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adopt convex hull from concaveman (#28)
* not ready * fix * use stable predicates * fix * fix * fix * not ready * fix * fix * reset * init orient 2d * add macro * update * clean * fix * fix * not ready * fix compile * fix * fix * fix * fix * fix * fix --------- Co-authored-by: tang zhixiong <[email protected]>
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| Original file line number | Diff line number | Diff line change |
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| // https://github.com/mapbox/concaveman/pull/17/files | ||
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| // https://github.com/mourner/robust-predicates/blob/main/src/orient2d.js | ||
| #pragma once | ||
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| #include "orient2d.hpp" | ||
| #include <vector> | ||
| #include <array> | ||
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| namespace cubao | ||
| { | ||
| namespace convex_hull2 | ||
| { | ||
| // https://github.com/mourner/robust-predicates/blob/main/src/orient2d.js | ||
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| inline double cross(const double *p1, const double *p2, const double *p3) | ||
| { | ||
| return robust_predicates::orient2d(p1[0], p1[1], // | ||
| p2[0], p2[1], // | ||
| p3[0], p3[1]); | ||
| } | ||
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| // https://github.com/mapbox/concaveman/blob/master/index.js | ||
| // check if the edges (p1,q1) and (p2,q2) intersect | ||
| inline bool intersects(const double *p1, const double *q1, // | ||
| const double *p2, const double *q2) | ||
| { | ||
| return !(p1[0] == q2[0] && p1[1] == q2[1]) && | ||
| !(q1[0] == p2[0] && q1[1] == p2[1]) && | ||
| (cross(p1, q1, p2) > 0) != (cross(p1, q1, q2) > 0) && | ||
| (cross(p2, q2, p1) > 0) != (cross(p2, q2, q1) > 0); | ||
| } | ||
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| inline std::vector<std::array<double, 3>> | ||
| convexHull(std::vector<std::array<double, 3>> points) | ||
| { | ||
| if (points.empty()) { | ||
| return {}; | ||
| } | ||
| std::sort( | ||
| points.begin(), points.end(), | ||
| [](const std::array<double, 3> &a, const std::array<double, 3> &b) { | ||
| return a[0] == b[0] ? a[1] < b[1] : a[0] < b[0]; | ||
| }); | ||
| points.erase(std::unique(points.begin(), points.end(), | ||
| [](const auto &a, const auto &b) { | ||
| return a[0] == b[0] && a[1] == b[1]; | ||
| }), | ||
| points.end()); | ||
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| std::vector<std::array<double, 3>> lower; | ||
| for (size_t i = 0; i < points.size(); i++) { | ||
| while (lower.size() >= 2 && | ||
| cross(lower[lower.size() - 2].data(), | ||
| lower[lower.size() - 1].data(), points[i].data()) <= 0) { | ||
| lower.pop_back(); | ||
| } | ||
| lower.push_back(points[i]); | ||
| } | ||
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| std::vector<std::array<double, 3>> upper; | ||
| for (int i = points.size() - 1; i >= 0; i--) { | ||
| while (upper.size() >= 2 && | ||
| cross(upper[upper.size() - 2].data(), | ||
| upper[upper.size() - 1].data(), points[i].data()) <= 0) { | ||
| upper.pop_back(); | ||
| } | ||
| upper.push_back(points[i]); | ||
| } | ||
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| upper.pop_back(); | ||
| lower.pop_back(); | ||
| lower.insert(lower.end(), upper.begin(), upper.end()); | ||
| return lower; | ||
| } | ||
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| // https://www.npmjs.com/package/point-in-polygon?activeTab=code | ||
