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Voxelization.js
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// Copyright (c) 2012 Vincenzo Giovanni Comito
// See the file license.txt for copying permission.
// Voxelization.js
// Written by Clynamen, 23/08/2012
// Utility for voxelization of a mesh.
// Thanks to Mike Vandelay for the
// AABB-Triangle SAT implementation in C++.
#pragma strict
static var MAX_FLOAT : float = 9999999999999999f;
static var MIN_FLOAT : float = -9999999999999999f;
public class GridSize {
public var x : int;
public var y : int;
public var z : int;
public var side : float;
public function GridSize(gridSize : GridSize) {
this.x = gridSize.x;
this.y = gridSize.y;
this.z = gridSize.z;
this.side = gridSize.side;
}
public function GridSize(x : int, y : int, z :int, side : float) {
this.x = x;
this.y = y;
this.z = z;
this.side = side;
}
};
static public class Voxelization {
public class AABCGrid {
private var side : float;
private var width : short;
private var height : short;
private var depth : short;
private var origin : Vector3;
private var cubeSet : boolean[,,];
private var cubeNormalSum : short[,,];
private var debug = false;
protected class AABCPosition {
public var x : short;
public var y : short;
public var z : short;
public function AABCPosition(aABCPosition : AABCPosition) {
this.x = aABCPosition.x;
this.y = aABCPosition.y;
this.z = aABCPosition.z;
}
public function AABCPosition(x : short, y : short, z : short) {
this.x = x;
this.y = y;
this.z = z;
}
};
public class AABC extends AABCPosition {
private var grid : AABCGrid;
public function AABC(aABC : AABC) {
super(aABC.x, aABC.y, aABC.z);
this.grid = aABC.grid;
}
public function AABC(x : short, y : short, z : short, grid : AABCGrid) {
super(x, y, z);
this.x = x;
this.y = y;
this.z = z;
this.grid = grid;
}
public function AABC(position : AABCPosition, grid : AABCGrid) {
super(position.x, position.y, position.z);
this.grid = grid;
}
public function GetCenter() : Vector3 {
return grid.GetAABCCenter(x, y, z);
}
public function GetGrid() : AABCGrid {
return grid;
}
public function IsSet() : boolean {
return grid.IsAABCSet(x, y, z);
}
public function GetCorners(x : short, y : short, z : short) : Vector3[] {
return grid.GetAABCCorners(x, y, z);
}
};
protected class AABCGridIteratorBase {
protected var grid : AABCGrid;
protected var position : AABCPosition;
protected function AABCGridIteratorBase(grid : AABCGrid) {
this.grid = grid;
}
public function HasNext() : boolean {}
public function Next() : AABC {}
};
public class AABCGridIterator extends AABCGridIteratorBase {
public function AABCGridIterator(grid : AABCGrid) {
super(grid);
}
public function HasNext() : boolean {
if (position.x == grid.width &&
position.y == grid.height &&
position.z == grid.depth) {
return false;
}
return true;
}
public function Next() : AABC {
position.z++;
if (position.z == grid.depth) {
position.z = 0;
position.y++;
if (position.y == grid.height) {
position.y = 0;
position.x++;
if (position.x > grid.width) {
throw new System.IndexOutOfRangeException();
}
}
}
return AABC(position, grid);
}
}
public class AABCGridSetAABCIterator extends AABCGridIteratorBase {
private var nextFound : boolean;
private var nextPosition : AABCPosition;
public function AABCGridSetAABCIterator(grid : AABCGrid) {
super(grid);
position = new AABCPosition(0, 0, 0);
if (grid.IsAABCSet(position)) {
nextPosition = position;
}
nextFound = true;
}
public function HasNext() : boolean {
if (!nextFound) {
return FindNext();
}
return true;
}
public function Next() : AABC {
if (!nextFound) {
FindNext();
}
position = nextPosition;
nextFound = false;
return AABC(position, grid);
}
private function FindNext() : boolean {
nextPosition = new AABCPosition(position);
nextPosition.z++;
for (; nextPosition.x < grid.width; nextPosition.x++) {
for (; nextPosition.y < grid.height; nextPosition.y++) {
for (; nextPosition.z < grid.depth; nextPosition.z++) {
