotation.size() == 3); + double angle = rotation.norm(); + Eigen::Vector3d axis = rotation / angle; + return Eigen::Quaternion(Eigen::AngleAxis(angle, axis)); + } + Eigen::MatrixXd transform_vertices(Eigen::ConstRef V) const { // Compute: R(θ) V + p diff --git a/src/ipc/dynamics/rigid/rigid_bodies.hpp b/src/ipc/dynamics/rigid/rigid_bodies.hpp index a6de70b3f..a46556ebb 100644 --- a/src/ipc/dynamics/rigid/rigid_bodies.hpp +++ b/src/ipc/dynamics/rigid/rigid_bodies.hpp @@ -38,9 +38,63 @@ class RigidBodies : public CollisionMesh { return V; } + /// @brief Get the rigid body at index i. + /// @param i Index of the rigid body. + /// @return Reference to the rigid body at index i. + const RigidBody& operator[](size_t i) const { return bodies[i]; } + + /// @brief Get the number of rigid bodies in the system. + /// @return Number of rigid bodies. size_t num_bodies() const { return bodies.size(); } - const RigidBody& operator[](size_t i) const { return bodies[i]; } + /// @brief Get the number of vertices in the i-th rigid body mesh. + /// @param i Index of the rigid body mesh. + /// @return Number of vertices in the i-th rigid body mesh. + size_t num_body_vertices(size_t i) const + { + return body_vertex_starts[i + 1] - body_vertex_starts[i]; + } + + /// @brief Get the number of edges in the i-th rigid body mesh. + /// @param i Index of the rigid body mesh. + /// @return Number of edges in the i-th rigid body mesh. + size_t num_body_edges(size_t i) const + { + return body_edge_starts[i + 1] - body_edge_starts[i]; + } + + /// @brief Get the number of faces in the i-th rigid body mesh. + /// @param i Index of the rigid body mesh. + /// @return Number of faces in the i-th rigid body mesh. + size_t num_body_faces(size_t i) const + { + return body_face_starts[i + 1] - body_face_starts[i]; + } + + /// @brief Get the vertices of the i-th rigid body mesh. + /// @param i Index of the rigid body mesh. + /// @return Vertices of the i-th rigid body mesh. + auto body_vertices(size_t i) const + { + return rest_positions().middleRows( + body_vertex_starts[i], num_body_vertices(i)); + } + + /// @brief Get the edges of the i-th rigid body mesh. + /// @param i Index of the rigid body mesh. + /// @return Edges of the i-th rigid body mesh. + auto body_edges(size_t i) const + { + return edges().middleRows(body_edge_starts[i], num_body_edges(i)); + } + + /// @brief Get the faces of the i-th rigid body mesh. + /// @param i Index of the rigid body mesh. + /// @return Faces of the i-th rigid body mesh. + auto body_faces(size_t i) const + { + return faces().middleRows(body_face_starts[i], num_body_faces(i)); + } private: std::vector bodies; diff --git a/src/ipc/dynamics/rigid/rigid_body.hpp b/src/ipc/dynamics/rigid/rigid_body.hpp index 54e8c2184..6216e669e 100644 --- a/src/ipc/dynamics/rigid/rigid_body.hpp +++ b/src/ipc/dynamics/rigid/rigid_body.hpp @@ -7,6 +7,16 @@ namespace ipc::rigid { class RigidBody { +public: + enum class Type { + /// @brief Static rigid body, does not move + STATIC, + /// @brief Kinematic rigid body, moves but does not respond to forces + KINEMATIC, + /// @brief Dynamic rigid body, moves and responds to forces + DYNAMIC + }; + public: RigidBody( Eigen::Ref vertices, diff --git a/src/ipc/dynamics/rigid/simulator.cpp b/src/ipc/dynamics/rigid/simulator.cpp index 2c7deaca6..34256f910 100644 --- a/src/ipc/dynamics/rigid/simulator.cpp +++ b/src/ipc/dynamics/rigid/simulator.cpp @@ -4,6 +4,8 @@ #include #include +#include + namespace ipc::rigid { Simulator::Simulator( @@ -12,14 +14,26 @@ Simulator::Simulator( const double dt) : m_bodies(std::move(_bodies)) { + assert(initial_poses.size() == m_bodies->num_bodies()); m_pose_history.push_back(initial_poses); Eigen::VectorXd x0 = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); for (size_t i = 0; i < m_bodies->num_bodies(); ++i) { x0.segment<3>(12 * i) = initial_poses[i].position; - x0.segment<9>(12 * i) = initial_poses[i].rotation_matrix().reshaped(); + x0.segment<9>(12 * i + 3) = + initial_poses[i].rotation_matrix().reshaped(); } Eigen::VectorXd v0 = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); + for (size_t i = 0; i < m_bodies->num_bodies(); ++i) { + // v0.segment<3>(12 * i).y() = 10; + + // ω = R₀ᵀω₀ (ω₀ expressed in body coordinates) + Eigen::Vector3d omega(-100 * igl::PI / 180, 0, 0); + omega = (*m_bodies)[i].R0().transpose() * omega; + Eigen::Matrix3d Q_t0 = initial_poses[i].rotation_matrix(); + v0.segment<9>(12 * i + 3) = + (Q_t0 * cross_product_matrix(omega)).reshaped(); + } Eigen::VectorXd a0 = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); // Initialize the time integrator @@ -53,22 +67,54 @@ void Simulator::step() { std::vector poses = m_pose_history.back(); - // TODO: Solve the implicit time integration problem here - // poses = m_solver->solve(poses); - Pose delta(Eigen::Vector3d::Zero(), Eigen::Vector3d(0.05, 0, 0)); - for (int i = 0; i < m_bodies->num_bodies(); ++i) { - poses[i] = delta * poses[i]; + m_inertial_term->update(*m_bodies); + + Eigen::VectorXd x = Eigen::VectorXd(6 * m_bodies->num_bodies()); + for (size_t i = 0; i < m_bodies->num_bodies(); ++i) { + x.segment<3>(6 * i) = m_pose_history.back()[i].position; + x.segment<3>(6 * i + 3) = m_pose_history.back()[i].rotation; + } + + double dx, grad_norm; + int iter = 0; + do { + Eigen::VectorXd grad = m_inertial_term->gradient(*m_bodies, x); + if ((grad_norm = grad.norm()) < 1e-6) { + break; + } + Eigen::MatrixXd hess = + m_inertial_term->hessian(*m_bodies, x, PSDProjectionMethod::ABS); + Eigen::VectorXd step = -hess.lu().solve(grad); + dx = step.norm(); + double alpha = 1.0; + double Ex = (*m_inertial_term)(*m_bodies, x); + while ((*m_inertial_term)(*m_bodies, x + alpha * step) >= Ex) { + alpha *= 0.5; + } + x += alpha * step; + logger().debug( + "step: dx={:g} norm(grad)={:g} norm(hess)={:g} alpha={:g}", dx, + grad_norm, hess.norm(), alpha); + } while (dx > m_time_integrator->dt * 1e-3 && ++iter < 100); + logger().info( + "converged: iter={} dx={:g} norm(grad)={:g} norm(hess)={:g}", iter, dx, + grad_norm); + + for (size_t i = 0; i < m_bodies->num_bodies(); ++i) { + poses[i].position = x.segment<3>(6 * i); + poses[i].rotation = x.segment<3>(6 * i + 3); } m_pose_history.push_back(poses); - Eigen::VectorXd x = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); + Eigen::VectorXd X = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); for (size_t i = 0; i < m_bodies->num_bodies(); ++i) { - x.segment<3>(12 * i) = poses[i].position; - x.segment<9>(12 * i) = poses[i].rotation_matrix().reshaped(); + X.segment<3>(12 * i) = x.segment<3>(6 * i); + X.segment<9>(12 * i + 3) = + rotation_vector_to_matrix(x.segment<3>(6 * i + 3)).reshaped(); } - m_time_integrator->update(x); + m_time_integrator->update(X); m_t += m_time_integrator->dt; } @@ -81,9 +127,9 @@ void Simulator::reset() Eigen::VectorXd x0 = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); for (size_t i = 0; i < m_bodies->num_bodies(); ++i) { - x0.segment<3>(12 * i) = m_pose_history[0][i].position; - x0.segment<9>(12 * i) = - m_pose_history[0][i].rotation_matrix().reshaped(); + x0.segment<3>(12 * i) = m_pose_history.front()[i].position; + x0.segment<9>(12 * i + 3) = + m_pose_history.front()[i].rotation_matrix().reshaped(); } Eigen::VectorXd v0 = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); Eigen::VectorXd a0 = Eigen::VectorXd::Zero(12 * m_bodies->num_bodies()); diff --git a/src/ipc/dynamics/rigid/simulator.hpp b/src/ipc/dynamics/rigid/simulator.hpp index afa5f4361..69f2b4fd9 100644 --- a/src/ipc/dynamics/rigid/simulator.hpp +++ b/src/ipc/dynamics/rigid/simulator.hpp @@ -43,7 +43,7 @@ class Simulator { // Accessors // ----------------------------------------------------------------------- - const std::vector>& poses_history() const + const std::list>& poses_history() const { return m_pose_history; } @@ -51,6 +51,14 @@ class Simulator { const std::shared_ptr& bodies() const { return m_bodies; } double t() const { return m_t; } + // double dt() const { return m_time_integrator->dt; } + // void set_dt(const double dt) { m_time_integrator->set_dt(dt); } + + // VectorMax3d gravity() const { return m_inertial_term->gravity(); } + // void set_gravity(const VectorMax3d& gravity) + // { + // m_inertial_term->set_gravity(gravity); + // } protected: /// @brief Bodies in the simulation @@ -62,7 +70,7 @@ class Simulator { /// @brief Inertial term for the rigid body dynamics std::shared_ptr m_inertial_term; - std::vector> m_pose_history; + std::list> m_pose_history; /// @brief t Current simulation time double m_t = 0.0; diff --git a/src/ipc/io/CMakeLists.txt b/src/ipc/io/CMakeLists.txt new file mode 100644 index 000000000..303126f4a --- /dev/null +++ b/src/ipc/io/CMakeLists.txt @@ -0,0 +1,8 @@ +set(SOURCES + write_candidates_obj.cpp + write_candidates_obj.hpp + write_gltf.cpp + write_gltf.hpp +) + +target_sources(ipc_toolkit PRIVATE ${SOURCES}) \ No newline at end of file diff --git a/src/ipc/utils/save_obj.cpp b/src/ipc/io/write_candidates_obj.cpp similarity index 95% rename from src/ipc/utils/save_obj.cpp rename to src/ipc/io/write_candidates_obj.cpp index 3672c35dd..4039618f3 100644 --- a/src/ipc/utils/save_obj.cpp +++ b/src/ipc/io/write_candidates_obj.cpp @@ -1,4 +1,4 @@ -#include "save_obj.hpp" +#include "write_candidates_obj.hpp" #include #include @@ -10,7 +10,7 @@ namespace ipc { template <> -void save_obj( +void write_candidates_obj( std::ostream& out, Eigen::ConstRef V, Eigen::ConstRef, @@ -26,7 +26,7 @@ void save_obj( } template <> -void save_obj( +void write_candidates_obj( std::ostream& out, Eigen::ConstRef V, Eigen::ConstRef E, @@ -46,7 +46,7 @@ void save_obj( } template <> -void save_obj( +void write_candidates_obj( std::ostream& out, Eigen::ConstRef V, Eigen::ConstRef E, @@ -68,7 +68,7 @@ void save_obj( } template <> -void save_obj( +void write_candidates_obj( std::ostream& out, Eigen::ConstRef V, Eigen::ConstRef E, @@ -89,7 +89,7 @@ void save_obj( } template <> -void save_obj( +void write_candidates_obj( std::ostream& out, Eigen::ConstRef V, Eigen::ConstRef E, diff --git a/src/ipc/utils/save_obj.hpp b/src/ipc/io/write_candidates_obj.hpp similarity index 87% rename from src/ipc/utils/save_obj.hpp rename to src/ipc/io/write_candidates_obj.hpp index 819b323f2..dc8adfad6 100644 --- a/src/ipc/utils/save_obj.hpp +++ b/src/ipc/io/write_candidates_obj.hpp @@ -9,7 +9,7 @@ namespace ipc { template -void save_obj( +void write_candidates_obj( std::ostream& out, Eigen::ConstRef V, Eigen::ConstRef E, @@ -18,7 +18,7 @@ void save_obj( const int v_offset = 0); template -bool save_obj( +bool write_candidates_obj( const std::string& filename, Eigen::ConstRef V, Eigen::ConstRef E, @@ -29,7 +29,7 @@ bool save_obj( if (!obj.is_open()) { return false; } - save_obj(obj, V, E, F, candidates); + write_candidates_obj(obj, V, E, F, candidates); return true; } diff --git a/src/ipc/io/write_gltf.cpp b/src/ipc/io/write_gltf.cpp new file mode 100644 index 000000000..d6efa3806 --- /dev/null +++ b/src/ipc/io/write_gltf.cpp @@ -0,0 +1,244 @@ +#include "write_gltf.hpp" + +#include + +#include + +namespace ipc::rigid { + +bool write_gltf( + const std::string& filename, + const RigidBodies& bodies, + const std::list>& poses, + double timestep, + bool embed_buffers, + bool write_binary, + bool prettyPrint) +{ + typedef float Float; + int float_component_type; + if (std::is_same::value) { + float_component_type = TINYGLTF_COMPONENT_TYPE_FLOAT; + } else { + // assert(std::is_same::value); + float_component_type = TINYGLTF_COMPONENT_TYPE_DOUBLE; + } + + using namespace tinygltf; + + assert(bodies.dim() == 3); + size_t num_bodies = bodies.num_bodies(); + assert(poses.size() > 0); + size_t num_steps = poses.size(); + + Model model; + model.defaultScene = 0; + + model.asset.version = "2.0"; + model.asset.generator = "RigidIPC"; + + Scene& scene = model.scenes.emplace_back(); + scene.name = "RigidIPCSimulation"; + scene.nodes.resize(num_bodies); + std::iota(scene.nodes.begin(), scene.nodes.end(), 0); + + model.nodes.resize(num_bodies); + model.animations.resize(1); + Animation& animation = model.animations[0]; + animation.name = "Simulation"; + animation.channels.resize(2 * num_bodies); + animation.samplers.resize(2 * num_bodies); + model.meshes.resize(num_bodies); + // Four accessors per bidy: vertices, faces, translations, and rotations + model.accessors.resize(4 * num_bodies + 1); + { + Accessor& accessor = model.accessors[2 * num_bodies]; + accessor.name = "Times"; + accessor.bufferView = 2 * num_bodies; + accessor.componentType = float_component_type; + accessor.count = num_steps; + accessor.minValues.push_back(timestep); + accessor.maxValues.push_back(num_steps * timestep); + accessor.type = TINYGLTF_TYPE_SCALAR; + } + + for (int i = 0; i < num_bodies; i++) { + Node& node = model.nodes[i]; + node.mesh = i; + std::string body_name = "Body" + std::to_string(i); + node.name = body_name; + node.translation = { { poses.front()[i].position.x(), + poses.front()[i].position.y(), + poses.front()[i].position.z() } }; + // NOTE: Use identity for the first frame by applying the initial + // rotation to the vertices and removing the rotation from further + // rotations. + // Eigen::Quaternion q = poses[0][i].construct_quaternion(); + Eigen::Quaternion q = Eigen::Quaternion::Identity(); + node.rotation = { { q.x(), q.y(), q.z(), q.w() } }; + + animation.channels[2 * i + 0].sampler = 2 * i; + animation.channels[2 * i + 0].target_node = i; + animation.channels[2 * i + 0].target_path = "translation"; + animation.channels[2 * i + 1].sampler = 2 * i + 1; + animation.channels[2 * i + 1].target_node = i; + animation.channels[2 * i + 1].target_path = "rotation"; + + animation.samplers[2 * i + 0].input = 2 * num_bodies; + animation.samplers[2 * i + 0].output = 2 * num_bodies + 2 * i + 1; + animation.samplers[2 * i + 0].interpolation = "LINEAR"; + animation.samplers[2 * i + 1].input = 2 * num_bodies; + animation.samplers[2 * i + 1].output = 2 * num_bodies + 2 * i + 2; + animation.samplers[2 * i + 1].interpolation = "LINEAR"; + + Mesh& mesh = model.meshes[i]; + mesh.name = body_name; + Primitive& primitive = mesh.primitives.emplace_back(); + primitive.attributes["POSITION"] = 2 * i; + primitive.indices = 2 * i + 1; + primitive.mode = TINYGLTF_MODE_TRIANGLES; + + Accessor* accessor = &model.accessors[2 * i]; + accessor->name = body_name + "Vertices"; + accessor->bufferView = 2 * i; + accessor->componentType = float_component_type; + accessor->count = bodies.num_body_vertices(i); + // accessor->max = ...; + // accessor->min = ...; + accessor->type = TINYGLTF_TYPE_VEC3; + + accessor = &model.accessors[2 * i + 1]; + accessor->name = body_name + "Faces"; + accessor->bufferView = 2 * i + 1; + accessor->componentType = TINYGLTF_COMPONENT_TYPE_UNSIGNED_INT; + accessor->count = 3 * bodies.num_body_faces(i); + accessor->type = TINYGLTF_TYPE_SCALAR; + + accessor = &model.accessors[2 * num_bodies + 2 * i + 1]; + accessor->name = body_name + "Translations"; + accessor->bufferView = 2 * num_bodies + 2 * i + 1; + accessor->componentType = float_component_type; + accessor->count = num_steps; + accessor->type = TINYGLTF_TYPE_VEC3; + + accessor = &model.accessors[2 * num_bodies + 2 * i + 2]; + accessor->name = body_name + "Rotations"; + accessor->bufferView = 2 * num_bodies + 2 * i + 2; + accessor->componentType = float_component_type; + accessor->count = num_steps; + accessor->type = TINYGLTF_TYPE_VEC4; + } + + /////////////////////////////////////////////////////////////////////////// + + model.bufferViews.resize(4 * num_bodies + 1); + size_t byte_offset = 0; + for (int i = 0; i < num_bodies; i++) { + std::string body_name = "Body" + std::to_string(i); + + BufferView* buffer_view = &model.bufferViews[2 * i]; + buffer_view->name = body_name + "Vertices"; + buffer_view->buffer = 0; + buffer_view->byteLength = + sizeof(Float) * bodies.body_vertices(i).size(); + buffer_view->byteOffset = byte_offset; + byte_offset += buffer_view->byteLength; + + buffer_view = &model.bufferViews[2 * i + 1]; + buffer_view->name = body_name + "Faces"; + buffer_view->buffer = 0; + buffer_view->byteLength = + sizeof(unsigned int) * bodies.body_faces(i).size(); + buffer_view->byteOffset = byte_offset; + byte_offset += buffer_view->byteLength; + } + { + BufferView& buffer_view = model.bufferViews[2 * num_bodies]; + buffer_view.name = "Times"; + buffer_view.buffer = 0; + buffer_view.byteLength = num_steps * sizeof(Float); + buffer_view.byteOffset = byte_offset; + byte_offset += buffer_view.byteLength; + } + for (int i = 0; i < num_bodies; i++) { + std::string body_name = "Body" + std::to_string(i); + + BufferView* buffer_view = + &model.bufferViews[2 * num_bodies + 2 * i + 1]; + buffer_view->name = body_name + "Translations"; + buffer_view->buffer = 0; + buffer_view->byteLength = 3 * sizeof(Float) * num_steps; + buffer_view->byteOffset = byte_offset; + byte_offset += buffer_view->byteLength; + + buffer_view = &model.bufferViews[2 * num_bodies + 2 * i + 2]; + buffer_view->name = body_name + "Rotations"; + buffer_view->buffer = 0; + buffer_view->byteLength = 4 * sizeof(Float) * num_steps; + buffer_view->byteOffset = byte_offset; + byte_offset += buffer_view->byteLength; + } + + /////////////////////////////////////////////////////////////////////////// + + std::vector byte_data(byte_offset); + size_t byte_i = 0; + for (int i = 0; i < num_bodies; i++) { + // NOTE: Apply the initial rotation to the vertices + Eigen::MatrixXd V = + bodies.body_vertices(i) * bodies[i].R0().transpose(); + for (int r = 0; r < V.rows(); r++) { + for (int c = 0; c < V.cols(); c++) { + Float v = V(r, c); + std::memcpy(&byte_data[byte_i], &v, sizeof(Float)); + byte_i += sizeof(Float); + } + } + + Eigen::MatrixXi F = bodies.body_faces(i); + for (int r = 0; r < F.rows(); r++) { + for (int c = 0; c < F.cols(); c++) { + unsigned int fij = F(r, c); + std::memcpy(&byte_data[byte_i], &fij, sizeof(unsigned int)); + byte_i += sizeof(unsigned int); + } + } + } + for (int i = 0; i < num_steps; i++) { + Float t = i * timestep; + std::memcpy(&byte_data[byte_i], &t, sizeof(Float)); + byte_i += sizeof(Float); + } + for (int i = 0; i < num_bodies; i++) { + for (const auto& poses_j : poses) { + Eigen::Vector3d p = poses_j[i].position; + for (int d = 0; d < p.size(); d++) { + Float pd = p[d]; + std::memcpy(&byte_data[byte_i], &pd, sizeof(Float)); + byte_i += sizeof(Float); + } + } + + const Eigen::Quaternion q0(Eigen::Matrix3d(bodies[i].R0())); + for (const auto& poses_j : poses) { + // NOTE: Apply the inverse of the initial rotation to the + // quaternion to get the rotation relative to the input orientation. + Eigen::Quaternion quat = + poses_j[i].quaternion() * q0.inverse(); + Eigen::Vector4d q(quat.x(), quat.y(), quat.z(), quat.w()); + for (int d = 0; d < q.size(); d++) { + Float qd = q[d]; + std::memcpy(&byte_data[byte_i], &qd, sizeof(Float)); + byte_i += sizeof(Float); + } + } + } + assert(byte_i == byte_data.size()); + + model.buffers.emplace_back().data = byte_data; + return TinyGLTF().WriteGltfSceneToFile( + &model, filename, + /*embedImages=*/true, embed_buffers, prettyPrint, write_binary); +} + +} // namespace ipc::rigid diff --git a/src/ipc/io/write_gltf.hpp b/src/ipc/io/write_gltf.hpp new file mode 100644 index 000000000..7205a0e1d --- /dev/null +++ b/src/ipc/io/write_gltf.hpp @@ -0,0 +1,19 @@ +#pragma once + +#include + +#include +#include + +namespace ipc::rigid { + +bool write_gltf( + const std::string& filename, + const RigidBodies& bodies, + const std::list>& poses, + double timestep, + bool embed_buffers = true, + bool write_binary = true, + bool prettyPrint = true); + +} // namespace ipc::rigid diff --git a/src/ipc/utils/CMakeLists.txt b/src/ipc/utils/CMakeLists.txt index a90e531e1..7aaab797a 100644 --- a/src/ipc/utils/CMakeLists.txt +++ b/src/ipc/utils/CMakeLists.txt @@ -11,8 +11,6 @@ set(SOURCES logger.cpp logger.hpp merge_thread_local.hpp - save_obj.cpp - save_obj.hpp sinc.cpp sinc.hpp unordered_map_and_set.cpp diff --git a/src/ipc/utils/eigen_ext.hpp b/src/ipc/utils/eigen_ext.hpp index bf0698245..da38f6556 100644 --- a/src/ipc/utils/eigen_ext.hpp +++ b/src/ipc/utils/eigen_ext.hpp @@ -204,6 +204,15 @@ inline Eigen::MatrixXd to_X3d(Eigen::ConstRef vertices) return vertices_3d; } +inline Eigen::Matrix3d cross_product_matrix(Eigen::ConstRef x) +{ + Eigen::Matrix3d X; + X << 0, -x.z(), x.y(), // + x.z(), 0, -x.x(), // + -x.y(), x.x(), 0; + return X; +} + /// Eigen IO Format to format vectors like vertex rows in an OBJ file. static const Eigen::IOFormat OBJ_VERTEX_FORMAT = Eigen::IOFormat( Eigen::FullPrecision, Eigen::DontAlignCols, " ", "", "v ", "\n", "", ""); diff --git a/tests/src/tests/utils/test_utils.cpp b/tests/src/tests/utils/test_utils.cpp index 101953c47..89ac2caf8 100644 --- a/tests/src/tests/utils/test_utils.cpp +++ b/tests/src/tests/utils/test_utils.cpp @@ -7,7 +7,7 @@ #include #include #include -#include +#include #include @@ -66,7 +66,7 @@ TEST_CASE("Project to PD", "[utils][project_to_pd]") CHECK(A_pd.isApprox(A)); } -TEST_CASE("Save OBJ of candidates", "[utils][save_obj]") +TEST_CASE("Write OBJ of candidates", "[utils][write_candidates_obj]") { Eigen::MatrixXd V(4, 3); V.row(0) << 0, 0, 0; @@ -81,21 +81,21 @@ TEST_CASE("Save OBJ of candidates", "[utils][save_obj]") SECTION("VertexVertexCandidate") { std::stringstream ss; - ipc::save_obj( + ipc::write_candidates_obj( ss, V, E, F, { { ipc::VertexVertexCandidate(0, 1) } }); CHECK(ss.str() == "o VV\nv 0 0 0\nv 1 0 0\n"); } SECTION("EdgeVertexCandidate") { std::stringstream ss; - ipc::save_obj( + ipc::write_candidates_obj( ss, V, E, F, { { ipc::EdgeVertexCandidate(0, 0) } }); CHECK(ss.str() == "o EV\nv 1 0 0\nv 0 1 0\nv 0 0 0\nl 1 2\n"); } SECTION("EdgeEdgeCandidate") { std::stringstream ss; - ipc::save_obj( + ipc::write_candidates_obj( ss, V, E, F, { { ipc::EdgeEdgeCandidate(0, 1) } }); CHECK( ss.str() @@ -104,7 +104,7 @@ TEST_CASE("Save OBJ of candidates", "[utils][save_obj]") SECTION("FaceVertexCandidate") { std::stringstream ss; - ipc::save_obj( + ipc::write_candidates_obj( ss, V, E, F, { { ipc::FaceVertexCandidate(0, 0) } }); CHECK( ss.str() == "o FV\nv 1 0 0\nv 0 1 0\nv 0 0 1\nv 0 0 0\nf 1 2 3\n"); @@ -112,7 +112,7 @@ TEST_CASE("Save OBJ of candidates", "[utils][save_obj]") SECTION("EdgeFaceCandidate") { std::stringstream ss; - ipc::save_obj( + ipc::write_candidates_obj( ss, V, E, F, { { ipc::EdgeFaceCandidate(0, 0) } }); CHECK( ss.str() From 69878721942e919a9fbf52a7185bf1dcba0a9e23 Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Sun, 17 Aug 2025 20:43:18 -0400 Subject: [PATCH 12/24] Remove duplicate cross_product_matrix function --- src/ipc/dynamics/rigid/body_forces.cpp | 6 ------ src/ipc/utils/eigen_ext.hpp | 9 --------- 2 files changed, 15 deletions(-) diff --git a/src/ipc/dynamics/rigid/body_forces.cpp b/src/ipc/dynamics/rigid/body_forces.cpp index 7bb38e124..bf0e936e3 100644 --- a/src/ipc/dynamics/rigid/body_forces.cpp +++ b/src/ipc/dynamics/rigid/body_forces.cpp @@ -45,8 +45,6 @@ void BodyForces::update(const RigidBodies& bodies) double BodyForces::operator()( const RigidBodies& bodies, Eigen::ConstRef x) { - assert(predicted_poses().size() == bodies.num_bodies()); - const int ndof = x.size() / bodies.num_bodies(); double energy = 0.0; @@ -60,8 +58,6 @@ double BodyForces::operator()( Eigen::VectorXd BodyForces::gradient( const RigidBodies& bodies, Eigen::ConstRef x) { - assert(predicted_poses().size() == bodies.num_bodies()); - const int ndof = x.size() / bodies.num_bodies(); Eigen::VectorXd grad = Eigen::VectorXd::Zero(x.size()); @@ -77,8 +73,6 @@ Eigen::MatrixXd BodyForces::hessian( Eigen::ConstRef x, const PSDProjectionMethod project_hessian_to_psd) { - assert(predicted_poses().size() == bodies.num_bodies()); - const int ndof = x.size() / bodies.num_bodies(); Eigen::MatrixXd hess(x.size(), x.size()); diff --git a/src/ipc/utils/eigen_ext.hpp b/src/ipc/utils/eigen_ext.hpp index ffbc25801..725323caa 100644 --- a/src/ipc/utils/eigen_ext.hpp +++ b/src/ipc/utils/eigen_ext.hpp @@ -246,15 +246,6 @@ inline Eigen::MatrixXd to_X3d(Eigen::ConstRef vertices) return vertices_3d; } -inline Eigen::Matrix3d cross_product_matrix(Eigen::ConstRef x) -{ - Eigen::Matrix3d X; - X << 0, -x.z(), x.y(), // - x.z(), 0, -x.x(), // - -x.y(), x.x(), 0; - return X; -} - /// Eigen IO Format to format vectors like vertex rows in an OBJ file. static const Eigen::IOFormat OBJ_VERTEX_FORMAT = Eigen::IOFormat( Eigen::FullPrecision, Eigen::DontAlignCols, " ", "", "v ", "\n", "", ""); From 3bb80293932910fb246db6f75b02ef7fc16df2ed Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Sun, 17 Aug 2025 21:02:36 -0400 Subject: [PATCH 13/24] Refactor error handling in matrix projection functions to use log_and_throw_error for consistency --- src/ipc/dynamics/rigid/simulator.cpp | 3 +-- src/ipc/utils/eigen_ext.tpp | 7 ++----- 2 files changed, 3 insertions(+), 7 deletions(-) diff --git a/src/ipc/dynamics/rigid/simulator.cpp b/src/ipc/dynamics/rigid/simulator.cpp index 34256f910..5d89213a0 100644 --- a/src/ipc/dynamics/rigid/simulator.cpp +++ b/src/ipc/dynamics/rigid/simulator.cpp @@ -97,8 +97,7 @@ void Simulator::step() grad_norm, hess.norm(), alpha); } while (dx > m_time_integrator->dt * 1e-3 && ++iter < 100); logger().info( - "converged: iter={} dx={:g} norm(grad)={:g} norm(hess)={:g}", iter, dx, - grad_norm); + "converged: iter={} dx={:g} norm(grad)={:g}", iter, dx, grad_norm); for (size_t i = 0; i < m_bodies->num_bodies(); ++i) { poses[i].position = x.segment<3>(6 * i); diff --git a/src/ipc/utils/eigen_ext.tpp b/src/ipc/utils/eigen_ext.tpp index 182b9c84a..2b3b3da89 100644 --- a/src/ipc/utils/eigen_ext.tpp +++ b/src/ipc/utils/eigen_ext.tpp @@ -31,8 +31,7 @@ project_to_pd( Eigen::Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>> eigensolver(A); if (eigensolver.info() != Eigen::Success) { - logger().error("unable to project matrix onto positive definite cone"); - throw std::runtime_error( + log_and_throw_error( "unable to project matrix onto positive definite cone"); } // Check if all eigen values are positive. @@ -76,10 +75,8 @@ project_to_psd( Eigen::Matrix<_Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols>> eigensolver(A); if (eigensolver.info() != Eigen::Success) { - logger().error( + log_and_throw_error( "unable to project matrix onto positive semi-definite cone"); - throw std::runtime_error( - "unable to project matrix onto positive definite cone"); } // Check if all eigen values are zero or positive. // The eigenvalues are sorted in increasing order. From f34250b2dbceb85876044a982f16ca9e25f22d1a Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Sun, 17 Aug 2025 23:03:18 -0400 Subject: [PATCH 14/24] Remove cross_product_matrix function from pose.cpp --- python/examples/find_ipctk.py | 24 ++++-------------------- src/ipc/dynamics/rigid/pose.cpp | 12 ------------ 2 files changed, 4 insertions(+), 32 deletions(-) diff --git a/python/examples/find_ipctk.py b/python/examples/find_ipctk.py index b3197cc04..8572b99da 100644 --- a/python/examples/find_ipctk.py +++ b/python/examples/find_ipctk.py @@ -1,20 +1,4 @@ -try: - import ipctk # Try to import the built module -except ImportError: - import sys - import pathlib - repo_root = pathlib.Path(__file__).parents[2] - possible_paths = [ - pathlib.Path("python").resolve(), - repo_root / "build" / "python", - repo_root / "build" / "release" / "python", - repo_root / "build" / "debug" / "python", - ] - for path in possible_paths: - if path.exists() and len(list(path.glob("ipctk.*"))) > 0: - sys.path.append(str(path)) - break - else: - raise ImportError("Could not find the ipctk module") - print(f"Using found ipctk module at {path}") - import ipctk # Try again +import sys +import pathlib +sys.path.append(str(pathlib.Path(__file__).parents[1])) +from _find_ipctk import ipctk # noqa diff --git a/src/ipc/dynamics/rigid/pose.cpp b/src/ipc/dynamics/rigid/pose.cpp index 55797b88a..63f11c8ad 100644 --- a/src/ipc/dynamics/rigid/pose.cpp +++ b/src/ipc/dynamics/rigid/pose.cpp @@ -4,18 +4,6 @@ namespace ipc::rigid { -namespace { - inline Eigen::Matrix3d - cross_product_matrix(Eigen::ConstRef x) - { - Eigen::Matrix3d X; - X << 0, -x.z(), x.y(), // - x.z(), 0, -x.x(), // - -x.y(), x.x(), 0; - return X; - } -} // namespace - Eigen::Matrix3d rotation_vector_to_matrix(Eigen::ConstRef theta) { From 42510aaed789e74ef2e96936b661530e141a2440 Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Sun, 17 Aug 2025 23:21:37 -0400 Subject: [PATCH 15/24] Fix CMake option syntax for CCD Query IO, filib, libigl, and scalable CCD recipes --- cmake/recipes/ccd_query_io.cmake | 4 ++-- cmake/recipes/filib.cmake | 2 +- cmake/recipes/libigl.cmake | 2 +- cmake/recipes/scalable_ccd.cmake | 2 +- 4 files changed, 5 insertions(+), 5 deletions(-) diff --git a/cmake/recipes/ccd_query_io.cmake b/cmake/recipes/ccd_query_io.cmake index ca1db9dc7..ca8c4ad46 100644 --- a/cmake/recipes/ccd_query_io.cmake +++ b/cmake/recipes/ccd_query_io.cmake @@ -11,6 +11,6 @@ include(ipc_toolkit_tests_data) include(CPM) CPMAddPackage( URI "gh:Continuous-Collision-Detection/CCD-Query-IO#36f6093af81a65acc27d9f05ad32d6b5729e8d15" - OPTIONS "CCD_IO_DOWNLOAD_SAMPLE_QUERIES=ON" - "CCD_IO_SAMPLE_QUERIES_DIR=${IPC_TOOLKIT_TESTS_DATA_DIR}/ccd-queries/" + OPTIONS "CCD_IO_DOWNLOAD_SAMPLE_QUERIES ON" + "CCD_IO_SAMPLE_QUERIES_DIR ${IPC_TOOLKIT_TESTS_DATA_DIR}/ccd-queries/" ) \ No newline at end of file diff --git a/cmake/recipes/filib.cmake b/cmake/recipes/filib.cmake index 07371ba67..c0fa879bd 100644 --- a/cmake/recipes/filib.cmake +++ b/cmake/recipes/filib.cmake @@ -15,4 +15,4 @@ include(CPM) CPMAddPackage("gh:zfergus/filib#7cf13519b0db72df2493c9c8997a8bef9e372848") # Folder name for IDE -set_target_properties(filib PROPERTIES FOLDER "ThirdParty") +set_target_properties(filib PROPERTIES FOLDER "ThirdParty") \ No newline at end of file diff --git a/cmake/recipes/libigl.cmake b/cmake/recipes/libigl.cmake index 28f25132c..681cee078 100644 --- a/cmake/recipes/libigl.cmake +++ b/cmake/recipes/libigl.cmake @@ -11,7 +11,7 @@ include(eigen) include(CPM) CPMAddPackage( URI "gh:libigl/libigl#89267b4a80b1904de3f6f2812a2053e5e9332b7e" - OPTIONS "LIBIGL_PREDICATES=ON" + OPTIONS "LIBIGL_PREDICATES ON" ) # Folder name for IDE diff --git a/cmake/recipes/scalable_ccd.cmake b/cmake/recipes/scalable_ccd.cmake index 52f5d6200..10d67efa0 100644 --- a/cmake/recipes/scalable_ccd.cmake +++ b/cmake/recipes/scalable_ccd.cmake @@ -9,7 +9,7 @@ message(STATUS "Third-party: creating target 'scalable_ccd::scalable_ccd'") include(CPM) CPMAddPackage( URI "gh:continuous-collision-detection/scalable-ccd#2c82b9ca43fba30b85f7e9aa83283464b1bb7843" - OPTIONS "SCALABLE_CCD_WITH_CUDA=${IPC_TOOLKIT_WITH_CUDA}" + OPTIONS "SCALABLE_CCD_WITH_CUDA ${IPC_TOOLKIT_WITH_CUDA}" ) # Folder name for IDE From e560de5b713c2066deaf8ff91c2b89490dadefd9 Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Sun, 17 Aug 2025 23:31:51 -0400 Subject: [PATCH 16/24] Initialize integral array in compute_mass_properties_3D with empty braces for clarity --- src/ipc/dynamics/rigid/mass.cpp | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/src/ipc/dynamics/rigid/mass.cpp b/src/ipc/dynamics/rigid/mass.cpp index 096a38515..4b7f3e23d 100644 --- a/src/ipc/dynamics/rigid/mass.cpp +++ b/src/ipc/dynamics/rigid/mass.cpp @@ -56,7 +56,7 @@ namespace { assert(faces.rows() > 0 && faces.cols() == 3); // order: 1, x, y, z, x^2, y^2, z^2, xy, yz, zx - std::array integral = { 0.0 }; + std::array integral {}; for (int i = 0; i < faces.rows(); i++) { // Get vertices of triangle i. From 3a9b3264ac06600c003819d136ddf986cb5c8aef Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Sun, 17 Aug 2025 23:54:24 -0400 Subject: [PATCH 17/24] Remove unicode from test names for Windows CI --- tests/src/tests/dynamics/rigid/test_pose.cpp | 16 ++++++++-------- tests/src/tests/utils/test_sinc.cpp | 4 ++-- 2 files changed, 10 insertions(+), 10 deletions(-) diff --git a/tests/src/tests/dynamics/rigid/test_pose.cpp b/tests/src/tests/dynamics/rigid/test_pose.cpp index 4a150198f..589e62cbb 100644 --- a/tests/src/tests/dynamics/rigid/test_pose.cpp +++ b/tests/src/tests/dynamics/rigid/test_pose.cpp @@ -10,7 +10,7 @@ using namespace ipc::rigid; -TEST_CASE("𝔰𝔬(3) ↦ SO(3)", "[rigid][pose]") +TEST_CASE("so(3) -> SO(3)", "[rigid][pose]") { double angle; Eigen::Vector3d axis; @@ -41,7 +41,7 @@ TEST_CASE("𝔰𝔬(3) ↦ SO(3)", "[rigid][pose]") CHECK((R_actual - R_expected).norm() == Catch::Approx(0).margin(1e-12)); } -TEST_CASE("∇²(𝔰𝔬(3) ↦ SO(3))", "[!benchmark][rigid][pose]") +TEST_CASE("Benchmark so(3) -> SO(3)", "[!benchmark][rigid][pose]") { Eigen::Vector3d theta = Eigen::Vector3d::Random(); @@ -59,7 +59,7 @@ TEST_CASE("∇²(𝔰𝔬(3) ↦ SO(3))", "[!benchmark][rigid][pose]") } #if false -TEST_CASE("Interval 𝔰𝔬(3) ↦ SO(3)", "[!benchmark][physics][pose]") +TEST_CASE("Interval so(3) -> SO(3)", "[!benchmark][physics][pose]") { using namespace ipc::rigid; double angle; @@ -79,19 +79,19 @@ TEST_CASE("Interval 𝔰𝔬(3) ↦ SO(3)", "[!benchmark][physics][pose]") Pose p = Pose::Zero(3); p.rotation = angle * axis; - BENCHMARK("Double 𝔰𝔬(3) ↦ SO(3)") + BENCHMARK("Double so(3) -> SO(3)") { Eigen::Matrix3d R = p.construct_rotation_matrix(); }; Pose pI = p.cast(); - BENCHMARK("Interval 𝔰𝔬(3) ↦ SO(3)") + BENCHMARK("Interval so(3) -> SO(3)") { Matrix3I R = pI.construct_rotation_matrix(); }; } #endif -TEST_CASE("𝔰𝔬(3) ↦ SO(3) derivatives", "[rigid][pose]") +TEST_CASE("so(3) -> SO(3) derivatives", "[rigid][pose]") { double angle; Eigen::Vector3d axis; @@ -150,7 +150,7 @@ TEST_CASE("𝔰𝔬(3) ↦ SO(3) derivatives", "[rigid][pose]") } } -TEST_CASE("SO(3) ↦ 𝔰𝔬(3)", "[rigid][pose]") +TEST_CASE("SO(3) -> so(3)", "[rigid][pose]") { double angle = GENERATE( 0.0, 1e-8, 1e-6, igl::PI / 4, igl::PI / 2, igl::PI * 0.75, @@ -182,7 +182,7 @@ TEST_CASE("SO(3) ↦ 𝔰𝔬(3)", "[rigid][pose]") // << std::endl; } -TEST_CASE("Benchmark SO(3) ↦ 𝔰𝔬(3)", "[!benchmark][rigid][pose]") +TEST_CASE("Benchmark SO(3) -> so(3)", "[!benchmark][rigid][pose]") { Eigen::Matrix3d R = Eigen::Matrix3d::Random(); Eigen::JacobiSVD svd( diff --git a/tests/src/tests/utils/test_sinc.cpp b/tests/src/tests/utils/test_sinc.cpp index 56cca5afa..23d31b69b 100644 --- a/tests/src/tests/utils/test_sinc.cpp +++ b/tests/src/tests/utils/test_sinc.cpp @@ -120,7 +120,7 @@ TEST_CASE("Interval sinc_norm_x", "[sinc][interval]") CHECK(expected_y.SUP == Catch::Approx(y.SUP).margin(1e-8)); } -TEST_CASE("∇sinc(||x||)", "[sinc][vector][diff]") +TEST_CASE("Grad sinc(||x||)", "[sinc][vector][diff]") { double sign = GENERATE(-1, 1); double val = GENERATE(0, 1e-8, igl::PI / 2, igl::PI, 5, 20, 100); @@ -135,7 +135,7 @@ TEST_CASE("∇sinc(||x||)", "[sinc][vector][diff]") CHECK(fd::compare_gradient(grad, fgrad)); } -TEST_CASE("∇²sinc(||x||)", "[sinc][vector][diff]") +TEST_CASE("Hess sinc(||x||)", "[sinc][vector][diff]") { double sign = GENERATE(-1, 1); double val = GENERATE(0, 1e-8, igl::PI / 2, igl::PI, 5, 20, 100); From 34912176cd94366c26387beb1e9ae5a80aa9497c Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Mon, 18 Aug 2025 20:26:03 -0400 Subject: [PATCH 18/24] Remove unused K_dKj_plus_K_dKj_T --- src/ipc/dynamics/rigid/pose.cpp | 1 - 1 file changed, 1 deletion(-) diff --git a/src/ipc/dynamics/rigid/pose.cpp b/src/ipc/dynamics/rigid/pose.cpp index 63f11c8ad..8420fd119 100644 --- a/src/ipc/dynamics/rigid/pose.cpp +++ b/src/ipc/dynamics/rigid/pose.cpp @@ -90,7 +90,6 @@ rotation_vector_to_matrix_hessian(Eigen::ConstRef theta) Eigen::Matrix d2R; for (int j = 0; j < 3; ++j) { const Eigen::Matrix3d K_dKj = K * dK[j]; - const Eigen::Matrix3d K_dKj_plus_K_dKj_T = K_dKj + K_dKj.transpose(); for (int i = j; i < 3; ++i) { const Eigen::Matrix3d dKj_dKi = dK[j] * dK[i]; d2R.col(j * 3 + i) = From e10542a4c5642879c0edc1b6489538ac7ffeb616 Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Tue, 19 Aug 2025 21:23:36 -0400 Subject: [PATCH 19/24] Add RigidBody class bindings to expose mass and inertia properties. --- python/examples/rigid.py | 32 ++++++++++++++++++++----- python/src/dynamics/rigid/simulator.cpp | 16 ++++++++++++- src/ipc/dynamics/rigid/simulator.cpp | 4 ++-- src/ipc/dynamics/rigid/simulator.hpp | 14 +++++------ 4 files changed, 50 insertions(+), 16 deletions(-) diff --git a/python/examples/rigid.py b/python/examples/rigid.py index a8da46311..00cb186e0 100644 --- a/python/examples/rigid.py +++ b/python/examples/rigid.py @@ -3,14 +3,17 @@ import polyscope as ps from polyscope import imgui import numpy as np +from scipy.spatial.transform import Rotation import pathlib -mesh = meshio.read(pathlib.Path(__file__).parents[2] / "tests/data/cube.ply") +mesh = meshio.read(pathlib.Path( + __file__).parents[2] / "tests/data/wing-nut.obj") initial_poses = ipctk.Poses([ ipctk.Pose(position=np.zeros(3), rotation=np.zeros(3)) ]) +# initial_poses[0].rotation = np.array([np.pi, 0, 0]) # Rotate around x-axis bodies = ipctk.RigidBodies( rest_positions=[mesh.points.astype("float64")], @@ -20,19 +23,36 @@ initial_poses=initial_poses ) -for pose in initial_poses: - print(pose) +# for pose in initial_poses: +# print(pose) ps.init() ps.set_give_focus_on_show(True) ps_mesh = ps.register_surface_mesh( - "bunny", + "rigid body", bodies.vertices(initial_poses), bodies.faces ) +ps_com = ps.register_point_cloud( + "rigid body com", + initial_poses[0].position.reshape(-1, 3) +) + +for i in range(3): + dim = np.zeros(3) + dim[i] = 100 * bodies[0].moment_of_inertia[i] + R = Rotation.from_rotvec( + initial_poses[0].rotation.copy()).as_matrix() + ps_com.add_vector_quantity( + "xyz"[i], + (R @ dim).reshape(-1, 3), + enabled=True, + vectortype="ambient" + ) + sim = ipctk.Simulator( bodies=bodies, initial_poses=initial_poses, @@ -50,13 +70,13 @@ def foo(): if imgui.Button("Step") or playing: sim.step() ps_mesh.update_vertex_positions( - bodies.vertices(sim.poses_history[-1]) + bodies.vertices(sim.pose_history[-1]) ) imgui.SameLine() if imgui.Button("Reset"): sim.reset() ps_mesh.update_vertex_positions( - bodies.vertices(sim.poses_history[-1]) + bodies.vertices(sim.pose_history[-1]) ) diff --git a/python/src/dynamics/rigid/simulator.cpp b/python/src/dynamics/rigid/simulator.cpp index 885545e95..705421485 100644 --- a/python/src/dynamics/rigid/simulator.cpp +++ b/python/src/dynamics/rigid/simulator.cpp @@ -42,6 +42,20 @@ void define_rigid_simulator(py::module_& m) "Pose(position={}, rotation={})", p.position, p.rotation); }); + py::class_(m, "RigidBody") + .def( + py::init< + Eigen::Ref, Eigen::ConstRef, + Eigen::ConstRef, const double, Pose&>(), + py::arg("vertices"), py::arg("edges"), py::arg("faces"), + py::arg("density"), py::arg("initial_pose")) + .def_property_readonly("mass", &RigidBody::mass) + .def_property_readonly( + "moment_of_inertia", &RigidBody::moment_of_inertia) + .def_property_readonly("J", &RigidBody::J) + .def_property_readonly("R0", &RigidBody::R0) + .def_property_readonly("external_force", &RigidBody::external_force); + py::class_, CollisionMesh>( m, "RigidBodies") .def( @@ -75,7 +89,7 @@ void define_rigid_simulator(py::module_& m) .def("step", &rigid::Simulator::step) .def("reset", &rigid::Simulator::reset) .def_property_readonly( - "poses_history", &rigid::Simulator::poses_history, + "pose_history", &rigid::Simulator::pose_history, R"ipc_Qu8mg5v7( Get the history of poses in the simulation. diff --git a/src/ipc/dynamics/rigid/simulator.cpp b/src/ipc/dynamics/rigid/simulator.cpp index 5d89213a0..905f8179c 100644 --- a/src/ipc/dynamics/rigid/simulator.cpp +++ b/src/ipc/dynamics/rigid/simulator.cpp @@ -28,7 +28,7 @@ Simulator::Simulator( // v0.segment<3>(12 * i).y() = 10; // ω = R₀ᵀω₀ (ω₀ expressed in body coordinates) - Eigen::Vector3d omega(-100 * igl::PI / 180, 0, 0); + Eigen::Vector3d omega(0, -100 * igl::PI / 180, 0); omega = (*m_bodies)[i].R0().transpose() * omega; Eigen::Matrix3d Q_t0 = initial_poses[i].rotation_matrix(); v0.segment<9>(12 * i + 3) = @@ -84,7 +84,7 @@ void Simulator::step() } Eigen::MatrixXd hess = m_inertial_term->hessian(*m_bodies, x, PSDProjectionMethod::ABS); - Eigen::VectorXd step = -hess.lu().solve(grad); + Eigen::VectorXd step = -hess.llt().solve(grad); dx = step.norm(); double alpha = 1.0; double Ex = (*m_inertial_term)(*m_bodies, x); diff --git a/src/ipc/dynamics/rigid/simulator.hpp b/src/ipc/dynamics/rigid/simulator.hpp index 69f2b4fd9..130ca1019 100644 --- a/src/ipc/dynamics/rigid/simulator.hpp +++ b/src/ipc/dynamics/rigid/simulator.hpp @@ -14,17 +14,17 @@ class InertialTerm; class Simulator { public: /// @brief Create a simulation box - /// @param corners Corners of the simulation box - /// @param gravity Gravity vector + /// @param bodies Rigid bodies in the simulation + /// @param initial_poses Initial poses of the rigid bodies + /// @param dt Time step Simulator( - const std::shared_ptr _bodies, + const std::shared_ptr bodies, const std::vector& initial_poses, const double dt); /// @brief Run the simulation /// @param t_end End time - /// @param dt Time step - /// @param callback + /// @param callback Callback function to be called at each step void run( // const double dt, const double t_end, @@ -43,12 +43,12 @@ class Simulator { // Accessors // ----------------------------------------------------------------------- - const std::list>& poses_history() const + const std::list>& pose_history() const { return m_pose_history; } - const std::shared_ptr& bodies() const { return m_bodies; } + std::shared_ptr bodies() const { return m_bodies; } double t() const { return m_t; } // double dt() const { return m_time_integrator->dt; } From ea38e5dd24372286ccdf9945a775b4c181c625e2 Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Sun, 24 Aug 2025 12:49:03 -0400 Subject: [PATCH 20/24] Fix broad phase benchmark --- .../broad_phase/benchmark_broad_phase.cpp | 40 ++++++++++++------- tests/src/tests/utils.cpp | 6 ++- tests/src/tests/utils.hpp | 2 + 3 files changed, 31 insertions(+), 17 deletions(-) diff --git a/tests/src/tests/broad_phase/benchmark_broad_phase.cpp b/tests/src/tests/broad_phase/benchmark_broad_phase.cpp index a5c637e97..58266f7df 100644 --- a/tests/src/tests/broad_phase/benchmark_broad_phase.cpp +++ b/tests/src/tests/broad_phase/benchmark_broad_phase.cpp @@ -65,6 +65,11 @@ TEST_CASE("Benchmark broad phase", "[!benchmark][broad_phase]") F_stack.bottomRows(F.rows()) = F.array() + n; F = F_stack; + Eigen::MatrixXi E_stack(2 * E.rows(), E.cols()); + E_stack.topRows(E.rows()) = E; + E_stack.bottomRows(E.rows()) = E.array() + n; + E = E_stack; + testcase_name = fmt::format("Interobject dx={}", dx); } @@ -75,13 +80,15 @@ TEST_CASE("Benchmark broad phase", "[!benchmark][broad_phase]") V0 = mesh.vertices(V0); V1 = mesh.vertices(V1); - const auto broad_phase = GENERATE(tests::BroadPhaseGenerator::create()); + const auto broad_phases = tests::broad_phases(); - BENCHMARK(fmt::format("BP {} ({})", testcase_name, broad_phase->name())) - { - Candidates candidates; - candidates.build(mesh, V0, V1, inflation_radius, broad_phase); - }; + for (const auto& broad_phase : broad_phases) { + BENCHMARK(fmt::format("BP {} ({})", testcase_name, broad_phase->name())) + { + Candidates candidates; + candidates.build(mesh, V0, V1, inflation_radius, broad_phase); + }; + } } TEST_CASE( @@ -125,14 +132,17 @@ TEST_CASE( V0 = mesh.vertices(V0); V1 = mesh.vertices(V1); - const auto broad_phase = GENERATE(tests::BroadPhaseGenerator::create()); - if (broad_phase->name() == "BruteForce") { - SKIP("Not benchmarking brute force"); - } + const auto broad_phases = tests::broad_phases(); - BENCHMARK(fmt::format("BP Real Data ({})", broad_phase->name())) - { - Candidates candidates; - candidates.build(mesh, V0, V1, inflation_radius, broad_phase); - }; + for (const auto& broad_phase : broad_phases) { + if (broad_phase->name() == "BruteForce") { + continue; + } + + BENCHMARK(fmt::format("BP Real Data ({})", broad_phase->name())) + { + Candidates candidates; + candidates.build(mesh, V0, V1, inflation_radius, broad_phase); + }; + } } diff --git a/tests/src/tests/utils.cpp b/tests/src/tests/utils.cpp index ba5ab21b9..4bcdfee66 100644 --- a/tests/src/tests/utils.cpp +++ b/tests/src/tests/utils.cpp @@ -20,9 +20,9 @@ namespace ipc::tests { -BroadPhaseGenerator::BroadPhaseGenerator() +std::vector> broad_phases() { - m_broad_phases = { { + return { { std::make_shared(), std::make_shared(), std::make_shared(), @@ -34,6 +34,8 @@ BroadPhaseGenerator::BroadPhaseGenerator() } }; } +BroadPhaseGenerator::BroadPhaseGenerator() { m_broad_phases = broad_phases(); } + // Attempts to move the generator to the next element. // Returns true if successful (and thus has another element that can be // read) diff --git a/tests/src/tests/utils.hpp b/tests/src/tests/utils.hpp index c6600c8fd..e814d739c 100644 --- a/tests/src/tests/utils.hpp +++ b/tests/src/tests/utils.hpp @@ -35,6 +35,8 @@ class BroadPhaseGenerator int m_current = 0; }; +std::vector> broad_phases(); + // ============================================================================ bool load_mesh( From f27fbe8a0593bf82a91485b9d018b1f6a4d88013 Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Sun, 24 Aug 2025 13:15:27 -0400 Subject: [PATCH 21/24] Update GIT_TAG for ipc_toolkit_tests_data and modify expected output in normal collisions test (#185) --- cmake/ipc_toolkit/ipc_toolkit_tests_data.cmake | 2 +- .../tests/collisions/test_normal_collisions.cpp | 16 ++++++++-------- 2 files changed, 9 insertions(+), 9 deletions(-) diff --git a/cmake/ipc_toolkit/ipc_toolkit_tests_data.cmake b/cmake/ipc_toolkit/ipc_toolkit_tests_data.cmake index 8c0b736ef..f51db2f7b 100644 --- a/cmake/ipc_toolkit/ipc_toolkit_tests_data.cmake +++ b/cmake/ipc_toolkit/ipc_toolkit_tests_data.cmake @@ -30,7 +30,7 @@ else() SOURCE_DIR ${IPC_TOOLKIT_TESTS_DATA_DIR} GIT_REPOSITORY https://github.com/ipc-sim/ipc-toolkit-tests-data.git - GIT_TAG 333aed25f87c5820bec8a7f82d7959ff87a9a502 + GIT_TAG 0c6ce752d020db32f62da37d7b8ca9f73c204b36 CONFIGURE_COMMAND "" BUILD_COMMAND "" diff --git a/tests/src/tests/collisions/test_normal_collisions.cpp b/tests/src/tests/collisions/test_normal_collisions.cpp index 8defa9c88..91e6e45b5 100644 --- a/tests/src/tests/collisions/test_normal_collisions.cpp +++ b/tests/src/tests/collisions/test_normal_collisions.cpp @@ -353,12 +353,12 @@ TEST_CASE("NormalCollisions::to_string", "[collisions]") std::string s = collisions.to_string(mesh, vertices); CHECK(s == R"ipc_Qu8mg5v7( -vv: 1 5, w: 1, d: 0.000913492 -vv: 160 163, w: 1, d: 0.000277936 -ev: 14=(24, 46) 205, w: 0.0140559, d: 0.00500364 -ev: 719=(237, 261) 128, w: 0.0122856, d: 0.00727213 -ee: 14=(24, 46) 456=(161, 205), w: -0.00297853, dtype: 0, d: 0.00538125 -ee: 346=(76, 128) 718=(236, 261), w: -0.00328539, dtype: 5, d: 0.00717647 -fv: 17=(46, 24, 72) 205, w: 0.0137957, d: 0.00500269 -fv: 471=(155, 238, 259) 64, w: 0.0160469, d: 0.00639199)ipc_Qu8mg5v7"); +vv: 4 140, w: -0.0128182, d: 0.00568928 +vv: 119 243, w: -0.0263598, d: 0.00727215 +ev: 14=(18, 37) 187, w: 0.0140559, d: 0.00500364 +ev: 719=(219, 243) 119, w: 0.0122856, d: 0.00727213 +ee: 14=(18, 37) 456=(144, 187), w: -0.00297852, dtype: 0, d: 0.00538125 +ee: 346=(67, 119) 718=(218, 243), w: -0.00328539, dtype: 5, d: 0.00717647 +fv: 17=(37, 18, 63) 187, w: 0.0137957, d: 0.00500269 +fv: 471=(140, 220, 241) 55, w: 0.0160469, d: 0.006392)ipc_Qu8mg5v7"); } \ No newline at end of file From 7f75e2544da002d457622a10ddb3ee36d4653727 Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Sun, 24 Aug 2025 13:56:15 -0400 Subject: [PATCH 22/24] Refactor broad phase collision detection methods - Introduce new overloads for build methods across various classes, allowing for the use of precomputed AABBs. - Update related documentation and ensure consistent handling of vertex boxes and edges. - Improve voxel size suggestion logic based on bounding box dimensions. --- src/ipc/broad_phase/broad_phase.cpp | 30 ++++-- src/ipc/broad_phase/broad_phase.hpp | 17 +++ src/ipc/broad_phase/bvh.cpp | 25 +---- src/ipc/broad_phase/bvh.hpp | 32 ++---- src/ipc/broad_phase/hash_grid.cpp | 50 +++------ src/ipc/broad_phase/hash_grid.hpp | 32 ++---- src/ipc/broad_phase/spatial_hash.cpp | 59 ++++++---- src/ipc/broad_phase/spatial_hash.hpp | 102 +++++++++++------- src/ipc/broad_phase/sweep_and_prune.cpp | 25 +++++ src/ipc/broad_phase/sweep_and_prune.hpp | 9 ++ .../broad_phase/sweep_and_tiniest_queue.cpp | 27 +++++ .../broad_phase/sweep_and_tiniest_queue.hpp | 9 ++ src/ipc/broad_phase/voxel_size_heuristic.cpp | 21 ++++ src/ipc/broad_phase/voxel_size_heuristic.hpp | 7 +- src/ipc/candidates/candidates.hpp | 18 ++++ src/ipc/ccd/narrow_phase_ccd.hpp | 46 ++++++++ src/ipc/dynamics/rigid/rigid_body.cpp | 6 +- src/ipc/dynamics/rigid/rigid_body.hpp | 13 +++ 18 files changed, 357 insertions(+), 171 deletions(-) diff --git a/src/ipc/broad_phase/broad_phase.cpp b/src/ipc/broad_phase/broad_phase.cpp index c5589c53c..95e5674b0 100644 --- a/src/ipc/broad_phase/broad_phase.cpp +++ b/src/ipc/broad_phase/broad_phase.cpp @@ -11,12 +11,9 @@ void BroadPhase::build( Eigen::ConstRef faces, const double inflation_radius) { - assert(edges.size() == 0 || edges.cols() == 2); - assert(faces.size() == 0 || faces.cols() == 3); clear(); build_vertex_boxes(vertices, vertex_boxes, inflation_radius); - build_edge_boxes(vertex_boxes, edges, edge_boxes); - build_face_boxes(vertex_boxes, faces, face_boxes); + build(edges, faces); } void BroadPhase::build( @@ -26,11 +23,32 @@ void BroadPhase::build( Eigen::ConstRef faces, const double inflation_radius) { - assert(edges.size() == 0 || edges.cols() == 2); - assert(faces.size() == 0 || faces.cols() == 3); clear(); build_vertex_boxes( vertices_t0, vertices_t1, vertex_boxes, inflation_radius); + build(edges, faces); +} + +void BroadPhase::build( + const std::vector& _vertex_boxes, + Eigen::ConstRef edges, + Eigen::ConstRef faces) +{ + clear(); + + assert(&(this->vertex_boxes) != &_vertex_boxes); + this->vertex_boxes = _vertex_boxes; + + build(edges, faces); +} + +void BroadPhase::build( + Eigen::ConstRef edges, + Eigen::ConstRef faces) +{ + assert(vertex_boxes.size() > 0); + assert(edges.size() == 0 || edges.cols() == 2); + assert(faces.size() == 0 || faces.cols() == 3); build_edge_boxes(vertex_boxes, edges, edge_boxes); build_face_boxes(vertex_boxes, faces, face_boxes); } diff --git a/src/ipc/broad_phase/broad_phase.hpp b/src/ipc/broad_phase/broad_phase.hpp index 446e0f598..d45518f96 100644 --- a/src/ipc/broad_phase/broad_phase.hpp +++ b/src/ipc/broad_phase/broad_phase.hpp @@ -48,6 +48,15 @@ class BroadPhase { Eigen::ConstRef faces, const double inflation_radius = 0); + /// @brief Build the broad phase for collision detection. + /// @param vertex_boxes AABBs for the vertices. + /// @param edges Collision mesh edges + /// @param faces Collision mesh faces + virtual void build( + const std::vector& vertex_boxes, + Eigen::ConstRef edges, + Eigen::ConstRef faces); + /// @brief Clear any built data. virtual void clear(); @@ -91,6 +100,14 @@ class BroadPhase { default_can_vertices_collide; protected: + /// @brief Build the broad phase for collision detection. + /// @note Assumes the vertex_boxes have been built. + /// @param edges Collision mesh edges + /// @param faces Collision mesh faces + virtual void build( + Eigen::ConstRef edges, + Eigen::ConstRef faces); + virtual bool can_edge_vertex_collide(size_t ei, size_t vi) const; virtual bool can_edges_collide(size_t eai, size_t ebi) const; virtual bool can_face_vertex_collide(size_t fi, size_t vi) const; diff --git a/src/ipc/broad_phase/bvh.cpp b/src/ipc/broad_phase/bvh.cpp index 57b5df729..668333726 100644 --- a/src/ipc/broad_phase/bvh.cpp +++ b/src/ipc/broad_phase/bvh.cpp @@ -22,25 +22,10 @@ BVH::BVH() BVH::~BVH() = default; void BVH::build( - Eigen::ConstRef vertices, Eigen::ConstRef edges, - Eigen::ConstRef faces, - const double inflation_radius) + Eigen::ConstRef faces) { - BroadPhase::build(vertices, edges, faces, inflation_radius); - init_bvh(vertex_boxes, *vertex_bvh); - init_bvh(edge_boxes, *edge_bvh); - init_bvh(face_boxes, *face_bvh); -} - -void BVH::build( - Eigen::ConstRef vertices_t0, - Eigen::ConstRef vertices_t1, - Eigen::ConstRef edges, - Eigen::ConstRef faces, - const double inflation_radius) -{ - BroadPhase::build(vertices_t0, vertices_t1, edges, faces, inflation_radius); + BroadPhase::build(edges, faces); // Build edge_boxes and face_boxes init_bvh(vertex_boxes, *vertex_bvh); init_bvh(edge_boxes, *edge_bvh); init_bvh(face_boxes, *face_bvh); @@ -74,9 +59,9 @@ void BVH::detect_candidates( const std::function& can_collide, std::vector& candidates) { - // O(n^2) or O(n^3) to build - // O(klog(n)) to do a single look up - // O(knlog(n)) to do all look ups + // O(n) or O(n⋅log(n)) to build + // O(k⋅log(n)) to do a single look up + // O(k⋅n⋅log(n)) to do all look ups tbb::enumerable_thread_specific> storage; diff --git a/src/ipc/broad_phase/bvh.hpp b/src/ipc/broad_phase/bvh.hpp index 0b19ec4de..4d97d358d 100644 --- a/src/ipc/broad_phase/bvh.hpp +++ b/src/ipc/broad_phase/bvh.hpp @@ -20,29 +20,7 @@ class BVH : public BroadPhase { /// @return The name of the broad phase method. std::string name() const override { return "BVH"; } - /// @brief Build the broad phase for static collision detection. - /// @param vertices Vertex positions - /// @param edges Collision mesh edges - /// @param faces Collision mesh faces - /// @param inflation_radius Radius of inflation around all elements. - void build( - Eigen::ConstRef vertices, - Eigen::ConstRef edges, - Eigen::ConstRef faces, - const double inflation_radius = 0) override; - - /// @brief Build the broad phase for continuous collision detection. - /// @param vertices_t0 Starting vertices of the vertices. - /// @param vertices_t1 Ending vertices of the vertices. - /// @param edges Collision mesh edges - /// @param faces Collision mesh faces - /// @param inflation_radius Radius of inflation around all elements. - void build( - Eigen::ConstRef vertices_t0, - Eigen::ConstRef vertices_t1, - Eigen::ConstRef edges, - Eigen::ConstRef faces, - const double inflation_radius = 0) override; + using BroadPhase::build; /// @brief Clear any built data. void clear() override; @@ -78,6 +56,14 @@ class BVH : public BroadPhase { std::vector& candidates) const override; protected: + /// @brief Build the broad phase for collision detection. + /// @note Assumes the vertex_boxes have been built. + /// @param edges Collision mesh edges + /// @param faces Collision mesh faces + void build( + Eigen::ConstRef edges, + Eigen::ConstRef faces) override; + /// @brief Initialize a BVH from a set of boxes. /// @param[in] boxes Set of boxes to initialize the BVH with. /// @param[out] bvh The BVH to initialize. diff --git a/src/ipc/broad_phase/hash_grid.cpp b/src/ipc/broad_phase/hash_grid.cpp index ac0f68123..80fd33d17 100644 --- a/src/ipc/broad_phase/hash_grid.cpp +++ b/src/ipc/broad_phase/hash_grid.cpp @@ -18,46 +18,20 @@ using namespace std::placeholders; namespace ipc { void HashGrid::build( - Eigen::ConstRef vertices, Eigen::ConstRef edges, - Eigen::ConstRef faces, - const double inflation_radius) + Eigen::ConstRef faces) { - BroadPhase::build(vertices, edges, faces, inflation_radius); - // BroadPhase::build also calls clear() + BroadPhase::build(edges, faces); - ArrayMax3d mesh_min = vertices.colwise().minCoeff().array(); - ArrayMax3d mesh_max = vertices.colwise().maxCoeff().array(); - AABB::conservative_inflation(mesh_min, mesh_max, inflation_radius); + ArrayMax3d mesh_min = vertex_boxes[0].min; + ArrayMax3d mesh_max = vertex_boxes[0].max; + for (const auto& box : vertex_boxes) { + mesh_min = mesh_min.min(box.min); + mesh_max = mesh_max.max(box.max); + } const double cell_size = - suggest_good_voxel_size(vertices, edges, inflation_radius); - resize(mesh_min, mesh_max, cell_size); - - insert_boxes(); -} - -void HashGrid::build( - Eigen::ConstRef vertices_t0, - Eigen::ConstRef vertices_t1, - Eigen::ConstRef edges, - Eigen::ConstRef faces, - const double inflation_radius) -{ - BroadPhase::build(vertices_t0, vertices_t1, edges, faces, inflation_radius); - // BroadPhase::build also calls clear() - - const ArrayMax3d mesh_min_t0 = vertices_t0.colwise().minCoeff(); - const ArrayMax3d mesh_max_t0 = vertices_t0.colwise().maxCoeff(); - const ArrayMax3d mesh_min_t1 = vertices_t1.colwise().minCoeff(); - const ArrayMax3d mesh_max_t1 = vertices_t1.colwise().maxCoeff(); - - ArrayMax3d mesh_min = mesh_min_t0.min(mesh_min_t1); - ArrayMax3d mesh_max = mesh_max_t0.max(mesh_max_t1); - AABB::conservative_inflation(mesh_min, mesh_max, inflation_radius); - - const double cell_size = suggest_good_voxel_size( - vertices_t0, vertices_t1, edges, inflation_radius); + suggest_good_voxel_size(edges.rows() > 0 ? edge_boxes : vertex_boxes); resize(mesh_min, mesh_max, cell_size); insert_boxes(); @@ -66,9 +40,9 @@ void HashGrid::build( void HashGrid::resize( Eigen::ConstRef domain_min, Eigen::ConstRef domain_max, - double cell_size) + const double cell_size) { - assert(cell_size != 0.0); + assert(cell_size > 0.0); assert(std::isfinite(cell_size)); m_domain_min = domain_min; @@ -77,6 +51,8 @@ void HashGrid::resize( m_grid_size = ((domain_max - domain_min) / cell_size).ceil().cast().max(1); + assert(m_grid_size.maxCoeff() < 200'000); + logger().trace( "hash-grid resized with a size of {:d}x{:d}x{:d}", grid_size()[0], grid_size()[1], grid_size().size() == 3 ? grid_size()[2] : 1); diff --git a/src/ipc/broad_phase/hash_grid.hpp b/src/ipc/broad_phase/hash_grid.hpp index 823feabda..eb3c168bb 100644 --- a/src/ipc/broad_phase/hash_grid.hpp +++ b/src/ipc/broad_phase/hash_grid.hpp @@ -33,29 +33,7 @@ class HashGrid : public BroadPhase { /// @return The name of the broad phase method. std::string name() const override { return "HashGrid"; } - /// @brief Build the broad phase for static collision detection. - /// @param vertices Vertex positions - /// @param edges Collision mesh edges - /// @param faces Collision mesh faces - /// @param inflation_radius Radius of inflation around all elements. - void build( - Eigen::ConstRef vertices, - Eigen::ConstRef edges, - Eigen::ConstRef faces, - double inflation_radius = 0) override; - - /// @brief Build the broad phase for continuous collision detection. - /// @param vertices_t0 Starting vertices of the vertices. - /// @param vertices_t1 Ending vertices of the vertices. - /// @param edges Collision mesh edges - /// @param faces Collision mesh faces - /// @param inflation_radius Radius of inflation around all elements. - void build( - Eigen::ConstRef vertices_t0, - Eigen::ConstRef vertices_t1, - Eigen::ConstRef edges, - Eigen::ConstRef faces, - double inflation_radius = 0) override; + using BroadPhase::build; /// @brief Clear the hash grid. void clear() override @@ -101,6 +79,14 @@ class HashGrid : public BroadPhase { const ArrayMax3d& domain_max() const { return m_domain_max; } protected: + /// @brief Build the broad phase for collision detection. + /// @note Assumes the vertex_boxes have been built. + /// @param edges Collision mesh edges + /// @param faces Collision mesh faces + void build( + Eigen::ConstRef edges, + Eigen::ConstRef faces) override; + void resize( Eigen::ConstRef domain_min, Eigen::ConstRef domain_max, diff --git a/src/ipc/broad_phase/spatial_hash.cpp b/src/ipc/broad_phase/spatial_hash.cpp index d4e44ff91..25154fc16 100644 --- a/src/ipc/broad_phase/spatial_hash.cpp +++ b/src/ipc/broad_phase/spatial_hash.cpp @@ -76,7 +76,9 @@ void SpatialHash::build( double inflation_radius, double voxel_size) { - build(vertices, vertices, edges, faces, inflation_radius, voxel_size); + clear(); + build_vertex_boxes(vertices, vertex_boxes, inflation_radius); + build(edges, faces, voxel_size); } void SpatialHash::build( @@ -87,28 +89,47 @@ void SpatialHash::build( double inflation_radius, double voxel_size) { - const size_t num_vertices = vertices_t0.rows(); - dim = vertices_t0.cols(); + clear(); + build_vertex_boxes( + vertices_t0, vertices_t1, vertex_boxes, inflation_radius); + build(edges, faces, voxel_size); +} - assert(vertices_t1.rows() == num_vertices && vertices_t1.cols() == dim); +void SpatialHash::build( + const std::vector& _vertex_boxes, + Eigen::ConstRef edges, + Eigen::ConstRef faces, + double voxel_size) +{ + // WARNING: Clear will reset vertex_boxes if this assert is triggered + assert(&(this->vertex_boxes) != &_vertex_boxes); + clear(); + this->vertex_boxes = _vertex_boxes; + build(edges, faces, voxel_size); +} - // also calls clear() - BroadPhase::build(vertices_t0, vertices_t1, edges, faces, inflation_radius); +void SpatialHash::build( + Eigen::ConstRef edges, + Eigen::ConstRef faces, + double voxel_size) +{ + const size_t num_vertices = vertex_boxes.size(); + assert(num_vertices > 0); + dim = vertex_boxes[0].min.size(); - built_in_radius = inflation_radius; + BroadPhase::build(edges, faces); if (voxel_size <= 0) { voxel_size = suggest_good_voxel_size( - vertices_t0, vertices_t1, edges, inflation_radius); + edges.rows() > 0 ? edge_boxes : vertex_boxes); } - left_bottom_corner = vertices_t0.colwise().minCoeff().cwiseMin( - vertices_t1.colwise().minCoeff()); - right_top_corner = vertices_t0.colwise().maxCoeff().cwiseMax( - vertices_t1.colwise().maxCoeff()); - - AABB::conservative_inflation( - left_bottom_corner, right_top_corner, inflation_radius); + left_bottom_corner = vertex_boxes[0].min; + right_top_corner = vertex_boxes[0].max; + for (const auto& box : vertex_boxes) { + left_bottom_corner = left_bottom_corner.min(box.min); + right_top_corner = right_top_corner.max(box.max); + } one_div_voxelSize = 1.0 / voxel_size; @@ -129,14 +150,10 @@ void SpatialHash::build( std::vector vertex_max_voxel_axis_index( num_vertices, Eigen::Array3i::Zero()); tbb::parallel_for(size_t(0), num_vertices, [&](size_t vi) { - ArrayMax3d v_min = vertices_t0.row(vi).cwiseMin(vertices_t1.row(vi)); - ArrayMax3d