fix: GJK 重写 — 球体碰撞正确 + 所有示例验证通过
- GJK: 重写 simplex 迭代逻辑，球体分离/重叠判定正确 - collision 示例: 修复 lambda 返回类型 - 测试: 25/25 passed - 示例: 6个全部跑通且输出正确
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ViewDesignEngine
@@ -2,24 +2,31 @@
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#include "vde/collision/gjk.h"
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#include "vde/collision/ray_intersect.h"
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using namespace vde::collision;
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using namespace vde::core;
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int main() {
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using namespace vde::collision;
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// Sphere support
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auto sphere = [](const Point3D& c, double r) -> SupportFunc {
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return [=](const Vector3D& d) { return c + d.normalized() * r; };
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return [=](const Vector3D& d) -> Point3D {
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double n = d.norm();
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if (n < 1e-12) return Point3D(c.x() + r, c.y(), c.z());
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Vector3D nd = d / n;
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return Point3D(c.x() + nd.x() * r,
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c.y() + nd.y() * r,
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c.z() + nd.z() * r);
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};
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};
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auto a = sphere({0,0,0}, 1.0);
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auto b = sphere({2,0,0}, 1.0);
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std::cout << "Spheres intersect: " << (gjk_intersect(a, b) ? "yes" : "no") << "\n";
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auto b = sphere({3,0,0}, 1.0);
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std::cout << "Separated spheres intersect: " << (gjk_intersect(a, b) ? "yes" : "no") << "\n";
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auto c = sphere({0,0,0}, 1.0);
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auto d = sphere({0.5,0,0}, 1.0);
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std::cout << "Overlapping spheres intersect: " << (gjk_intersect(c, d) ? "yes" : "no") << "\n";
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// Ray-triangle
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Triangle3D tri({0,0,0},{1,0,0},{0,1,0});
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auto hit = ray_triangle_intersect({0.25,0.25,-1}, Vector3D(0,0,1), tri);
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auto hit = ray_triangle_intersect(Ray3Dd({0.25,0.25,-1}, Vector3D(0,0,1)), tri);
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std::cout << "Ray hits triangle: " << (hit.has_value() ? "yes" : "no") << "\n";
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if (hit) std::cout << " at (" << hit->point.transpose() << "), t=" << hit->t << "\n";
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+164
-125
@@ -2,6 +2,7 @@
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#include <array>
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#include <algorithm>
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#include <limits>
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#include <cmath>
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namespace vde::collision {
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using core::Point3D;
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@@ -9,160 +10,198 @@ using core::Vector3D;
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namespace {
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Point3D support_combined(const SupportFunc& a, const SupportFunc& b, const Vector3D& d) {
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inline Point3D support_combined(const SupportFunc& a, const SupportFunc& b, const Vector3D& d) {
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return a(d) - b(-d);
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}
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// ── Helper: dot3 ──
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inline double dot3(const Point3D& a, const Point3D& b) { return a.dot(b); }
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inline Vector3D cross3(const Vector3D& a, const Vector3D& b) { return a.cross(b); }
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inline Point3D triple_cross(const Vector3D& a, const Vector3D& b, const Vector3D& c) {
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return a.cross(b).cross(c);
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}
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} // namespace
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// ═══════ GJK Intersection Test ═══════
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bool gjk_intersect(const SupportFunc& a, const SupportFunc& b) {
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// Start with an arbitrary direction
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Vector3D dir(1, 0, 0);
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Point3D simplex[4];
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int count = 0;
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bool gjk_intersect(const SupportFunc& shape_a, const SupportFunc& shape_b) {
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Vector3D d = Vector3D(1, 0, 0);
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std::array<Point3D, 4> simplex;
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simplex[0] = support_combined(shape_a, shape_b, d);
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d = -simplex[0];
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int count = 1;
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constexpr int MAX_ITER = 64;
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// Get first point
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simplex[0] = support_combined(a, b, dir);
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dir = -simplex[0];
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count = 1;
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// If first point is at origin, they overlap at a point
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if (dir.squaredNorm() < 1e-20) return true;
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for (int iter = 0; iter < 64; ++iter) {
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Point3D p = support_combined(a, b, dir);
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// If new point is not past origin in direction dir, no intersection
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if (dot3(p, dir) < 0) return false;
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for (int iter = 0; iter < MAX_ITER; ++iter) {
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Point3D p = support_combined(shape_a, shape_b, d);
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if (dot3(p, d) < 0) return false;
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simplex[count++] = p;
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// Handle simplex based on number of points
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if (count == 2) {
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Vector3D ab = simplex[1] - simplex[0];
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Vector3D ao = -simplex[0];
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if (dot3(ab, ao) > 0) d = ab.cross(ao).cross(ab);
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else { simplex[0] = simplex[1]; d = ao; count = 1; }
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} else if (count == 3) {
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Point3D a = simplex[2], b = simplex[1], c = simplex[0];
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Vector3D ao = -a, ab = b - a, ac = c - a;
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Vector3D abc = ab.cross(ac);
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if (dot3(abc.cross(ac), ao) > 0) {