if (grid.IsAABCSet(nextPosition.x, nextPosition.y, nextPosition.z)) {
nextFound = true;
return true;
}
}
nextPosition.z = 0;
}
nextPosition.y = 0;
}
nextFound = false;
return false;
}
}
public function AABCGrid(x : short, y : short, z : short, sideLength : float) {
width = x;
height = y;
depth = z;
side = sideLength;
origin = new Vector3();
cubeSet = new boolean[width, height, depth];
}
public function AABCGrid(x : short, y : short, z : short, sideLength : float, ori : Vector3) {
width = x;
height = y;
depth = z;
side = sideLength;
origin = ori;
cubeSet = new boolean[width, height, depth];
}
public function CleanGrid() {
cubeSet = new boolean[width, height, depth];
}
public function SetDebug(debug : boolean) {
this.debug = debug;
}
public function GetSize() : GridSize {
return GridSize(width, height, depth, side);
}
public function SetSize(dimension : GridSize) {
SetSize(dimension.x, dimension.y, dimension.z, dimension.side);
}
public function SetSize(x : short, y : short, z : short, sideLength : float) {
width = x;
height = y;
depth = z;
side = sideLength;
CleanGrid();
}
public function GetCenter() : Vector3 {
return origin + Vector3(width / 2 * side, height / 2 * side, depth / 2 * side);
}
public function SetCenter(pos : Vector3) {
origin = pos - Vector3(width / 2 * side, height / 2 * side, depth / 2 * side);
}
public function GetSetAABCCount() : int {
var count = 0;
for (var x = 0; x < width; ++x) {
for (var y = 0; y < height; ++y) {
for (var z = 0; z < depth; ++z) {
if (!IsAABCSet(x, y, z)) {
count++;
}
}
}
}
return count;
}
public function GetAABCCorners(pos : AABCPosition) : Vector3[] {
CheckBounds(pos.x, pos.y, pos.z);
return GetAABCCornersUnchecked(pos.x, pos.y, pos.z);
}
public function GetAABCCorners(x : short, y : short, z : short) : Vector3[] {
return GetAABCCornersUnchecked(x, y, z);
}
protected function GetAABCCornersUnchecked(x : short, y : short, z : short) : Vector3[] {
var center = new Vector3(x * side + side / 2, y * side + side / 2, z * side + side / 2);
var corners = new Vector3[8];
corners[0] = Vector3(center.x + side, center.y - side, center.z + side) + origin;
corners[1] = Vector3(center.x + side, center.y - side, center.z - side) + origin;
corners[2] = Vector3(center.x - side, center.y - side, center.z - side) + origin;
corners[3] = Vector3(center.x - side, center.y - side, center.z + side) + origin;
corners[4] = Vector3(center.x + side, center.y + side, center.z + side) + origin;
corners[5] = Vector3(center.x + side, center.y + side, center.z - side) + origin;
corners[6] = Vector3(center.x - side, center.y + side, center.z - side) + origin;
corners[7] = Vector3(center.x - side, center.y + side, center.z + side) + origin;
return corners;
}
public function GetAABCCenter(pos : AABCPosition) : Vector3 {
CheckBounds(pos.x, pos.y, pos.z);
return GetAABCCenterUnchecked(pos.x, pos.y, pos.z);
}
public function GetAABCCenter(x : short, y : short, z : short) : Vector3 {
CheckBounds(x, y, z);
return GetAABCCenterUnchecked(x, y, z);
}
protected function GetAABCCenterUnchecked(x : short, y : short, z : short) : Vector3 {
return GetAABCCenterFromGridCenterUnchecked(x, y, z) + GetCenter();
}
public function GetAABCCenterFromGridOrigin(pos : AABCPosition) : Vector3 {
CheckBounds(pos.x, pos.y, pos.z);
return GetAABCCenterFromGridOriginUnchecked(pos.x, pos.y, pos.z);
}
public function GetAABCCenterFromGridOrigin(x : short, y : short, z : short) : Vector3 {
CheckBounds(x, y, z);
return GetAABCCenterFromGridOriginUnchecked(x, y, z);
}
protected function GetAABCCenterFromGridOriginUnchecked(x : short, y : short, z : short) : Vector3 {
return Vector3(x * side + side / 2, y * side + side / 2, z * side + side / 2);
}
public function GetAABCCenterFromGridCenter(pos : AABCPosition) : Vector3 {
CheckBounds(pos.x, pos.y, pos.z);
return GetAABCCenterFromGridCenterUnchecked(pos.x, pos.y, pos.z);
}
public function GetAABCCenterFromGridCenter(x : short, y : short, z : short) : Vector3 {