v_max = vertices_t0.row(vi).cwiseMax(vertices_t1.row(vi)); - AABB::conservative_inflation(v_min, v_max, inflation_radius); - vertex_min_voxel_axis_index[vi].head(dim) = - locate_voxel_axis_index(v_min); + locate_voxel_axis_index(vertex_boxes[vi].min); vertex_max_voxel_axis_index[vi].head(dim) = - locate_voxel_axis_index(v_max); + locate_voxel_axis_index(vertex_boxes[vi].max); }); // ------------------------------------------------------------------------ diff --git a/src/ipc/broad_phase/spatial_hash.hpp b/src/ipc/broad_phase/spatial_hash.hpp index 7b783d00f..933ec39f8 100644 --- a/src/ipc/broad_phase/spatial_hash.hpp +++ b/src/ipc/broad_phase/spatial_hash.hpp @@ -12,43 +12,6 @@ namespace ipc { /// @brief Spatial hash broad phase collision detection. class SpatialHash : public BroadPhase { -public: // data - /// @brief The left bottom corner of the world bounding box. - ArrayMax3d left_bottom_corner; - - /// @brief The right top corner of the world bounding box. - ArrayMax3d right_top_corner; - - /// @brief The number of voxels in each dimension. - ArrayMax3i voxel_count; - - /// @brief 1.0 / voxel_size - double one_div_voxelSize; - - /// @brief The number of voxels in the first two dimensions. - int voxel_count_0x1; - - // // The index of the first edge in voxel_occupancies - int edge_start_ind; - // // The index of the first triangle in voxel_occupancies - int tri_start_ind; - - /// @brief Map from voxel index to the primitive indices it contains. - unordered_map> voxel_to_primitives; - - /// @brief Map from point index to the voxel indices it occupies. - std::vector> point_to_voxels; - - /// @brief Map from edge index to the voxel indices it occupies. - std::vector> edge_to_voxels; - - /// @brief Map from face index to the voxel indices it occupies. - std::vector> face_to_voxels; - -protected: - int dim; - double built_in_radius; - public: // constructor SpatialHash() = default; @@ -79,7 +42,11 @@ class SpatialHash : public BroadPhase { /// @return The name of the broad phase method. std::string name() const override { return "SpatialHash"; } -public: // API + // ------------------------------------------------------------------------ + // BroadPhase::build() + + using BroadPhase::build; + void build( Eigen::ConstRef vertices, Eigen::ConstRef edges, @@ -101,6 +68,17 @@ class SpatialHash : public BroadPhase { /*voxel_size=*/-1); } + void build( + const std::vector& vertex_boxes, + Eigen::ConstRef edges, + Eigen::ConstRef faces) override + { + build(vertex_boxes, edges, faces, /*voxel_size=*/-1); + } + + // ------------------------------------------------------------------------ + // SpatialHash::build(..., voxel_size) + void build( Eigen::ConstRef vertices, Eigen::ConstRef edges, @@ -116,6 +94,12 @@ class SpatialHash : public BroadPhase { double inflation_radius, double voxel_size); + void build( + const std::vector& vertex_boxes, + Eigen::ConstRef edges, + Eigen::ConstRef faces, + double voxel_size); + void clear() override { BroadPhase::clear(); @@ -182,7 +166,47 @@ class SpatialHash : public BroadPhase { void detect_face_face_candidates( std::vector& candidates) const override; + // ======================================================================== + // Data + + /// @brief The left bottom corner of the world bounding box. + ArrayMax3d left_bottom_corner; + + /// @brief The right top corner of the world bounding box. + ArrayMax3d right_top_corner; + + /// @brief The number of voxels in each dimension. + ArrayMax3i voxel_count; + + /// @brief 1.0 / voxel_size + double one_div_voxelSize; + + /// @brief The number of voxels in the first two dimensions. + int voxel_count_0x1; + + // // The index of the first edge in voxel_occupancies + int edge_start_ind; + // // The index of the first triangle in voxel_occupancies + int tri_start_ind; + + /// @brief Map from voxel index to the primitive indices it contains. + unordered_map> voxel_to_primitives; + + /// @brief Map from point index to the voxel indices it occupies. + std::vector> point_to_voxels; + + /// @brief Map from edge index to the voxel indices it occupies. + std::vector> edge_to_voxels; + + /// @brief Map from face index to the voxel indices it occupies. + std::vector> face_to_voxels; + protected: // helper functions + void build( + Eigen::ConstRef edges, + Eigen::ConstRef faces, + double voxel_size); + void query_point_for_points(int vi, unordered_set& vert_inds) const; void query_point_for_edges(int vi, unordered_set& edge_inds) const; @@ -214,6 +238,8 @@ class SpatialHash : public BroadPhase { int voxel_axis_index_to_voxel_index(int ix, int iy, int iz) const; + int dim; + private: /// @brief Detect candidate collisions between type A and type B. /// @tparam Candidate Type of candidate collision. diff --git a/src/ipc/broad_phase/sweep_and_prune.cpp b/src/ipc/broad_phase/sweep_and_prune.cpp index 4f5ae6f97..2e5302903 100644 --- a/src/ipc/broad_phase/sweep_and_prune.cpp +++ b/src/ipc/broad_phase/sweep_and_prune.cpp @@ -54,6 +54,31 @@ void SweepAndPrune::build( scalable_ccd::build_face_boxes(boxes->vertices, faces, boxes->faces); } +void SweepAndPrune::build( + const std::vector& vertex_boxes, + Eigen::ConstRef edges, + Eigen::ConstRef faces) +{ + assert(edges.size() == 0 || edges.cols() == 2); + assert(faces.size() == 0 || faces.cols() == 3); + + clear(); + + // Convert from ipc::AABB to scalable_ccd::AABB (additional element_id) + boxes->vertices.resize(vertex_boxes.size()); + for (int i = 0; i < vertex_boxes.size(); ++i) { + boxes->vertices[i].min = vertex_boxes[i].min; + boxes->vertices[i].max = vertex_boxes[i].max; + for (int j = 0; j < 3; ++j) { + boxes->vertices[i].vertex_ids[j] = vertex_boxes[i].vertex_ids[j]; + } + boxes->vertices[i].element_id = i; + } + + scalable_ccd::build_edge_boxes(boxes->vertices, edges, boxes->edges); + scalable_ccd::build_face_boxes(boxes->vertices, faces, boxes->faces); +} + void SweepAndPrune::clear() { BroadPhase::clear(); diff --git a/src/ipc/broad_phase/sweep_and_prune.hpp b/src/ipc/broad_phase/sweep_and_prune.hpp index e157fbbcc..f996b7848 100644 --- a/src/ipc/broad_phase/sweep_and_prune.hpp +++ b/src/ipc/broad_phase/sweep_and_prune.hpp @@ -38,6 +38,15 @@ class SweepAndPrune : public BroadPhase { Eigen::ConstRef faces, double inflation_radius = 0) override; + /// @brief Build the broad phase from precomputed AABBs. + /// @param vertex_boxes Precomputed vertex AABBs + /// @param edges Collision mesh edges + /// @param faces Collision mesh faces + void build( + const std::vector& vertex_boxes, + Eigen::ConstRef edges, + Eigen::ConstRef faces) override; + /// @brief Clear any built data. void clear() override; diff --git a/src/ipc/broad_phase/sweep_and_tiniest_queue.cpp b/src/ipc/broad_phase/sweep_and_tiniest_queue.cpp index d6f198643..7446f53c8 100644 --- a/src/ipc/broad_phase/sweep_and_tiniest_queue.cpp +++ b/src/ipc/broad_phase/sweep_and_tiniest_queue.cpp @@ -66,6 +66,33 @@ void SweepAndTiniestQueue::build( scalable_ccd::cuda::build_face_boxes(boxes->vertices, faces, boxes->faces); } +void SweepAndTiniestQueue::build( + const std::vector& vertex_boxes, + Eigen::ConstRef edges, + Eigen::ConstRef faces) +{ + assert(edges.size() == 0 || edges.cols() == 2); + assert(faces.size() == 0 || faces.cols() == 3); + + clear(); + + // Convert from ipc::AABB to scalable_ccd::cuda::AABB + boxes->vertices.resize(vertex_boxes.size()); + for (int i = 0; i < vertex_boxes.size(); ++i) { + for (int d = 0; d < 3; ++d) { + boxes->vertices[i].min[d] = + vertex_boxes[i].min.size() > d ? vertex_boxes[i].min[d] : 0; + boxes->vertices[i].max[d] = + vertex_boxes[i].max.size() > d ? vertex_boxes[i].max[d] : 0; + boxes->vertices[i].vertex_ids[d] = vertex_boxes[i].vertex_ids[d]; + } + boxes->vertices[i].element_id = i; + } + + scalable_ccd::cuda::build_edge_boxes(boxes->vertices, edges, boxes->edges); + scalable_ccd::cuda::build_face_boxes(boxes->vertices, faces, boxes->faces); +} + void SweepAndTiniestQueue::clear() { BroadPhase::clear(); diff --git a/src/ipc/broad_phase/sweep_and_tiniest_queue.hpp b/src/ipc/broad_phase/sweep_and_tiniest_queue.hpp index 1d7e308ab..8f249b812 100644 --- a/src/ipc/broad_phase/sweep_and_tiniest_queue.hpp +++ b/src/ipc/broad_phase/sweep_and_tiniest_queue.hpp @@ -42,6 +42,15 @@ class SweepAndTiniestQueue : public BroadPhase { Eigen::ConstRef faces, double inflation_radius = 0) override; + /// @brief Build the broad phase from precomputed AABBs. + /// @param vertex_boxes Precomputed vertex AABBs + /// @param edges Collision mesh edges + /// @param faces Collision mesh faces + void build( + const std::vector& vertex_boxes, + Eigen::ConstRef edges, + Eigen::ConstRef faces) override; + /// @brief Clear any built data. void clear() override; diff --git a/src/ipc/broad_phase/voxel_size_heuristic.cpp b/src/ipc/broad_phase/voxel_size_heuristic.cpp index 9712c8a43..3f6455e1c 100644 --- a/src/ipc/broad_phase/voxel_size_heuristic.cpp +++ b/src/ipc/broad_phase/voxel_size_heuristic.cpp @@ -77,6 +77,27 @@ double suggest_good_voxel_size( return voxel_size; } +double suggest_good_voxel_size(const std::vector& boxes) +{ + assert(boxes.size() > 0); + + Eigen::VectorXd box_sizes(boxes.size()); + for (size_t i = 0; i < boxes.size(); ++i) { + box_sizes(i) = (boxes[i].max - boxes[i].min).maxCoeff(); + } + + double voxel_size; + igl::median(box_sizes, voxel_size); + + if (voxel_size <= 0) { + voxel_size = std::numeric_limits::max(); + } + assert(std::isfinite(voxel_size)); + + logger().trace("suggesting voxel size of {}", voxel_size); + return voxel_size; +} + double mean_edge_length( Eigen::ConstRef vertices_t0, Eigen::ConstRef vertices_t1, diff --git a/src/ipc/broad_phase/voxel_size_heuristic.hpp b/src/ipc/broad_phase/voxel_size_heuristic.hpp index a124ad39d..5bb3f1016 100644 --- a/src/ipc/broad_phase/voxel_size_heuristic.hpp +++ b/src/ipc/broad_phase/voxel_size_heuristic.hpp @@ -1,6 +1,6 @@ #pragma once -#include +#include namespace ipc { @@ -26,6 +26,11 @@ double suggest_good_voxel_size( Eigen::ConstRef edges, const double inflation_radius = 0); +/// @brief Suggest a good voxel size for the given mesh. +/// @param boxes The axis-aligned bounding boxes of the mesh. +/// @return The suggested voxel size. +double suggest_good_voxel_size(const std::vector& boxes); + /// @brief Compute the average edge length of a mesh. /// @param vertices_t0 The vertex positions of the mesh at time t0. /// @param vertices_t1 The vertex positions of the mesh at time t1. diff --git a/src/ipc/candidates/candidates.hpp b/src/ipc/candidates/candidates.hpp index 10e26a82a..f87575bfa 100644 --- a/src/ipc/candidates/candidates.hpp +++ b/src/ipc/candidates/candidates.hpp @@ -44,13 +44,25 @@ class Candidates { const std::shared_ptr broad_phase = make_default_broad_phase()); + /// @brief Get the number of collision candidates. + /// @return The number of collision candidates. size_t size() const; + /// @brief Check if there are no collision candidates. + /// @return True if there are no collision candidates, false otherwise. bool empty() const; + /// @brief Clear all collision candidates. void clear(); + /// @brief Get a collision stencil by index. + /// @param i The index of the collision stencil. + /// @return A reference to the collision stencil. CollisionStencil& operator[](size_t i); + + /// @brief Get a collision stencil by index. + /// @param i The index of the collision stencil. + /// @return A const reference to the collision stencil. const CollisionStencil& operator[](size_t i) const; /// @brief Determine if the step is collision free from the set of candidates. @@ -113,6 +125,12 @@ class Candidates { const NarrowPhaseCCD& narrow_phase_ccd = DEFAULT_NARROW_PHASE_CCD) const; + /// @brief Write collision candidates to a file. + /// @param filename The name of the file to write to. + /// @param vertices The vertex positions. + /// @param edges The edge connectivity. + /// @param faces The face connectivity. + /// @return True if the write was successful, false otherwise. bool write_obj( const std::string& filename, Eigen::ConstRef vertices, diff --git a/src/ipc/ccd/narrow_phase_ccd.hpp b/src/ipc/ccd/narrow_phase_ccd.hpp index 04c44441b..3911f9954 100644 --- a/src/ipc/ccd/narrow_phase_ccd.hpp +++ b/src/ipc/ccd/narrow_phase_ccd.hpp @@ -11,6 +11,15 @@ class NarrowPhaseCCD { virtual ~NarrowPhaseCCD() = default; + /// @brief Perform narrow phase CCD between two points. + /// @param p0_t0 The starting position of the first point. + /// @param p1_t0 The starting position of the second point. + /// @param p0_t1 The ending position of the first point. + /// @param p1_t1 The ending position of the second point. + /// @param toi The time of impact. + /// @param min_distance The minimum distance between the two points. + /// @param tmax The maximum time to check for collision. + /// @return True if a collision was detected, false otherwise. virtual bool point_point_ccd( Eigen::ConstRef p0_t0, Eigen::ConstRef p1_t0, @@ -20,6 +29,17 @@ class NarrowPhaseCCD { const double min_distance = 0.0, const double tmax = 1.0) const = 0; + /// @brief Perform narrow phase CCD between a point and a linear edge. + /// @param p_t0 The starting position of the point. + /// @param e0_t0 The starting position of the first endpoint of the edge. + /// @param e1_t0 The starting position of the second endpoint of the edge. + /// @param p_t1 The ending position of the point. + /// @param e0_t1 The ending position of the first endpoint of the edge. + /// @param e1_t1 The ending position of the second endpoint of the edge. + /// @param toi The time of impact. + /// @param min_distance The minimum distance between the point and the edge. + /// @param tmax The maximum time to check for collision. + /// @return True if a collision was detected, false otherwise. virtual bool point_edge_ccd( Eigen::ConstRef p_t0, Eigen::ConstRef e0_t0, @@ -31,6 +51,19 @@ class NarrowPhaseCCD { const double min_distance = 0.0, const double tmax = 1.0) const = 0; + /// @brief Perform narrow phase CCD between a point and a linear triangle. + /// @param p_t0 The starting position of the point. + /// @param t0_t0 The starting position of the first vertex of the triangle. + /// @param t1_t0 The starting position of the second vertex of the triangle. + /// @param t2_t0 The starting position of the third vertex of the triangle. + /// @param p_t1 The ending position of the point. + /// @param t0_t1 The ending position of the first vertex of the triangle. + /// @param t1_t1 The ending position of the second vertex of the triangle. + /// @param t2_t1 The ending position of the third vertex of the triangle. + /// @param toi The time of impact. + /// @param min_distance The minimum distance between the point and the triangle. + /// @param tmax The maximum time to check for collision. + /// @return True if a collision was detected, false otherwise. virtual bool point_triangle_ccd( Eigen::ConstRef p_t0, Eigen::ConstRef t0_t0, @@ -44,6 +77,19 @@ class NarrowPhaseCCD { const double min_distance = 0.0, const double tmax = 1.0) const = 0; + /// @brief Perform narrow phase CCD between two linear edges. + /// @param ea0_t0 The starting position of the first edge's first endpoint. + /// @param ea1_t0 The starting position of the first edge's second endpoint. + /// @param eb0_t0 The starting position of the second edge's first endpoint. + /// @param eb1_t0 The starting position of the second