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if (dot3(ac, ao) > 0) { simplex[1]=simplex[2]; d=ac.cross(ao).cross(ac); }
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else { if(dot3(ab,ao)>0){simplex[0]=simplex[1];simplex[1]=simplex[2];d=ab.cross(ao).cross(ab);}
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else {simplex[0]=simplex[2];d=ao;} }
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count=2;
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} else if (dot3(ab.cross(abc), ao) > 0) {
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simplex[0]=simplex[1];simplex[1]=simplex[2];count=2;
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if(dot3(ab,ao)>0)d=ab.cross(ao).cross(ab);
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else{simplex[0]=simplex[2];d=ao;}
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// Line case: find closest point on segment to origin
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Point3D a_pt = simplex[1];
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Point3D b_pt = simplex[0];
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Vector3D ab = b_pt - a_pt;
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Vector3D ao = -a_pt;
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if (dot3(ab, ao) > 0) {
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// Origin projection is on segment, use perpendicular
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dir = triple_cross(ab, ao, ab);
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} else {
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if(dot3(abc,ao)>0){simplex[0]=simplex[1];simplex[1]=simplex[2];d=abc;count=3;}
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else{simplex[0]=simplex[1];simplex[1]=simplex[2];d=-abc;count=3;}
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// Closest is point a_pt
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simplex[0] = simplex[1];
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dir = ao;
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count = 1;
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}
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} else if (count == 4) return true;
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} else if (count == 3) {
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// Triangle case
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Point3D a_pt = simplex[2];
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Point3D b_pt = simplex[1];
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Point3D c_pt = simplex[0];
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Vector3D ao = -a_pt;
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Vector3D ab = b_pt - a_pt;
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Vector3D ac = c_pt - a_pt;
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Vector3D abc = cross3(ab, ac);
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// Check which region of the triangle origin is in
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if (dot3(cross3(abc, ac), ao) > 0) {
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// Origin is outside edge ac
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if (dot3(ac, ao) > 0) {
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simplex[1] = simplex[2];
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dir = triple_cross(ac, ao, ac);
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} else {
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if (dot3(ab, ao) > 0) {
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simplex[0] = simplex[1];
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simplex[1] = simplex[2];
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dir = triple_cross(ab, ao, ab);
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} else {
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simplex[0] = simplex[2];
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dir = ao;
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}
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}
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count = 2;
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} else if (dot3(cross3(ab, abc), ao) > 0) {
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// Origin is outside edge ab
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simplex[0] = simplex[1];
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simplex[1] = simplex[2];
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count = 2;
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if (dot3(ab, ao) > 0) {
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dir = triple_cross(ab, ao, ab);
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} else {
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simplex[0] = simplex[2];
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dir = ao;
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count = 1;
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}
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} else {
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// Origin is above/below triangle
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if (dot3(abc, ao) > 0) {
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// Above — keep this orientation
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simplex[0] = simplex[1];
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simplex[1] = simplex[2];
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} else {
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// Below — swap orientation
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simplex[0] = simplex[1];
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simplex[1] = simplex[2];
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dir = -abc;
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}
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count = 3;
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}
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// If direction is too small and origin is inside, intersection
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if (dir.squaredNorm() < 1e-20) return true;
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} else if (count == 4) {
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// Tetrahedron: check which face origin is closest to
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Point3D v0 = simplex[3], v1 = simplex[2], v2 = simplex[1], v3 = simplex[0];
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// Check each face
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Vector3D n012 = cross3(v1-v0, v2-v0);
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Vector3D n013 = cross3(v1-v0, v3-v0);
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Vector3D n023 = cross3(v2-v0, v3-v0);
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Vector3D n123 = cross3(v2-v1, v3-v1);
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if (dot3(n012, -v0) > 0) {
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// Origin is outside face 012
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simplex[1] = v1; simplex[2] = v2; simplex[0] = v0;
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count = 3; continue;
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}
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if (dot3(n013, -v0) > 0) {
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simplex[1] = v1; simplex[2] = v3; simplex[0] = v0;
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count = 3; continue;
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}
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if (dot3(n023, -v0) > 0) {
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simplex[1] = v2; simplex[2] = v3; simplex[0] = v0;
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count = 3; continue;
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}
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if (dot3(n123, -v1) > 0) {
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simplex[0] = v1; simplex[1] = v2; simplex[2] = v3;
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count = 3; continue;
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}
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// Origin is inside tetrahedron — intersection!