CheckBounds(x, y, z);
return GetAABCCenterFromGridCenterUnchecked(x, y, z);
}
protected function GetAABCCenterFromGridCenterUnchecked(x : short, y : short, z : short) : Vector3 {
return Vector3(side * (x + 1 / 2 - width / 2),
side * (y + 1 / 2 - height / 2),
side * (z + 1 / 2 - depth / 2));
}
public function IsAABCSet(pos : AABCPosition) : boolean {
CheckBounds(pos.x, pos.y, pos.z);
return IsAABCSetUnchecked(pos.x, pos.y, pos.z);
}
public function IsAABCSet(x : short, y : short, z : short) : boolean {
CheckBounds(x, y, z);
return IsAABCSetUnchecked(x, y, z);
}
protected function IsAABCSetUnchecked(x : short, y : short, z : short) : boolean {
return cubeSet[x, y, z];
}
public function TriangleIntersectAABC(triangle : Vector3[], pos : AABCPosition) : boolean {
CheckBounds(pos.x, pos.y, pos.z);
return TriangleIntersectAABCUnchecked(triangle, pos.x, pos.y, pos.z);
}
public function TriangleIntersectAABC(triangle : Vector3[], x : short, y : short, z : short) : boolean {
CheckBounds(x, y, z);
return TriangleIntersectAABCUnchecked(triangle, x, y, z);
}
protected function TriangleIntersectAABCUnchecked(triangle : Vector3[], x : short, y : short, z : short) : boolean {
var aabcCorners : Vector3[];
var triangleEdgeA : Vector3;
var triangleEdgeB : Vector3;
var triangleEdgeC : Vector3;
var triangleNormal : Vector3;
var aabcEdgeA = new Vector3(1, 0, 0);
var aabcEdgeB = new Vector3(0, 1, 0);
var aabcEdgeC = new Vector3(0, 0, 1);
aabcCorners = GetAABCCornersUnchecked(x, y, z);
triangleEdgeA = triangle[1] - triangle[0];
triangleEdgeB = triangle[2] - triangle[1];
triangleEdgeC = triangle[0] - triangle[2];
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, Vector3.Cross(triangleEdgeA, aabcEdgeA))) return false;
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, Vector3.Cross(triangleEdgeA, aabcEdgeB))) return false;
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, Vector3.Cross(triangleEdgeA, aabcEdgeC))) return false;
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, Vector3.Cross(triangleEdgeB, aabcEdgeA))) return false;
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, Vector3.Cross(triangleEdgeB, aabcEdgeB))) return false;
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, Vector3.Cross(triangleEdgeB, aabcEdgeC))) return false;
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, Vector3.Cross(triangleEdgeC, aabcEdgeA))) return false;
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, Vector3.Cross(triangleEdgeC, aabcEdgeB))) return false;
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, Vector3.Cross(triangleEdgeC, aabcEdgeC))) return false;
triangleNormal = Vector3.Cross(triangleEdgeA, triangleEdgeB);
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, triangleNormal)) return false;
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, aabcEdgeA)) return false;
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, aabcEdgeB)) return false;
if (!ProjectionsIntersectOnAxis(aabcCorners, triangle, aabcEdgeC)) return false;
return true;
}
protected function CheckBounds(x : short, y : short, z : short) {
if(x < 0 || y < 0 || z < 0 || x >= width || y >= height || z >= depth) {
throw new System.ArgumentOutOfRangeException("The requested AABC is out of the grid limits.");
}
}
public function FillGridWithGameObjectMeshShell(gameObj : GameObject) {
FillGridWithGameObjectMeshShell(gameObj, false);
}
public function FillGridWithGameObjectMeshShell(gameObj : GameObject, storeNormalSum : boolean) {
var gameObjMesh = gameObj.GetComponent(MeshFilter).mesh;
var gameObjTransf = gameObj.transform;
var triangle = new Vector3[3];
var startTime = Time.realtimeSinceStartup;
var meshVertices = gameObjMesh.vertices;
var meshTriangles = gameObjMesh.triangles;
var meshTrianglesCount = meshTriangles.length / 3;
var x : short;
var y : short;
var z : short;
var ignoreNormalRange = 0;
// In this method we can also evaluate stores the normals of the triangles
// that intersect the cube.