edge's second endpoint. + /// @param ea0_t1 The ending position of the first edge's first endpoint. + /// @param ea1_t1 The ending position of the first edge's second endpoint. + /// @param eb0_t1 The ending position of the second edge's first endpoint. + /// @param eb1_t1 The ending position of the second edge's second endpoint. + /// @param toi The time of impact. + /// @param min_distance The minimum distance between the two edges. + /// @param tmax The maximum time to check for collision. + /// @return True if a collision was detected, false otherwise. virtual bool edge_edge_ccd( Eigen::ConstRef ea0_t0, Eigen::ConstRef ea1_t0, diff --git a/src/ipc/dynamics/rigid/rigid_body.cpp b/src/ipc/dynamics/rigid/rigid_body.cpp index a05394074..e43c71148 100644 --- a/src/ipc/dynamics/rigid/rigid_body.cpp +++ b/src/ipc/dynamics/rigid/rigid_body.cpp @@ -1,5 +1,6 @@ #include "rigid_body.hpp" +#include #include #include @@ -159,7 +160,7 @@ RigidBody::RigidBody( // mass_matrix.diagonal().head(pos_ndof()).setConstant(mass); // mass_matrix.diagonal().tail(rot_ndof()) = moment_of_inertia; - // r_max = this->vertices.rowwise().norm().maxCoeff(); + m_bounding_radius = vertices.rowwise().norm().maxCoeff(); // average_edge_length = 0; // for (long i = 0; i < edges.rows(); i++) { @@ -173,7 +174,8 @@ RigidBody::RigidBody( // } // assert(std::isfinite(average_edge_length)); - // init_bvh(); + m_bvh = std::make_shared(); + m_bvh->build(vertices, edges, faces); } } // namespace ipc::rigid \ No newline at end of file diff --git a/src/ipc/dynamics/rigid/rigid_body.hpp b/src/ipc/dynamics/rigid/rigid_body.hpp index 6216e669e..54c10dcc0 100644 --- a/src/ipc/dynamics/rigid/rigid_body.hpp +++ b/src/ipc/dynamics/rigid/rigid_body.hpp @@ -4,6 +4,10 @@ #include #include +namespace ipc { +class BVH; +} + namespace ipc::rigid { class RigidBody { @@ -30,6 +34,8 @@ class RigidBody { const Eigen::DiagonalMatrix& J() const { return m_J; } const MatrixMax3d& R0() const { return m_R0; } const Pose& external_force() const { return m_external_force; } + std::shared_ptr bvh() const { return m_bvh; } + double bounding_radius() const { return m_bounding_radius; } private: /// @brief Total mass of the rigid body @@ -49,6 +55,13 @@ class RigidBody { /// @brief External force and torque applied to the rigid body Pose m_external_force; + + /// @brief Statically constructed bounding volume hierarchy for collision detection + /// @note This is defined in the inertial reference frame + std::shared_ptr m_bvh; + + /// @brief Bounding radius of the rigid body + double m_bounding_radius; }; } // namespace ipc::rigid \ No newline at end of file From 0c00276d790160e5cc9dda0ecb7c6f3ba92e2333 Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Wed, 27 Aug 2025 20:31:31 -0400 Subject: [PATCH 23/24] Refactor nonlinear CCD methods to use NonlinearCCD class and simplify function signatures --- python/src/ccd/nonlinear_ccd.cpp | 312 ++++++++---------- .../broad_phase/sweep_and_tiniest_queue.cpp | 16 +- src/ipc/ccd/nonlinear_ccd.cpp | 44 ++- src/ipc/ccd/nonlinear_ccd.hpp | 237 +++++++------ tests/src/tests/ccd/test_nonlinear_ccd.cpp | 40 +-- 5 files changed, 303 insertions(+), 346 deletions(-) diff --git a/python/src/ccd/nonlinear_ccd.cpp b/python/src/ccd/nonlinear_ccd.cpp index 2f836da10..f89097a5c 100644 --- a/python/src/ccd/nonlinear_ccd.cpp +++ b/python/src/ccd/nonlinear_ccd.cpp @@ -77,185 +77,149 @@ void define_nonlinear_ccd(py::module_& m) "t0"_a, "t1"_a); #endif - m.def( - "point_point_nonlinear_ccd", - [](const NonlinearTrajectory& p0, const NonlinearTrajectory& p1, - const double tmax, const double min_distance, const double tolerance, - const long max_iterations, const double conservative_rescaling) { - double toi; - bool r = point_point_nonlinear_ccd( - p0, p1, toi, tmax, min_distance, tolerance, max_iterations, - conservative_rescaling); - return std::make_tuple(r, toi); - }, - R"ipc_Qu8mg5v7( - Perform nonlinear CCD between two points moving along nonlinear trajectories. - - Parameters: - p0: First point's trajectory - p1: Second point's trajectory - tmax: Maximum time to check for collision - min_distance: Minimum separation distance between the two points - tolerance: Tolerance for the linear CCD algorithm - max_iterations: Maximum number of iterations for the linear CCD algorithm - conservative_rescaling: Conservative rescaling of the time of impact - - Returns: - Tuple of: - True if the two points collide, false otherwise. - Output time of impact - )ipc_Qu8mg5v7", - "p0"_a, "p1"_a, "tmax"_a = 1.0, "min_distance"_a = 0, - "tolerance"_a = TightInclusionCCD::DEFAULT_TOLERANCE, - "max_iterations"_a = TightInclusionCCD::DEFAULT_MAX_ITERATIONS, - "conservative_rescaling"_a = - TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING); - - m.def( - "point_edge_nonlinear_ccd", - [](const NonlinearTrajectory& p, const NonlinearTrajectory& e0, - const NonlinearTrajectory& e1, const double tmax, - const double min_distance, const double tolerance, - const long max_iterations, const double conservative_rescaling) { - double toi; - bool r = point_edge_nonlinear_ccd( - p, e0, e1, toi, tmax, min_distance, tolerance, max_iterations, - conservative_rescaling); - return std::make_tuple(r, toi); - }, - R"ipc_Qu8mg5v7( - Perform nonlinear CCD between a point and a linear edge moving along nonlinear trajectories. - - Parameters: - p: Point's trajectory - e0: Edge's first endpoint's trajectory - e1: Edge's second endpoint's trajectory - tmax: Maximum time to check for collision - min_distance: Minimum separation distance between the point and the edge - tolerance: Tolerance for the linear CCD algorithm - max_iterations: Maximum number of iterations for the linear CCD algorithm - conservative_rescaling: Conservative rescaling of the time of impact - - Returns: - Tuple of: - True if the point and edge collide, false otherwise. - Output time of impact - )ipc_Qu8mg5v7", - "p"_a, "e0"_a, "e1"_a, "tmax"_a = 1.0, "min_distance"_a = 0, - "tolerance"_a = TightInclusionCCD::DEFAULT_TOLERANCE, - "max_iterations"_a = TightInclusionCCD::DEFAULT_MAX_ITERATIONS, - "conservative_rescaling"_a = - TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING); - - m.def( - "edge_edge_nonlinear_ccd", - [](const NonlinearTrajectory& ea0, const NonlinearTrajectory& ea1, - const NonlinearTrajectory& eb0, const NonlinearTrajectory& eb1, - const double tmax, const double min_distance, const double tolerance, - const long max_iterations, const double conservative_rescaling) { - double toi; - bool r = edge_edge_nonlinear_ccd( - ea0, ea1, eb0, eb1, toi, tmax, min_distance, tolerance, - max_iterations, conservative_rescaling); - return std::make_tuple(r, toi); - }, - R"ipc_Qu8mg5v7( - Perform nonlinear CCD between two linear edges moving along nonlinear trajectories. - - Parameters: - ea0: First edge's first endpoint's trajectory - ea1: First edge's second endpoint's trajectory - eb0: Second edge's first endpoint's trajectory - eb1: Second edge's second endpoint's trajectory - tmax: Maximum time to check for collision - min_distance: Minimum separation distance between the two edges - tolerance: Tolerance for the linear CCD algorithm - max_iterations: Maximum number of iterations for the linear CCD algorithm - conservative_rescaling: Conservative rescaling of the time of impact - - Returns: - Tuple of: - True if the two edges collide, false otherwise. - Output time of impact - )ipc_Qu8mg5v7", - "ea0"_a, "ea1"_a, "eb0"_a, "eb1"_a, "tmax"_a = 1.0, - "min_distance"_a = 0, - "tolerance"_a = TightInclusionCCD::DEFAULT_TOLERANCE, - "max_iterations"_a = TightInclusionCCD::DEFAULT_MAX_ITERATIONS, - "conservative_rescaling"_a = - TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING); + py::class_(m, "NonlinearCCD") + .def(py::init<>()) + .def( + "point_point_ccd", + [](const NonlinearCCD& self, const NonlinearTrajectory& p0, + const NonlinearTrajectory& p1, const double min_distance, + const double tmax) { + double toi; + bool r = self.point_point_ccd(p0, p1, toi, min_distance, tmax); + return std::make_tuple(r, toi); + }, + R"ipc_Qu8mg5v7( + Perform nonlinear CCD between two points moving along nonlinear trajectories. - m.def( - "point_triangle_nonlinear_ccd", - [](const NonlinearTrajectory& p, const NonlinearTrajectory& t0, - const NonlinearTrajectory& t1, const NonlinearTrajectory& t2, - const double tmax, const double min_distance, const double tolerance, - const long max_iterations, const double conservative_rescaling) { - double toi; - bool r = point_triangle_nonlinear_ccd( - p, t0, t1, t2, toi, tmax, min_distance, tolerance, - max_iterations, conservative_rescaling); - return std::make_tuple(r, toi); - }, - R"ipc_Qu8mg5v7( - Perform nonlinear CCD between a point and a linear triangle moving along nonlinear trajectories. + Parameters: + p0: First point's trajectory + p1: Second point's trajectory + tmax: Maximum time to check for collision + min_distance: Minimum separation distance between the two points + + Returns: + Tuple of: + True if the two points collide, false otherwise. + Output time of impact + )ipc_Qu8mg5v7", + "p0"_a, "p1"_a, "min_distance"_a = 0, "tmax"_a = 1.0) + .def( + "point_edge_ccd", + [](const NonlinearCCD& self, const NonlinearTrajectory& p, + const NonlinearTrajectory& e0, const NonlinearTrajectory& e1, + const double min_distance, const double tmax) { + double toi; + bool r = + self.point_edge_ccd(p, e0, e1, toi, min_distance, tmax); + return std::make_tuple(r, toi); + }, + R"ipc_Qu8mg5v7( + Perform nonlinear CCD between a point and a linear edge moving along nonlinear trajectories. - Parameters: - p: Point's trajectory - t0: Triangle's first vertex's trajectory - t1: Triangle's second vertex's trajectory - t2: Triangle's third vertex's trajectory - tmax: Maximum time to check for collision - min_distance: Minimum separation distance between the two edges - tolerance: Tolerance for the linear CCD algorithm - max_iterations: Maximum number of iterations for the linear CCD algorithm - conservative_rescaling: Conservative rescaling of the time of impact + Parameters: + p: Point's trajectory + e0: Edge's first endpoint's trajectory + e1: Edge's second endpoint's trajectory + min_distance: Minimum separation distance between the point and the edge + tmax: Maximum time to check for collision + + Returns: + Tuple of: + True if the point and edge collide, false otherwise. + Output time of impact + )ipc_Qu8mg5v7", + "p"_a, "e0"_a, "e1"_a, "min_distance"_a = 0, "tmax"_a = 1.0) + .def( + "edge_edge_ccd", + [](const NonlinearCCD& self, const NonlinearTrajectory& ea0, + const NonlinearTrajectory& ea1, const NonlinearTrajectory& eb0, + const NonlinearTrajectory& eb1, const double min_distance, + const double tmax) { + double toi; + bool r = self.edge_edge_ccd( + ea0, ea1, eb0, eb1, toi, min_distance, tmax); + return std::make_tuple(r, toi); + }, + R"ipc_Qu8mg5v7( + Perform nonlinear CCD between two linear edges moving along nonlinear trajectories. - Returns: - Tuple of: - True if the point and triangle collide, false otherwise. - Output time of impact - )ipc_Qu8mg5v7", - "p"_a, "t0"_a, "t1"_a, "t2"_a, "tmax"_a = 1.0, "min_distance"_a = 0, - "tolerance"_a = TightInclusionCCD::DEFAULT_TOLERANCE, - "max_iterations"_a = TightInclusionCCD::DEFAULT_MAX_ITERATIONS, - "conservative_rescaling"_a = - TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING); + Parameters: + ea0: First edge's first endpoint's trajectory + ea1: First edge's second endpoint's trajectory + eb0: Second edge's first endpoint's trajectory + eb1: Second edge's second endpoint's trajectory + min_distance: Minimum separation distance between the two edges + tmax: Maximum time to check for collision + + Returns: + Tuple of: + True if the two edges collide, false otherwise. + Output time of impact + )ipc_Qu8mg5v7", + "ea0"_a, "ea1"_a, "eb0"_a, "eb1"_a, "tmax"_a = 1.0, + "min_distance"_a = 0) + .def( + "point_triangle_ccd", + [](const NonlinearCCD& self, const NonlinearTrajectory& p, + const NonlinearTrajectory& t0, const NonlinearTrajectory& t1, + const NonlinearTrajectory& t2, const double min_distance, + const double tmax) { + double toi; + bool r = self.point_triangle_ccd( + p, t0, t1, t2, toi, min_distance, tmax); + return std::make_tuple(r, toi); + }, + R"ipc_Qu8mg5v7( + Perform nonlinear CCD between a point and a linear triangle moving along nonlinear trajectories. - m.def( - "conservative_piecewise_linear_ccd", - [](const std::function& distance, - const std::function& - max_distance_from_linear, - const std::function& - linear_ccd, - const double tmax, const double min_distance, - const double conservative_rescaling) { - double toi; - bool r = conservative_piecewise_linear_ccd( - distance, max_distance_from_linear, linear_ccd, toi, tmax, - min_distance, conservative_rescaling); - return std::make_tuple(r, toi); - }, - R"ipc_Qu8mg5v7( - Perform conservative piecewise linear CCD of a nonlinear trajectories. + Parameters: + p: Point's trajectory + t0: Triangle's first vertex's trajectory + t1: Triangle's second vertex's trajectory + t2: Triangle's third vertex's trajectory + min_distance: Minimum separation distance between the two edges + tmax: Maximum time to check for collision + + Returns: + Tuple of: + True if the point and triangle collide, false otherwise. + Output time of impact + )ipc_Qu8mg5v7", + "p"_a, "t0"_a, "t1"_a, "t2"_a, "min_distance"_a = 0, "tmax"_a = 1.0) + .def_static( + "conservative_piecewise_linear_ccd", + [](const std::function& distance, + const std::function& + max_distance_from_linear, + const std::function& linear_ccd, + const double min_distance, const double tmax, + const double conservative_rescaling) { + double toi; + bool r = NonlinearCCD::conservative_piecewise_linear_ccd( + distance, max_distance_from_linear, linear_ccd, toi, + min_distance, tmax, conservative_rescaling); + return std::make_tuple(r, toi); + }, + R"ipc_Qu8mg5v7( + Perform conservative piecewise linear CCD of a nonlinear trajectories. - Parameters: - distance: Return the distance for a given time in [0, 1]. - max_distance_from_linear: Return the maximum distance from the linearized trajectory for a given time interval. - linear_ccd: Perform linear CCD on a given time interval. - tmax: Maximum time to check for collision. - min_distance: Minimum separation distance between the objects. - conservative_rescaling: Conservative rescaling of the time of impact. + Parameters: + distance: Return the distance for a given time in [0, 1]. + max_distance_from_linear: Return the maximum distance from the linearized trajectory for a given time interval. + linear_ccd: Perform linear CCD on a given time interval. + tmax: Maximum time to check for collision. + min_distance: Minimum separation distance between the objects. + conservative_rescaling: Conservative rescaling of the time of impact. - Returns: - Tuple of: + Returns: + Tuple of: - Output time of impact. - )ipc_Qu8mg5v7", - "distance"_a, "max_distance_from_linear"_a, "linear_ccd"_a, - "tmax"_a = 1.0, "min_distance"_a = 0, - "conservative_rescaling"_a = - TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING); + Output time of impact. + )ipc_Qu8mg5v7", + "distance"_a, "max_distance_from_linear"_a, "linear_ccd"_a, + "min_distance"_a = 0, "tmax"_a = 1.0, + "conservative_rescaling"_a = + TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING); } diff --git