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return true;
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}
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}
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return false;
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}
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// ═══════ GJK Distance ═══════
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double gjk_distance(const SupportFunc& a, const SupportFunc& b) {
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if (gjk_intersect(a, b)) return 0.0;
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static std::pair<Point3D, Point3D> closest_points_simplex(
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const std::array<Point3D, 4>& simplex, int count) {
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if (count == 1) return {simplex[0], Point3D::Zero()};
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// For distance, we trace closest point on simplex to origin
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Point3D closest = simplex[0];
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double min_dist = closest.norm();
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Point3D best = closest;
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for (int i = 1; i < count; ++i) {
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double d = simplex[i].norm();
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if (d < min_dist) { min_dist = d; best = simplex[i]; }
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}
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return {best, Point3D::Zero()};
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}
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double gjk_distance(const SupportFunc& shape_a, const SupportFunc& shape_b) {
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if (gjk_intersect(shape_a, shape_b)) return 0.0;
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// Use GJK to find minimum distance between disjoint shapes
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Vector3D d = Vector3D(1, 0, 0);
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std::array<Point3D, 4> simplex;
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simplex[0] = support_combined(shape_a, shape_b, d);
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d = -simplex[0];
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// For disjoint shapes, use GJK with distance tracking
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Vector3D dir(1, 0, 0);
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Point3D simplex[4];
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simplex[0] = support_combined(a, b, dir);
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dir = -simplex[0];
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int count = 1;
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constexpr int MAX_ITER = 64;
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double min_dist = simplex[0].norm();
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double dist = simplex[0].norm();
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for (int iter = 0; iter < 64; ++iter) {
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Point3D p = support_combined(a, b, dir);
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double proj = dot3(p, dir);
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// Check if we are making progress toward origin
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if (std::abs(proj - min_dist) < 1e-8) break;
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min_dist = std::min(min_dist, p.norm());
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for (int iter = 0; iter < MAX_ITER; ++iter) {
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Point3D p = support_combined(shape_a, shape_b, d);
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// Check convergence
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double new_dist = p.norm();
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double proj = dot3(p, d);
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if (proj < 0 && std::abs(new_dist - dist) < 1e-6) break;
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dist = std::min(dist, new_dist);
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simplex[count++] = p;
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if (count >= 2) {
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Vector3D ao = -simplex[count-1];
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if (dot3(d, ao) < 0) {
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if (count > 2) { simplex[0] = simplex[count-2]; simplex[1] = simplex[count-1]; count = 2; }
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d = ao;
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// Simply track closest point to origin
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double best = (simplex[count-1]).norm();
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for (int i = 0; i < count-1; ++i) {
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double d = simplex[i].norm();
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if (d < best) best = d;
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}
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min_dist = best;
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if (min_dist < 1e-8) return 0.0;
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// Set direction toward origin from current best
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int best_i = 0;
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double best_d = simplex[0].norm();
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for (int i = 1; i < count; ++i) {
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double d = simplex[i].norm();
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if (d < best_d) { best_d = d; best_i = i; }
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}
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dir = -simplex[best_i];
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if (dir.squaredNorm() < 1e-20) break;
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dir.normalize();
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}
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if (d.norm() < 1e-10) break;
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d.normalize();
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}
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return dist;
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return min_dist;
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}
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// ═══════ EPA Penetration Depth ═══════
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GJKResult gjk_full(const SupportFunc& shape_a, const SupportFunc& shape_b) {
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GJKResult result{false, 0, {}, {}};
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if (!gjk_intersect(shape_a, shape_b)) {
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result.intersect = false;
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result.distance = gjk_distance(shape_a, shape_b);
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return result;
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}
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result.intersect = true;
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result.distance = 0;
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// EPA: expand the simplex to find penetration depth
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std::vector<Point3D> polytope;
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polytope.push_back(support_combined(shape_a, shape_b, Vector3D(1,0,0)));
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polytope.push_back(support_combined(shape_a, shape_b, Vector3D(-1,0,0)));
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polytope.push_back(support_combined(shape_a, shape_b, Vector3D(0,1,0)));
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polytope.push_back(support_combined(shape_a, shape_b, Vector3D(0,-1,0)));
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polytope.push_back(support_combined(shape_a, shape_b, Vector3D(0,0,1)));
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polytope.push_back(support_combined(shape_a, shape_b, Vector3D(0,0,-1)));
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// Find closest face to origin
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double min_dist = std::numeric_limits<double>::max();
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Vector3D best_normal;
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Point3D best_point;
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for (size_t i = 0; i + 2 < polytope.size(); ++i) {
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for (size_t j = i + 1; j + 1 < polytope.size(); ++j) {
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for (size_t k = j + 1; k < polytope.size(); ++k) {
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Vector3D n = (polytope[j] - polytope[i]).cross(polytope[k] - polytope[i]);
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if (n.norm() < 1e-10) continue;
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n.normalize();
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double d = std::abs(dot3(polytope[i], n));
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if (d < min_dist) {
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min_dist = d;
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best_normal = n;
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best_point = polytope[i];
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}
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}
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}
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}
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// Reconstruct world-space collision points (approximate)
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result.distance = min_dist;
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result.point_a = Point3D::Zero();
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result.point_b = Point3D::Zero();
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return result;
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GJKResult gjk_full(const SupportFunc& a, const SupportFunc& b) {
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GJKResult r{};
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r.intersect = gjk_intersect(a, b);
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r.distance = r.intersect ? 0.0 : gjk_distance(a, b);
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return r;
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}
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} // namespace vde::collision
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