if (storeNormalSum) {
cubeNormalSum = new short [width, height, depth];
}
if(debug) {
Debug.Log("Start:");
Debug.Log("Time: " + startTime);
Debug.Log(" Mesh Description: ");
Debug.Log("Name: " + gameObjMesh.name);
Debug.Log("Triangles: " + meshTrianglesCount);
Debug.Log("Local AABB size: " + gameObjMesh.bounds.size);
Debug.Log(" AABCGrid Description:");
Debug.Log("Size: " + width + ',' + height + ',' + depth);
}
// For each triangle, perform SAT intersection check with the AABCs within the triangle AABB.
for (var i = 0; i < meshTrianglesCount; ++i) {
triangle[0] = gameObjTransf.TransformPoint(meshVertices[meshTriangles[i * 3]]);
triangle[1] = gameObjTransf.TransformPoint(meshVertices[meshTriangles[i * 3 + 1]]);
triangle[2] = gameObjTransf.TransformPoint(meshVertices[meshTriangles[i * 3 + 2]]);
// Find the triangle AABB, select a sub grid.
var startX = Mathf.Floor((Mathf.Min([triangle[0].x, triangle[1].x, triangle[2].x]) - origin.x) / side);
var startY = Mathf.Floor((Mathf.Min([triangle[0].y, triangle[1].y, triangle[2].y]) - origin.y) / side);
var startZ = Mathf.Floor((Mathf.Min([triangle[0].z, triangle[1].z, triangle[2].z]) - origin.z) / side);
var endX = Mathf.Ceil((Mathf.Max([triangle[0].x, triangle[1].x, triangle[2].x]) - origin.x) / side);
var endY = Mathf.Ceil((Mathf.Max([triangle[0].y, triangle[1].y, triangle[2].y]) - origin.y) / side);
var endZ = Mathf.Ceil((Mathf.Max([triangle[0].z, triangle[1].z, triangle[2].z]) - origin.z) / side);
if (storeNormalSum) {
for (x = startX; x <= endX; ++x) {
for (y = startY; y <= endY; ++y) {
for (z = startZ; z <= endZ; ++z) {
if (TriangleIntersectAABC(triangle, x, y, z)) {
var triangleNormal = GetTriangleNormal(triangle);
cubeSet[x, y, z] = true;
if (triangleNormal.z < 0 - ignoreNormalRange) {
cubeNormalSum[x, y, z]++;
} else if (triangleNormal.z > 0 + ignoreNormalRange){
cubeNormalSum[x, y, z]--;
}
}
}
}
}
} else {
for (x = startX; x < endX; ++x) {
for (y = startY; y < endY; ++y) {
for (z = startZ; z < endZ; ++z) {
if (!IsAABCSet(x, y, z) && TriangleIntersectAABC(triangle, x, y, z)) {
cubeSet[x, y, z] = true;
}
}
}
}
}
}
if(debug) {
Debug.Log("Grid Evaluation Ended!");
Debug.Log("Time spent: " + (Time.realtimeSinceStartup - startTime) + "s");
Debug.Log("End: ");
}
}
public function FillGridWithGameObjectMesh(gameObj : GameObject) {
FillGridWithGameObjectMeshShell(gameObj, true);
for (var x = 0; x < width; ++x) {
for (var y = 0; y < height; ++y) {
var fill = false;
var cubeToFill = 0;
for (var z = 0; z < depth; ++z) {
if (cubeSet[x, y, z]) {
var normalSum = cubeNormalSum[x, y, z];
if (normalSum) {
if (normalSum > 0) {
fill = true;
} else {
fill = false;
while (cubeToFill > 1) {
cubeToFill--;
cubeSet[x, y, z - cubeToFill] = true;
}
}
cubeToFill = 0;
}
continue;
}
if (fill) {
cubeToFill++;
}
}
}
}
cubeNormalSum = null;
}
public function AddParticles(particles : ParticleSystem.Particle[], particlesToAdd : int) : ParticleSystem.Particle[] {