| inline bool pointInPolygon(const double *point, // | ||
| const double *polygon, size_t length, // | ||
| int start = -1, int end = -1) | ||
| { | ||
| double x = point[0], y = point[1]; | ||
| bool inside = false; | ||
| if (start < 0) | ||
| start = 0; | ||
| if (end < 0) | ||
| end = length; | ||
| int len = end - start; | ||
| for (int i = 0, j = len - 1; i < len; j = i++) { | ||
| double xi = polygon[(i + start) * 2], yi = polygon[(i + start) * 2 + 1]; | ||
| double xj = polygon[(j + start) * 2], yj = polygon[(j + start) * 2 + 1]; | ||
| bool intersect = ((yi > y) != (yj > y)) && | ||
| (x < (xj - xi) * (y - yi) / (yj - yi) + xi); | ||
| if (intersect) | ||
| inside = !inside; | ||
| } | ||
| return inside; | ||
| } | ||
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| // speed up convex hull by filtering out points inside quadrilateral formed by 4 | ||
| // extreme points | ||
| inline std::vector<std::array<double, 3>> | ||
| fastConvexHull(const std::vector<std::array<double, 3>> &points) | ||
| { | ||
| if (points.empty()) { | ||
| return {}; | ||
| } | ||
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| auto left = points[0]; | ||
| auto top = points[0]; | ||
| auto right = points[0]; | ||
| auto bottom = points[0]; | ||
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| // find the leftmost, rightmost, topmost and bottommost points | ||
| for (const auto &p : points) { | ||
| if (p[0] < left[0]) | ||
| left = p; | ||
| if (p[0] > right[0]) | ||
| right = p; | ||
| if (p[1] < top[1]) | ||
| top = p; | ||
| if (p[1] > bottom[1]) | ||
| bottom = p; | ||
| } | ||
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| // filter out points that are inside the resulting quadrilateral | ||
| std::vector<std::array<double, 2>> cull = {{left[0], left[1]}, | ||
| {top[0], top[1]}, | ||
| {right[0], right[1]}, | ||
| {bottom[0], bottom[1]}}; | ||
| std::vector<std::array<double, 3>> filtered = {left, top, right, bottom}; | ||
| for (const auto &p : points) { | ||
| if (!pointInPolygon(&p[0], &cull[0][0], cull.size())) { | ||
| filtered.push_back(p); | ||
| } | ||
| } | ||
| // get convex hull around the filtered points | ||
| return convexHull(filtered); | ||
| } | ||
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| } // namespace convex_hull2 | ||
| } // namespace cubao |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,135 @@ | ||
| #pragma once | ||
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| #include <cmath> | ||
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| namespace cubao | ||
| { | ||
| namespace robust_predicates | ||
| { | ||
| // https://github.com/mourner/robust-predicates/blob/312178014c173cfa5ed0a8cb5496baaf82a63663/compile.js#L6 | ||
| #define Fast_Two_Sum(a, b, x, y) \ | ||
| do { \ | ||
| x = a + b; \ | ||
| y = b - (x - a); \ | ||
| } while (0) | ||
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| #define Two_Sum(a, b, x, y) \ | ||
| do { \ | ||
| double bvirt; \ | ||
| x = a + b; \ | ||
| bvirt = x - a; \ | ||
| y = a - (x - bvirt) + (b - bvirt); \ | ||
| } while (0) | ||
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| #define Two_Diff_Tail(a, b, x, y) \ | ||
| do { \ | ||
| double bvirt = a - x; \ | ||
| y = a - (x + bvirt) + (bvirt - b); \ | ||
| } while (0) | ||
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| #define Two_Diff(a, b, x, y) \ | ||
| do { \ | ||
| x = a - b; \ | ||
| Two_Diff_Tail(a, b, x, y); \ | ||
| } while (0) | ||