a/src/ipc/broad_phase/sweep_and_tiniest_queue.cpp b/src/ipc/broad_phase/sweep_and_tiniest_queue.cpp index 7446f53c8..eacb22175 100644 --- a/src/ipc/broad_phase/sweep_and_tiniest_queue.cpp +++ b/src/ipc/broad_phase/sweep_and_tiniest_queue.cpp @@ -79,13 +79,15 @@ void SweepAndTiniestQueue::build( // Convert from ipc::AABB to scalable_ccd::cuda::AABB boxes->vertices.resize(vertex_boxes.size()); for (int i = 0; i < vertex_boxes.size(); ++i) { - for (int d = 0; d < 3; ++d) { - boxes->vertices[i].min[d] = - vertex_boxes[i].min.size() > d ? vertex_boxes[i].min[d] : 0; - boxes->vertices[i].max[d] = - vertex_boxes[i].max.size() > d ? vertex_boxes[i].max[d] : 0; - boxes->vertices[i].vertex_ids[d] = vertex_boxes[i].vertex_ids[d]; - } + boxes->vertices[i].min = Scalar3( + vertex_boxes[i].min.x(), vertex_boxes[i].min.y(), + vertex_boxes[i].min.size() > 2 ? vertex_boxes[i].min.z() : 0); + boxes->vertices[i].max = Scalar3( + vertex_boxes[i].max.x(), vertex_boxes[i].max.y(), + vertex_boxes[i].max.size() > 2 ? vertex_boxes[i].max.z() : 0); + boxes->vertices[i].vertex_ids = int3( + vertex_boxes[i].vertex_ids[0], vertex_boxes[i].vertex_ids[1], + vertex_boxes[i].vertex_ids[2]); boxes->vertices[i].element_id = i; } diff --git a/src/ipc/ccd/nonlinear_ccd.cpp b/src/ipc/ccd/nonlinear_ccd.cpp index 5f2305c7d..d0a4c0502 100644 --- a/src/ipc/ccd/nonlinear_ccd.cpp +++ b/src/ipc/ccd/nonlinear_ccd.cpp @@ -51,7 +51,17 @@ double IntervalNonlinearTrajectory::max_distance_from_linear( // ============================================================================ -bool conservative_piecewise_linear_ccd( +NonlinearCCD::NonlinearCCD( + const double _tolerance, + const long _max_iterations, + const double _conservative_rescaling) + : tolerance(_tolerance) + , max_iterations(_max_iterations) + , conservative_rescaling(_conservative_rescaling) +{ +} + +bool NonlinearCCD::conservative_piecewise_linear_ccd( const std::function& distance, const std::function& max_distance_from_linear, @@ -150,15 +160,12 @@ bool conservative_piecewise_linear_ccd( // ============================================================================ -bool point_point_nonlinear_ccd( +bool NonlinearCCD::point_point_ccd( const NonlinearTrajectory& p0, const NonlinearTrajectory& p1, double& toi, - const double tmax, const double min_distance, - const double tolerance, - const long max_iterations, - const double conservative_rescaling) + const double tmax) const { return conservative_piecewise_linear_ccd( [&](const double t) { @@ -187,16 +194,13 @@ bool point_point_nonlinear_ccd( toi, tmax, min_distance, conservative_rescaling); } -bool point_edge_nonlinear_ccd( +bool NonlinearCCD::point_edge_ccd( const NonlinearTrajectory& p, const NonlinearTrajectory& e0, const NonlinearTrajectory& e1, double& toi, - const double tmax, const double min_distance, - const double tolerance, - const long max_iterations, - const double conservative_rescaling) + const double tmax) const { return conservative_piecewise_linear_ccd( [&](const double t) { @@ -226,17 +230,14 @@ bool point_edge_nonlinear_ccd( toi, tmax, min_distance, conservative_rescaling); } -bool edge_edge_nonlinear_ccd( +bool NonlinearCCD::edge_edge_ccd( const NonlinearTrajectory& ea0, const NonlinearTrajectory& ea1, const NonlinearTrajectory& eb0, const NonlinearTrajectory& eb1, double& toi, - const double tmax, - const double min_sep_distance, - const double tolerance, - const long max_iterations, - const double conservative_rescaling) + const double min_distance, + const double tmax) const { return conservative_piecewise_linear_ccd( [&](const double t) { @@ -265,20 +266,17 @@ bool edge_edge_nonlinear_ccd( output_tolerance, // delta_actual no_zero_toi); // no zero toi }, - toi, tmax, min_sep_distance, conservative_rescaling); + toi, tmax, min_distance, conservative_rescaling); } -bool point_triangle_nonlinear_ccd( +bool NonlinearCCD::point_triangle_ccd( const NonlinearTrajectory& p, const NonlinearTrajectory& t0, const NonlinearTrajectory& t1, const NonlinearTrajectory& t2, double& toi, - const double tmax, const double min_distance, - const double tolerance, - const long max_iterations, - const double conservative_rescaling) + const double tmax) const { return conservative_piecewise_linear_ccd( [&](const double t) { diff --git a/src/ipc/ccd/nonlinear_ccd.hpp b/src/ipc/ccd/nonlinear_ccd.hpp index 3bc4a2eb2..90a13300a 100644 --- a/src/ipc/ccd/nonlinear_ccd.hpp +++ b/src/ipc/ccd/nonlinear_ccd.hpp @@ -48,124 +48,123 @@ class IntervalNonlinearTrajectory : virtual public NonlinearTrajectory { }; #endif -/// @brief Perform nonlinear CCD between two points moving along nonlinear trajectories. -/// @param[in] p0 First point's trajectory -/// @param[in] p1 Second point's trajectory -/// @param[out] toi Output time of impact -/// @param[in] tmax Maximum time to check for collision -/// @param[in] min_distance Minimum separation distance between the two points -/// @param[in] tolerance Tolerance for the linear CCD algorithm -/// @param[in] max_iterations Maximum number of iterations for the linear CCD algorithm -/// @param[in] conservative_rescaling Conservative rescaling of the time of impact -/// @return True if the two points collide, false otherwise. -bool point_point_nonlinear_ccd( - const NonlinearTrajectory& p0, - const NonlinearTrajectory& p1, - double& toi, - const double tmax = 1.0, - const double min_distance = 0, - const double tolerance = TightInclusionCCD::DEFAULT_TOLERANCE, - const long max_iterations = TightInclusionCCD::DEFAULT_MAX_ITERATIONS, - const double conservative_rescaling = - TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING); - -/// @brief Perform nonlinear CCD between a point and a linear edge moving along nonlinear trajectories. -/// @param[in] p Point's trajectory -/// @param[in] e0 Edge's first endpoint's trajectory -/// @param[in] e1 Edge's second endpoint's trajectory -/// @param[out] toi Output time of impact -/// @param[in] tmax Maximum time to check for collision -/// @param[in] min_distance Minimum separation distance between the point and the edge -/// @param[in] tolerance Tolerance for the linear CCD algorithm -/// @param[in] max_iterations Maximum number of iterations for the linear CCD algorithm -/// @param[in] conservative_rescaling Conservative rescaling of the time of impact -/// @return True if the point and edge collide, false otherwise. -bool point_edge_nonlinear_ccd( - const NonlinearTrajectory& p, - const NonlinearTrajectory& e0, - const NonlinearTrajectory& e1, - double& toi, - const double tmax = 1.0, - const double min_distance = 0, - const double tolerance = TightInclusionCCD::DEFAULT_TOLERANCE, - const long max_iterations = TightInclusionCCD::DEFAULT_MAX_ITERATIONS, - const double conservative_rescaling = - TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING); - -/// @brief Perform nonlinear CCD between two linear edges moving along nonlinear trajectories. -/// @ingroup ccd -/// @param[in] ea0 First edge's first endpoint's trajectory -/// @param[in] ea1 First edge's second endpoint's trajectory -/// @param[in] eb0 Second edge's first endpoint's trajectory -/// @param[in] eb1 Second edge's second endpoint's trajectory -/// @param[out] toi Output time of impact -/// @param[in] tmax Maximum time to check for collision -/// @param[in] min_distance Minimum separation distance between the two edges -/// @param[in] tolerance Tolerance for the linear CCD algorithm -/// @param[in] max_iterations Maximum number of iterations for the linear CCD algorithm -/// @param[in] conservative_rescaling Conservative rescaling of the time of impact -/// @return True if the two edges collide, false otherwise. -bool edge_edge_nonlinear_ccd( - const NonlinearTrajectory& ea0, - const NonlinearTrajectory& ea1, - const NonlinearTrajectory& eb0, - const NonlinearTrajectory& eb1, - double& toi, - const double tmax = 1.0, - const double min_distance = 0, - const double tolerance = TightInclusionCCD::DEFAULT_TOLERANCE, - const long max_iterations = TightInclusionCCD::DEFAULT_MAX_ITERATIONS, - const double conservative_rescaling = - TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING); - -/// @brief Perform nonlinear CCD between a point and a linear triangle moving along nonlinear trajectories. -/// @param[in] p Point's trajectory -/// @param[in] t0 Triangle's first vertex's trajectory -/// @param[in] t1 Triangle's second vertex's trajectory -/// @param[in] t2 Triangle's third vertex's trajectory -/// @param[out] toi Output time of impact -/// @param[in] tmax Maximum time to check for collision -/// @param[in] min_distance Minimum separation distance between the two edges -/// @param[in] tolerance Tolerance for the linear CCD algorithm -/// @param[in] max_iterations Maximum number of iterations for the linear CCD algorithm -/// @param[in] conservative_rescaling Conservative rescaling of the time of impact -/// @return True if the point and triangle collide, false otherwise. -bool point_triangle_nonlinear_ccd( - const NonlinearTrajectory& p, - const NonlinearTrajectory& t0, - const NonlinearTrajectory& t1, - const NonlinearTrajectory& t2, - double& toi, - const double tmax = 1.0, - const double min_distance = 0, - const double tolerance = TightInclusionCCD::DEFAULT_TOLERANCE, - const long max_iterations = TightInclusionCCD::DEFAULT_MAX_ITERATIONS, - const double conservative_rescaling = - TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING); - -/// @brief Perform conservative piecewise linear CCD of a nonlinear trajectories. -/// @param[in] distance Return the distance for a given time in [0, 1]. -/// @param[in] max_distance_from_linear Return the maximum distance from the linearized trajectory for a given time interval. -/// @param[in] linear_ccd Perform linear CCD on a given time interval. -/// @param[out] toi Output time of impact. -/// @param[in] tmax Maximum time to check for collision. -/// @param[in] min_distance Minimum separation distance between the objects. -/// @param[in] conservative_rescaling Conservative rescaling of the time of impact. -/// @return True if a collision was detected, false otherwise. -bool conservative_piecewise_linear_ccd( - const std::function& distance, - const std::function& - max_distance_from_linear, - const std::function& linear_ccd, - double& toi, - const double tmax = 1.0, - const double min_distance = 0, - const double conservative_rescaling = - TightInclusionCCD::DEFAULT_CONSERVATIVE_RESCALING); +class NonlinearCCD { +public: + /// The default tolerance used with Tight-Inclusion CCD. + static constexpr double DEFAULT_TOLERANCE = 1e-6; + /// The default maximum number of iterations used with Tight-Inclusion CCD. + static constexpr long DEFAULT_MAX_ITERATIONS = 10'000'000l; + /// The default conservative rescaling value used to avoid taking steps + /// exactly to impact. + static constexpr double DEFAULT_CONSERVATIVE_RESCALING = 0.8; + + NonlinearCCD( + const double tolerance = DEFAULT_TOLERANCE, + const long max_iterations = DEFAULT_MAX_ITERATIONS, + const double conservative_rescaling = DEFAULT_CONSERVATIVE_RESCALING); + + virtual ~NonlinearCCD() = default; + + /// @brief Perform nonlinear CCD between two points moving along nonlinear trajectories. + /// @param[in] p0 First point's trajectory + /// @param[in] p1 Second point's trajectory + /// @param[out] toi Output time of impact + /// @param[in] min_distance Minimum separation distance between the two points + /// @param[in] tmax Maximum time to check for collision + /// @return True if the two points collide, false otherwise. + virtual bool point_point_ccd( + const NonlinearTrajectory& p0, + const NonlinearTrajectory& p1, + double& toi, + const double min_distance = 0, + const double tmax = 1.0) const; + + /// @brief Perform nonlinear CCD between a point and a linear edge moving along nonlinear trajectories. + /// @param[in] p Point's trajectory + /// @param[in] e0 Edge's first endpoint's trajectory + /// @param[in] e1 Edge's second endpoint's trajectory + /// @param[out] toi Output time of impact + /// @param[in] min_distance Minimum separation distance between the point and the edge + /// @param[in] tmax Maximum time to check for collision + /// @return True if the point and edge collide, false otherwise. + virtual bool point_edge_ccd( + const NonlinearTrajectory& p, + const NonlinearTrajectory& e0, + const NonlinearTrajectory& e1, + double& toi, + const double min_distance = 0, + const double tmax = 1.0) const; + + /// @brief Perform nonlinear CCD between two linear edges moving along nonlinear trajectories. + /// @ingroup ccd + /// @param[in] ea0 First edge's first endpoint's trajectory + /// @param[in] ea1 First edge's second endpoint's trajectory + /// @param[in] eb0 Second edge's first endpoint's trajectory + /// @param[in] eb1 Second edge's second endpoint's trajectory + /// @param[out] toi Output time of impact + /// @param[in] min_distance Minimum separation distance between the two edges + /// @param[in] tmax Maximum time to check for collision + /// @return True if the two edges collide, false otherwise. + virtual bool edge_edge_ccd( + const NonlinearTrajectory& ea0, + const NonlinearTrajectory& ea1, + const NonlinearTrajectory& eb0, + const NonlinearTrajectory& eb1, + double& toi, + const double min_distance = 0, + const double tmax = 1.0) const; + + /// @brief Perform nonlinear CCD between a point and a linear triangle moving along nonlinear trajectories. + /// @param[in] p Point's trajectory + /// @param[in] t0 Triangle's first vertex's trajectory + /// @param[in] t1 Triangle's second vertex's trajectory + /// @param[in] t2 Triangle's third vertex's trajectory + /// @param[out] toi Output time of impact + /// @param[in] min_distance Minimum separation distance between the two edges + /// @param[in] tmax Maximum time to check for collision + /// @return True if the point and triangle collide, false otherwise. + bool point_triangle_ccd( + const NonlinearTrajectory& p, + const NonlinearTrajectory& t0, + const NonlinearTrajectory& t1, + const NonlinearTrajectory& t2, + double& toi, + const double min_distance = 0.0, + const double tmax = 1.0) const; + + /// @brief Solver tolerance. + double tolerance; + + /// @brief Maximum number of iterations. + long max_iterations; + + /// @brief Conservative rescaling of the time of impact. + double conservative_rescaling; + +public: + /// @brief Perform conservative piecewise linear CCD of a nonlinear trajectories. + /// @param[in] distance Return the distance for a given time in [0, 1]. + /// @param[in] max_distance_from_linear Return the maximum distance from the linearized trajectory for a given time interval. + /// @param[in] linear_ccd Perform linear CCD on a given time interval. + /// @param[out] toi Output time of impact. + /// @param[in] tmax Maximum time to check for collision. + /// @param[in] min_distance Minimum separation distance between the objects. + /// @param[in] conservative_rescaling Conservative rescaling of the time of impact. + /// @return True if a collision was detected, false otherwise. + static bool conservative_piecewise_linear_ccd( + const std::function& distance, + const std::function& + max_distance_from_linear, + const std::function& linear_ccd, + double& toi, + const double min_distance = 0, + const double tmax = 1.0, + const double conservative_rescaling = DEFAULT_CONSERVATIVE_RESCALING); +}; } // namespace ipc diff --git