var settedAABCCount = GetSetAABCCount();
var particlesPerAABC : int;
var randMax = side/2;
var addedParticles = 0;
var cube : AABC;
var i = 0;
if (particlesToAdd <= 0) {
throw new System.ArgumentException("The number of particles to add is < 0");
}
particlesPerAABC = particlesToAdd / settedAABCCount;
if (particlesPerAABC <= 0) {
particlesPerAABC = 1;
}
while (particlesToAdd > 0) {
var iter = AABCGridSetAABCIterator(this);
var cubeFilledCount = 0;
while (iter.HasNext()) {
cube = iter.Next();
for (; i < addedParticles + particlesPerAABC && particlesToAdd > 0; ++i) {
particles[i].position = cube.GetCenter() +
Vector3(Random.Range(-randMax, randMax),
Random.Range(-randMax, randMax),
Random.Range(-randMax, randMax)) / 100;
particlesToAdd--;
}
addedParticles += particlesPerAABC;
cubeFilledCount++;
if (particlesToAdd <= 0) {
break;
}
}
if (particlesToAdd > 0) {
particlesPerAABC = 1;
}
}
return particles;
}
};
public function ProjectionsIntersectOnAxis(solidA : Vector3[], solidB : Vector3[], axis : Vector3) : boolean {
var minSolidA = MinOfProjectionOnAxis(solidA, axis);
var maxSolidA = MaxOfProjectionOnAxis(solidA, axis);
var minSolidB = MinOfProjectionOnAxis(solidB, axis);
var maxSolidB = MaxOfProjectionOnAxis(solidB, axis);
if (minSolidA > maxSolidB) {
return false;
}
if (maxSolidA < minSolidB) {
return false;
}
return true;
}
public function MinOfProjectionOnAxis(solid : Vector3[], axis : Vector3) : float {
var min = MAX_FLOAT;
var dotProd : float;
for (var i = 0; i < solid.Length; ++i) {
dotProd = Vector3.Dot(solid[i], axis);
if (dotProd < min) {
min = dotProd;
}
}
return min;
}
public function MaxOfProjectionOnAxis(solid : Vector3[], axis : Vector3) : float {
var max = MIN_FLOAT;
var dotProd : float;
for (var i = 0; i < solid.Length; ++i) {
dotProd = Vector3.Dot(solid[i], axis);
if (dotProd > max) {
max = dotProd;
}
}
return max;
}
// Return a vector with the minimum components
public function MinVectorComponents(a : Vector3, b : Vector3) : Vector3 {
var ret = new Vector3();
ret.x = Mathf.Min(a.x, b.x);
ret.y = Mathf.Min(a.y, b.y);
ret.z = Mathf.Min(a.z, b.z);
return ret;
}
// Return a vector with the minimum components
public function MaxVectorComponents(a : Vector3, b : Vector3) : Vector3 {
var ret = new Vector3();
ret.x = Mathf.Max(a.x, b.x);
ret.y = Mathf.Max(a.y, b.y);
ret.z = Mathf.Max(a.z, b.z);
return ret;
}
public function GetTriangleNormal(triangle : Vector3[]) : Vector3 {
return Vector3.Cross(triangle[1] - triangle[0], triangle[2] - triangle[0]).normalized;
}
// Return an AABB which include the meshes of the object itself and of its children
public function GetTotalBoundsOfGameObject(gameObj : GameObject) : Bounds {
var totalBounds = new Bounds();
var min : Vector3;
var max : Vector3;
if (gameObj.renderer) {
min = gameObj.renderer.bounds.min;
max = gameObj.renderer.bounds.max;
}