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| #define Split(a, ahi, alo) \ | ||
| do { \ | ||
| double c = splitter * a; \ | ||
| ahi = c - (c - a); \ | ||
| alo = a - ahi; \ | ||
| } while (0) | ||
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| #define Two_Product(a, b, x, y) \ | ||
| do { \ | ||
| double ahi, alo, bhi, blo; \ | ||
| x = a * b; \ | ||
| Split(a, ahi, alo); \ | ||
| Split(b, bhi, blo); \ | ||
| y = alo * blo - (x - ahi * bhi - alo * bhi - ahi * blo); \ | ||
| } while (0) | ||
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| #define Two_Product_Presplit(a, b, bhi, blo, x, y) \ | ||
| do { \ | ||
| double ahi, alo; \ | ||
| x = a * b; \ | ||
| Split(a, ahi, alo); \ | ||
| y = alo * blo - (x - ahi * bhi - alo * bhi - ahi * blo); \ | ||
| } while (0) | ||
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| #define Square(a, x, y) \ | ||
| do { \ | ||
| double ahi, alo; \ | ||
| x = a * a; \ | ||
| Split(a, ahi, alo); \ | ||
| y = alo * alo - (x - ahi * ahi - (ahi + ahi) * alo); \ | ||
| } while (0) | ||
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| #define Two_One_Sum(a1, a0, b, x2, x1, x0) \ | ||
| do { \ | ||
| double _i; \ | ||
| Two_Sum(a0, b, _i, x0); \ | ||
| Two_Sum(a1, _i, x2, x1); \ | ||
| } while (0) | ||
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| #define Two_One_Diff(a1, a0, b, x2, x1, x0) \ | ||
| do { \ | ||
| double _i; \ | ||
| Two_Diff(a0, b, _i, x0); \ | ||
| Two_Sum(a1, _i, x2, x1); \ | ||
| } while (0) | ||
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| #define Two_Two_Sum(a1, a0, b1, b0, x3, x2, x1, x0) \ | ||
| do { \ | ||
| double _j, _0; \ | ||
| Two_One_Sum(a1, a0, b0, _j, _0, x0); \ | ||
| Two_One_Sum(_j, _0, b1, x3, x2, x1); \ | ||
| } while (0) | ||
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| #define Two_Two_Diff(a1, a0, b1, b0, x3, x2, x1, x0) \ | ||
| do { \ | ||
| double _j, _0; \ | ||
| Two_One_Diff(a1, a0, b0, _j, _0, x0); \ | ||
| Two_One_Diff(_j, _0, b1, x3, x2, x1); \ | ||
| } while (0) | ||
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| #define Two_One_Product(a1, a0, b, D) \ | ||
| do { \ | ||
| double bhi, blo, _i, _j, _0, _k, u3; \ | ||
| Split(b, bhi, blo); \ | ||
| Two_Product_Presplit(a0, b, bhi, blo, _i, D[0]); \ | ||
| Two_Product_Presplit(a1, b, bhi, blo, _j, _0); \ | ||
| Two_Sum(_i, _0, _k, D[1]); \ | ||
| Fast_Two_Sum(_j, _k, u3, D[2]); \ | ||
| D[3] = u3; \ | ||
| } while (0) | ||
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| #define Cross_Product(a, b, c, d, D) \ | ||
| do { \ | ||
| double s1, s0, t1, t0, u3; \ | ||
| Two_Product(a, d, s1, s0); \ | ||
| Two_Product(c, b, t1, t0); \ | ||
| Two_Two_Diff(s1, s0, t1, t0, u3, D[2], D[1], D[0]); \ | ||
| D[3] = u3; \ | ||
| } while (0) | ||
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| #define Two_Product_Sum(a, b, c, d, D) \ | ||
| do { \ | ||
| double s1, s0, t1, t0, u3; \ | ||
| Two_Product(a, b, s1, s0); \ | ||
| Two_Product(c, d, t1, t0); \ | ||
| Two_Two_Sum(s1, s0, t1, t0, u3, D[2], D[1], D[0]); \ | ||
| D[3] = u3; \ | ||
| } while (0) | ||
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| #define Square_Sum(a, b, D) \ | ||
| do { \ | ||
| double s1, s0, t1, t0, u3; \ | ||
| Square(a, s1, s0); \ | ||
| Square(b, t1, t0); \ | ||
| Two_Two_Sum(s1, s0, t1, t0, u3, D[2], D[1], D[0]); \ | ||
| D[3] = u3; \ | ||
| } while (0) | ||
|
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| } // namespace robust_predicates | ||
| } // namespace cubao |
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