a/tests/src/tests/ccd/test_nonlinear_ccd.cpp b/tests/src/tests/ccd/test_nonlinear_ccd.cpp index cc4cb284a..45218285e 100644 --- a/tests/src/tests/ccd/test_nonlinear_ccd.cpp +++ b/tests/src/tests/ccd/test_nonlinear_ccd.cpp @@ -179,12 +179,11 @@ TEST_CASE("Nonlinear Point-Point CCD", "[ccd][nonlinear][point-point]") } #endif + NonlinearCCD ccd; + ccd.conservative_rescaling = 0.9; + double toi; - bool collision = point_point_nonlinear_ccd( - p0, *p1, toi, /*tmax=*/1.0, /*min_distance=*/0, - TightInclusionCCD::DEFAULT_TOLERANCE, - TightInclusionCCD::DEFAULT_MAX_ITERATIONS, - /*conservative_rescaling=*/0.9); + bool collision = ccd.point_point_ccd(p0, *p1, toi); CHECK(collision); CHECK(toi <= 0.5); @@ -199,12 +198,11 @@ TEST_CASE("Nonlinear Point-Edge CCD", "[ccd][nonlinear][point-edge]") const RotationalTrajectory e1( Eigen::Vector2d(1, 0), Eigen::Vector2d::Zero(), 2 * igl::PI); + NonlinearCCD ccd; + ccd.conservative_rescaling = 0.9; + double toi; - bool collision = point_edge_nonlinear_ccd( - p, e0, e1, toi, /*tmax=*/1.0, /*min_distance=*/0, - TightInclusionCCD::DEFAULT_TOLERANCE, - TightInclusionCCD::DEFAULT_MAX_ITERATIONS, - /*conservative_rescaling=*/0.9); + bool collision = ccd.point_edge_ccd(p, e0, e1, toi); CHECK(collision); CHECK(toi <= 0.25); @@ -226,14 +224,11 @@ TEST_CASE("Rigid 2D Trajectory", "[ccd][nonlinear][point-edge]") Eigen::Vector2d(+1, 0), Eigen::Vector2d::Zero(), Eigen::Vector2d::Zero(), 0, igl::PI); + NonlinearCCD ccd; + ccd.conservative_rescaling = 0.9; + double toi; - bool collision = ipc::point_edge_nonlinear_ccd( - p, e0, e1, toi, /*tmax=*/1.0, /*min_distance=*/0, - TightInclusionCCD::DEFAULT_TOLERANCE, - TightInclusionCCD::DEFAULT_MAX_ITERATIONS, - // increase the conservative_rescaling from 0.8 to 0.9 to get a more - // accurate estimate - /*conservative_rescaling=*/0.9); + bool collision = ccd.point_edge_ccd(p, e0, e1, toi); CHECK(collision); CHECK((0.49 <= toi && toi <= 0.5)); // conservative estimate @@ -250,7 +245,7 @@ TEST_CASE("Nonlinear Edge-Edge CCD", "[ccd][nonlinear][edge-edge]") const StaticTrajectory eb1(Eigen::Vector3d(1, 0.5, 0)); double toi; - bool collision = edge_edge_nonlinear_ccd(ea0, ea1, eb0, eb1, toi); + bool collision = NonlinearCCD().edge_edge_ccd(ea0, ea1, eb0, eb1, toi); CHECK(collision); CHECK(toi <= 30 / 360.0); @@ -269,12 +264,11 @@ TEST_CASE("Nonlinear Point-Triangle CCD", "[ccd][nonlinear][point-triangle]") Eigen::Vector3d(x, 0, -1), Eigen::Vector3d::Zero(), igl::PI); const StaticTrajectory p(Eigen::Vector3d(0, 0.5, 0)); + NonlinearCCD ccd; + ccd.conservative_rescaling = 0.9; + double toi; - bool collision = point_triangle_nonlinear_ccd( - p, t0, t1, t2, toi, /*tmax=*/1.0, /*min_distance=*/0, - TightInclusionCCD::DEFAULT_TOLERANCE, - TightInclusionCCD::DEFAULT_MAX_ITERATIONS, - /*conservative_rescaling=*/0.9); + bool collision = ccd.point_triangle_ccd(p, t0, t1, t2, toi); CHECK(collision); CHECK(toi <= 0.5); From 0f3bc003c17983690d62bd7e6c0e92095d081c0d Mon Sep 17 00:00:00 2001 From: Zachary Ferguson Date: Wed, 27 Aug 2025 20:32:04 -0400 Subject: [PATCH 24/24] Add RigidCandidates class for managing collision candidates and implement collision detection methods --- src/ipc/dynamics/rigid/rigid_candidates.cpp | 277 ++++++++++++++++++++ src/ipc/dynamics/rigid/rigid_candidates.hpp | 111 ++++++++ 2 files changed, 388 insertions(+) create mode 100644 src/ipc/dynamics/rigid/rigid_candidates.cpp create mode 100644 src/ipc/dynamics/rigid/rigid_candidates.hpp diff --git a/src/ipc/dynamics/rigid/rigid_candidates.cpp b/src/ipc/dynamics/rigid/rigid_candidates.cpp new file mode 100644 index 000000000..1d14b759d --- /dev/null +++ b/src/ipc/dynamics/rigid/rigid_candidates.cpp @@ -0,0 +1,277 @@ +#include "candidates.hpp" + +#include +#include +#include +#include +#include + +#include +#include +#include + +#include +#include + +namespace ipc { + +void RigidCandidates::build( + const RigidBodies& bodies, + const std::vector& poses_t0, + const std::vector& poses_t1, + const double inflation_radius, + const std::shared_ptr broad_phase) +{ + assert(poses_t0.size() == bodies.num_bodies()); + assert(poses_t1.size() == bodies.num_bodies()); + assert(broad_phase != nullptr); + + clear(); + + const int dim = poses_t0[0].position.size(); + + // 1. Broad phase between bodies + std::vector> body_pairs; + { + Eigen::MatrixXd V(2 * bodies.num_bodies(), dim); + Eigen::MatrixXi E(bodies.num_bodies(), 2); + // Eigen::VectorXi group_ids(2 * num_bodies()); + double max_radius = 0; + for (int i = 0; i < num_bodies(); i++) { + V.row(2 * i + 0) = poses_t0[i].position; + V.row(2 * i + 1) = poses_t1[i].position; + E(i, 0) = 2 * i + 0; + E(i, 1) = 2 * i + 1; + max_radius = std::max(m_rbs[i].r_max, max_radius); + group_ids[2 * i + 1] = group_ids[2 * i] = m_rbs[i].group_id; + } + } +} + +bool RigidCandidates::is_step_collision_free( + const CollisionMesh& mesh, + Eigen::ConstRef vertices_t0, + Eigen::ConstRef vertices_t1, + const double min_distance, + const NarrowPhaseCCD& narrow_phase_ccd) const +{ + assert(vertices_t0.rows() == mesh.num_vertices()); + assert(vertices_t1.rows() == mesh.num_vertices()); + + // Narrow phase + for (size_t i = 0; i < size(); i++) { + const CollisionStencil& candidate = (*this)[i]; + + double toi; + bool is_collision = candidate.ccd( + candidate.dof(vertices_t0, mesh.edges(), mesh.faces()), + candidate.dof(vertices_t1, mesh.edges(), mesh.faces()), // + toi, min_distance, /*tmax=*/1.0, narrow_phase_ccd); + + if (is_collision) { + return false; + } + } + + return true; +} + +double RigidCandidates::compute_collision_free_stepsize( + const CollisionMesh& mesh, + Eigen::ConstRef vertices_t0, + Eigen::ConstRef vertices_t1, + const double min_distance, + const NarrowPhaseCCD& narrow_phase_ccd) const +{ + assert(vertices_t0.rows() == mesh.num_vertices()); + assert(vertices_t1.rows() == mesh.num_vertices()); + + if (empty()) { + return 1; // No possible collisions, so can take full step. + } + + double earliest_toi = 1; + std::shared_mutex earliest_toi_mutex; + + tbb::parallel_for( + tbb::blocked_range(0, size()), + [&](tbb::blocked_range r) { + for (size_t i = r.begin(); i < r.end(); i++) { + // Use the mutex to read as well in case writing double takes + // more than one clock cycle. + double tmax; + { + std::shared_lock lock(earliest_toi_mutex); + tmax = earliest_toi; + } + + const CollisionStencil& candidate = (*this)[i]; + + double toi = std::numeric_limits::infinity(); // output + const bool are_colliding = candidate.ccd( + candidate.dof(vertices_t0, mesh.edges(), mesh.faces()), + candidate.dof(vertices_t1, mesh.edges(), mesh.faces()), // + toi, min_distance, tmax, narrow_phase_ccd); + + if (are_colliding) { + std::unique_lock lock(earliest_toi_mutex); + if (toi < earliest_toi) { + earliest_toi = toi; + } + } + } + }); + + assert(earliest_toi >= 0 && earliest_toi <= 1.0); + return earliest_toi; +} + +double RigidCandidates::compute_noncandidate_conservative_stepsize( + const CollisionMesh& mesh, + Eigen::ConstRef displacements, + const double dhat) const +{ + assert(displacements.rows() == mesh.num_vertices()); + + if (empty()) { + return 1; // No possible collisions, so can take full step. + } + + const Eigen::MatrixXi& E = mesh.edges(); + const Eigen::MatrixXi& F = mesh.faces(); + + std::vector is_vertex_a_candidates(mesh.num_vertices(), false); + for (size_t i = 0; i < size(); i++) { + for (const index_t vid : (*this)[i].vertex_ids(E, F)) { + if (vid < 0) { + break; + } + is_vertex_a_candidates[vid] = true; + } + } + + double max_displacement = 0; + for (size_t i = 0; i < displacements.rows(); i++) { + if (!is_vertex_a_candidates[i]) { + continue; + } + max_displacement = + std::max(max_displacement, displacements.row(i).norm()); + } + + return 0.5 * dhat / max_displacement; +} + +double RigidCandidates::compute_cfl_stepsize( + const CollisionMesh& mesh, + Eigen::ConstRef vertices_t0, + Eigen::ConstRef vertices_t1, + const double dhat, + const double min_distance, + const std::shared_ptr broad_phase, + const NarrowPhaseCCD& narrow_phase_ccd) const +{ + assert(vertices_t0.rows() == mesh.num_vertices()); + assert(vertices_t1.rows() == mesh.num_vertices()); + + const double alpha_C = this->compute_collision_free_stepsize( + mesh, vertices_t0, vertices_t1, min_distance, narrow_phase_ccd); + + const double alpha_F = this->compute_noncandidate_conservative_stepsize( + mesh, vertices_t1 - vertices_t0, dhat); + + // If alpha_F < 0.5 * alpha_C, then we should do full CCD. + if (alpha_F < 0.5 * alpha_C) { + return ipc::compute_collision_free_stepsize( + mesh, vertices_t0, vertices_t1, min_distance, broad_phase, + narrow_phase_ccd); + } + return std::min(alpha_C, alpha_F); +} + +size_t RigidCandidates::size() const +{ + return vv_candidates.size() + ev_candidates.size() + ee_candidates.size() + + fv_candidates.size(); +} + +bool RigidCandidates::empty() const +{ + return vv_candidates.empty() && ev_candidates.empty() + && ee_candidates.empty() && fv_candidates.empty(); +} + +void RigidCandidates::clear() +{ + vv_candidates.clear(); + ev_candidates.clear(); + ee_candidates.clear(); + fv_candidates.clear(); +} + +CollisionStencil& RigidCandidates::operator[](size_t i) +{ + if (i < vv_candidates.size()) { + return vv_candidates[i]; + } + i -= vv_candidates.size(); + if (i < ev_candidates.size()) { + return ev_candidates[i]; + } + i -= ev_candidates.size(); + if (i < ee_candidates.size()) { + return ee_candidates[i]; + } + i -= ee_candidates.size(); + if (i < fv_candidates.size()) { + return fv_candidates[i]; + } + throw std::out_of_range("Candidate index is out of range!"); +} + +const CollisionStencil& RigidCandidates::operator[](size_t i) const +{ + if (i < vv_candidates.size()) { + return vv_candidates[i]; + } + i -= vv_candidates.size(); + if (i < ev_candidates.size()) { + return ev_candidates[i]; + } + i -= ev_candidates.size(); + if (i < ee_candidates.size()) { + return ee_candidates[i]; + } + i -= ee_candidates.size(); + if (i < fv_candidates.size()) { + return fv_candidates[i]; + } + throw std::out_of_range("Candidate index is out of range!"); +} + +bool RigidCandidates::write_obj( + const std::string& filename, + Eigen::ConstRef vertices, + Eigen::ConstRef edges, + Eigen::ConstRef faces) const +{ + std::ofstream obj(filename, std::ios::out); + if (!obj.is_open()) { + return false; + } + int v_offset = 0; + ipc::write_candidates_obj( + obj, vertices, edges, faces, vv_candidates, v_offset); + v_offset += vv_candidates.size() * 2; + ipc::write_candidates_obj( + obj, vertices, edges, faces, ev_candidates, v_offset); + v_offset += ev_candidates.size() * 3; + ipc::write_candidates_obj( + obj, vertices, edges, faces, ee_candidates, v_offset); + v_offset += ee_candidates.size() * 4; + ipc::write_candidates_obj( + obj, vertices, faces, faces, fv_candidates, v_offset); + return true; +} + +} // namespace ipc diff --git a/src/ipc/dynamics/rigid/rigid_candidates.hpp b/src/ipc/dynamics/rigid/rigid_candidates.hpp new file mode 100644 index 000000000..3feec20fd --- /dev/null +++ b/src/ipc/dynamics/rigid/rigid_candidates.hpp @@ -0,0 +1,111 @@ +#pragma once + +#include +#include + +namespace ipc { + +/// @brief A class for storing and managing collision candidates. +class RigidCandidates : public Candidates { +public: + RigidCandidates() = default; + + using Candidates::build; + + /// @brief Initialize the set of discrete collision detection candidates. + /// @param bodies The rigid bodies. + /// @param poses The poses of the rigid bodies. + /// @param inflation_radius Amount to inflate the bounding boxes. + /// @param broad_phase Broad phase method to use. + void build( + const RigidBodies& bodies, + const std::vector& poses, + const double inflation_radius = 0, + const std::shared_ptr broad_phase = + make_default_broad_phase()) + { + // TODO: Customize this to us + return Candidates::build( + bodies, bodies.vertices(poses), inflation_radius, broad_phase); + } + + /// @brief Initialize the set of continuous collision detection candidates. + /// @note Assumes the trajectory is linear. + /// @param bodies The rigid bodies. + /// @param poses_t0 The starting poses of the rigid bodies. + /// @param poses_t1 The ending poses of the rigid bodies. + /// @param inflation_radius Amount to inflate the bounding boxes. + /// @param broad_phase Broad phase method to use. + void build( + const RigidBodies& bodies, + const std::vector& poses_t0, + const std::vector& poses_t1, + const double inflation_radius = 0, + const std::shared_ptr broad_phase = + make_default_broad_phase()); + + /// @brief Determine if the step is collision free from the set of candidates. + /// @note Assumes the trajectory is linear. + /// @param bodies The rigid bodies. + /// @param poses_t0 The starting poses of the rigid bodies. + /// @param poses_t1 The ending poses of the rigid bodies. + /// @param min_distance The minimum distance allowable between any two elements. + /// @param narrow_phase_ccd The narrow phase CCD algorithm to use. + /// @returns True if any collisions occur. + bool is_step_collision_free( + const CollisionMesh& mesh, + const std::vector& poses_t0, + const std::vector& poses_t1, + const double min_distance = 0.0, + const NonlinearCCD& nonlinear_ccd = NonlinearCCD()) const; + + /// @brief Computes a maximal step size that is collision free using the set of collision candidates. + /// @note Assumes the trajectory is linear. + /// @param bodies The rigid bodies. + /// @param poses_t0 The starting poses of the rigid bodies. + /// @param poses_t1 The ending poses of the rigid bodies. + /// @param min_distance The minimum distance allowable between any two elements. + /// @param narrow_phase_ccd The narrow phase CCD algorithm to use. + /// @returns A step-size \f$\in [0, 1]\f$ that is collision free. A value of 1.0 if a full step and 0.0 is no step. + double compute_collision_free_stepsize( + const CollisionMesh& mesh, + const std::vector& poses_t0, + const std::vector& poses_t1, + const double min_distance = 0.0, + const NonlinearCCD& nonlinear_ccd = NonlinearCCD()) const; + + /// @brief Computes a conservative bound on the largest-feasible step size for surface primitives not in collision. + /// @param bodies The rigid bodies. + /// @param displacements Surface vertex displacements (rowwise). + /// @param dhat Barrier activation distance. + double compute_noncandidate_conservative_stepsize( + const CollisionMesh& mesh, + Eigen::ConstRef displacements, + const double dhat) const; + + /// @brief Computes a CFL-inspired CCD maximum step step size. + /// @param bodies The rigid bodies. + /// @param poses_t0 The starting poses of the rigid bodies. + /// @param poses_t1 The ending poses of the rigid bodies. + /// @param dhat Barrier activation distance. + /// @param min_distance The minimum distance allowable between any two elements. + /// @param broad_phase The broad phase algorithm to use. + /// @param narrow_phase_ccd The narrow phase CCD algorithm to use. + double compute_cfl_stepsize( + const CollisionMesh& mesh, + const std::vector& poses_t0, + const std::vector& poses_t1, + const double dhat, + const double min_distance = 0.0, + const std::shared_ptr broad_phase = + make_default_broad_phase(), + const NonlinearCCD& nonlinear_ccd = NonlinearCCD()) const; + +public: + std::vector vv_candidates; + std::vector ev_candidates; + std::vector ee_candidates; + std::vector fv_candidates; +}; + +} // namespace ipc