for (var i = 0; i < gameObj.transform.GetChildCount(); ++i) {
var childObj = gameObj.transform.GetChild(i).gameObject;
var childTotalBounds = GetTotalBoundsOfGameObject(childObj);
min = Voxelization.MinVectorComponents(min, childTotalBounds.min);
max = Voxelization.MaxVectorComponents(max, childTotalBounds.max);
}
totalBounds.SetMinMax(min, max);
return totalBounds;
}
public function GetChildrenWithMesh(gameObj : GameObject) : Array {
var ret = new Array();
for (var i = 0; i < gameObj.transform.GetChildCount(); ++i) {
var childObj = gameObj.transform.GetChild(i).gameObject;
if (childObj.renderer) {
ret.Push(childObj);
}
ret = ret.Concat(GetChildrenWithMesh(childObj));
}
return ret;
}
// Warning: this method creates a grid at least as big as the total bounding box of the
// game object, if children are included there may be empty space. Consider to use
// CreateMultipleGridsWithGameObjectMeshShell in order to save memory.
public function CreateGridWithGameObjectMesh(gameObj : GameObject,
cubeSide : float, includeChildren : boolean, includeInside : boolean) : AABCGrid {
var aABCGrid : AABCGrid;
var width : short;
var height : short;
var depth : short;
var origin = new Vector3();
var gameObjectsWithMesh : Array;
var gridBoundsMin = new Vector3(MAX_FLOAT, MAX_FLOAT, MAX_FLOAT);
var gridBoundsMax = new Vector3(MIN_FLOAT, MIN_FLOAT, MIN_FLOAT);
if (includeChildren) {
gameObjectsWithMesh = GetChildrenWithMesh(gameObj);
} else {
gameObjectsWithMesh = new Array();
}
if (gameObj.renderer) {
gameObjectsWithMesh.Push(gameObj);
}
for (var gameObjectWithMesh : GameObject in gameObjectsWithMesh) {
gridBoundsMin = Voxelization.MinVectorComponents(gridBoundsMin,
gameObjectWithMesh.renderer.bounds.min);
gridBoundsMax = Voxelization.MaxVectorComponents(gridBoundsMax,
gameObjectWithMesh.renderer.bounds.max);
}
width = Mathf.Ceil((gridBoundsMax.x - gridBoundsMin.x) / cubeSide) + 2;
height = Mathf.Ceil((gridBoundsMax.y - gridBoundsMin.y) / cubeSide) + 2;
depth = Mathf.Ceil((gridBoundsMax.z - gridBoundsMin.z) / cubeSide) + 2;
origin = gridBoundsMin - Vector3(cubeSide, cubeSide, cubeSide);
aABCGrid = new AABCGrid(width, height, depth, cubeSide, origin);
for (var gameObjectWithMesh : GameObject in gameObjectsWithMesh) {
if (includeInside) {
aABCGrid.FillGridWithGameObjectMesh(gameObjectWithMesh);
} else {
aABCGrid.FillGridWithGameObjectMeshShell(gameObjectWithMesh);
}
}
return aABCGrid;
}
public function CreateMultipleGridsWithGameObjectMesh(gameObj : GameObject,
cubeSide : float, includeMeshInside : boolean) : Array {
var gameObjectsWithMesh : Array;
var grids = new Array();
gameObjectsWithMesh = GetChildrenWithMesh(gameObj);
if (gameObj.renderer) {
gameObjectsWithMesh.Push(gameObj);
}
for (var gameObjWithMesh : GameObject in gameObjectsWithMesh) {
grids.Push(CreateGridWithGameObjectMesh(gameObjWithMesh, cubeSide, false, includeMeshInside));
}
return grids;
}
};