#include "CollisionUtil.hpp" #include "CCollisionInfo.hpp" #include "CCollisionInfoList.hpp" namespace urde::CollisionUtil { bool LineIntersectsOBBox(const zeus::COBBox& obb, const zeus::CMRay& ray, float& d) { zeus::CVector3f norm; return RayAABoxIntersection(ray.getInvUnscaledTransformRay(obb.transform), {-obb.extents, obb.extents}, norm, d); } u32 RayAABoxIntersection(const zeus::CMRay& ray, const zeus::CAABox& aabb, float& tMin, float& tMax) { tMin = -999999.f; tMax = 999999.f; for (int i=0 ; i<3 ; ++i) { if (std::fabs(ray.dir[i]) < 0.00001f) { if (ray.start[i] < aabb.min[i] || ray.start[i] > aabb.max[i]) return 0; } else { if (ray.dir[i] < 0.f) { float startToMax = aabb.max[i] - ray.start[i]; float startToMin = aabb.min[i] - ray.start[i]; float dirRecip = 1.f / ray.dir[i]; if (startToMax < tMin * ray.dir[i]) tMin = startToMax * dirRecip; if (startToMin > tMax * ray.dir[i]) tMax = startToMin * dirRecip; } else { float startToMin = aabb.min[i] - ray.start[i]; float startToMax = aabb.max[i] - ray.start[i]; float dirRecip = 1.f / ray.dir[i]; if (startToMin > tMin * ray.dir[i]) tMin = startToMin * dirRecip; if (startToMax < tMax * ray.dir[i]) tMax = startToMax * dirRecip; } } } return tMin <= tMax ? 2 : 0; } u32 RayAABoxIntersection(const zeus::CMRay& ray, const zeus::CAABox& aabb, zeus::CVector3f& norm, float& d) { int sign[] = {2, 2, 2}; bool bad = true; zeus::CVector3f rayStart = ray.start; zeus::CVector3f rayDelta = ray.delta; zeus::CVector3f aabbMin = aabb.min; zeus::CVector3f aabbMax = aabb.max; zeus::CVector3f vec0 = {-1.f, -1.f, -1.f}; zeus::CVector3f vec1; if (rayDelta.x != 0.f && rayDelta.y != 0.f && rayDelta.z != 0.f) { for (int i=0 ; i<3 ; ++i) { if (rayStart[i] < aabbMin[i]) { sign[i] = 1; bad = false; vec0[i] = (aabbMin[i] - rayStart[i]) / rayDelta[i]; } else if (rayStart[i] > aabbMax[i]) { sign[i] = 0; bad = false; vec0[i] = (aabbMax[i] - rayStart[i]) / rayDelta[i]; } } if (bad) { d = 0.f; return 1; } } else { zeus::CVector3f end; for (int i=0 ; i<3 ; ++i) { if (rayStart[i] < aabbMin[i]) { sign[i] = 1; bad = false; end[i] = aabbMin[i]; } else if (rayStart[i] > aabbMax[i]) { sign[i] = 0; bad = false; end[i] = aabbMax[i]; } } if (bad) { d = 0.f; return 1; } for (int i=0 ; i<3 ; ++i) if (sign[i] != 2 && rayDelta[i] != 0.f) vec0[i] = (end[i] - rayStart[i]) / rayDelta[i]; } float maxComp = vec0.x; int maxCompIdx = 0; if (maxComp < vec0.y) { maxComp = vec0.y; maxCompIdx = 1; } if (maxComp < vec0.z) { maxComp = vec0.z; maxCompIdx = 2; } if (maxComp < 0.f || maxComp > 1.f) return 0; for (int i=0 ; i<3 ; ++i) { if (maxCompIdx != i) { vec1[i] = maxComp * rayDelta[i] + rayStart[i]; if (vec1[i] > aabbMax[i]) return 0; } } d = maxComp; norm = zeus::CVector3f::skZero; norm[maxCompIdx] = (sign[maxCompIdx] == 1) ? -1.f : 1.f; return 2; } u32 RayAABoxIntersection_Double(const zeus::CMRay& ray, const zeus::CAABox& aabb, zeus::CVector3f& norm, double& d) { int sign[] = {2, 2, 2}; bool bad = true; zeus::CVector3d rayStart = ray.start; zeus::CVector3d rayDelta = ray.delta; zeus::CVector3d aabbMin = aabb.min; zeus::CVector3d aabbMax = aabb.max; zeus::CVector3d vec0 = {-1.0, -1.0, -1.0}; zeus::CVector3d vec1; if (rayDelta.x != 0.0 && rayDelta.y != 0.0 && rayDelta.z != 0.0) { for (int i=0 ; i<3 ; ++i) { if (rayStart[i] < aabbMin[i]) { sign[i] = 1; bad = false; vec0[i] = (aabbMin[i] - rayStart[i]) / rayDelta[i]; } else if (rayStart[i] > aabbMax[i]) { sign[i] = 0; bad = false; vec0[i] = (aabbMax[i] - rayStart[i]) / rayDelta[i]; } } if (bad) { d = 0.0; return 1; } } else { zeus::CVector3d end; for (int i=0 ; i<3 ; ++i) { if (rayStart[i] < aabbMin[i]) { sign[i] = 1; bad = false; end[i] = aabbMin[i]; } else if (rayStart[i] > aabbMax[i]) { sign[i] = 0; bad = false; end[i] = aabbMax[i]; } } if (bad) { d = 0.0; return 1; } for (int i=0 ; i<3 ; ++i) if (sign[i] != 2 && rayDelta[i] != 0.0) vec0[i] = (end[i] - rayStart[i]) / rayDelta[i]; } double maxComp = vec0.x; int maxCompIdx = 0; if (maxComp < vec0.y) { maxComp = vec0.y; maxCompIdx = 1; } if (maxComp < vec0.z) { maxComp = vec0.z; maxCompIdx = 2; } if (maxComp < 0.0 || maxComp > 1.0) return 0; for (int i=0 ; i<3 ; ++i) { if (maxCompIdx != i) { vec1[i] = maxComp * rayDelta[i] + rayStart[i]; if (vec1[i] > aabbMax[i]) return 0; } } d = maxComp; norm = zeus::CVector3f::skZero; norm[maxCompIdx] = (sign[maxCompIdx] == 1) ? -1.0 : 1.0; return 2; } bool RaySphereIntersection_Double(const zeus::CSphere& sphere, const zeus::CVector3f& pos, const zeus::CVector3f& dir, double& T) { zeus::CVector3d sPosD = sphere.position; zeus::CVector3d posD = pos; zeus::CVector3d sphereToPos = posD - sPosD; double f30 = sphereToPos.dot(zeus::CVector3d(dir)) * 2.0; double f1 = f30 * f30 - 4.0 * (sphereToPos.magSquared() - sphere.radius * sphere.radius); if (f1 >= 0.0) { double intersectT = 0.5 * (-f30 - std::sqrt(f1)); if (T == 0 || intersectT < T) { T = intersectT; return true; } } return false; } bool RaySphereIntersection(const zeus::CSphere& sphere, const zeus::CVector3f& pos, const zeus::CVector3f& dir, float mag, float& T, zeus::CVector3f& point) { zeus::CVector3f rayToSphere = sphere.position - pos; float magSq = rayToSphere.magSquared(); float dirDot = rayToSphere.dot(dir); float radSq = sphere.radius * sphere.radius; if (dirDot < 0.f && magSq > radSq) return false; float intersectSq = radSq - (magSq - dirDot * dirDot); if (intersectSq < 0.f) return false; T = magSq > radSq ? dirDot - std::sqrt(intersectSq) : dirDot + std::sqrt(intersectSq); if (T < mag || mag == 0.f) { point = pos + T * dir; return true; } return false; } bool RayTriangleIntersection_Double(const zeus::CVector3f& point, const zeus::CVector3f& dir, const zeus::CVector3f* verts, double& d) { zeus::CVector3d v0tov1 = verts[1] - verts[0]; zeus::CVector3d v0tov2 = verts[2] - verts[0]; zeus::CVector3d cross0 = zeus::CVector3d(dir).cross(v0tov2); double dot0 = v0tov1.dot(cross0); if (dot0 < DBL_EPSILON) return false; zeus::CVector3d v0toPoint = point - verts[0]; double dot1 = v0toPoint.dot(cross0); if (dot1 < 0.0 || dot1 > dot0) return false; zeus::CVector3d cross1 = v0toPoint.cross(v0tov1); double dot2 = cross1.dot(dir); if (dot2 < 0.0 || dot1 + dot2 > dot0) return false; double final = 1.0 / dot0 * cross1.dot(v0tov2); if (final < 0.0 || final >= d) return false; d = final; return true; } bool RayTriangleIntersection(const zeus::CVector3f& point, const zeus::CVector3f& dir, const zeus::CVector3f* verts, float& d) { zeus::CVector3f v0tov1 = verts[1] - verts[0]; zeus::CVector3f v0tov2 = verts[2] - verts[0]; zeus::CVector3f cross0 = dir.cross(v0tov2); float dot0 = v0tov1.dot(cross0); if (dot0 < DBL_EPSILON) return false; zeus::CVector3f v0toPoint = point - verts[0]; float dot1 = v0toPoint.dot(cross0); if (dot1 < 0.f || dot1 > dot0) return false; zeus::CVector3f cross1 = v0toPoint.cross(v0tov1); float dot2 = cross1.dot(dir); if (dot2 < 0.f || dot1 + dot2 > dot0) return false; float final = 1.f / dot0 * cross1.dot(v0tov2); if (final < 0.f || final >= d) return false; d = final; return true; } void FilterOutBackfaces(const zeus::CVector3f& vec, const CCollisionInfoList& in, CCollisionInfoList& out) { if (vec.canBeNormalized()) { zeus::CVector3f norm = vec.normalized(); for (const CCollisionInfo& info : in) { if (info.GetNormalLeft().dot(norm) < 0.001f) out.Add(info, false); } } else { out = in; } } void FilterByClosestNormal(const zeus::CVector3f& norm, const CCollisionInfoList& in, CCollisionInfoList& out) { float maxDot = -1.1f; int idx = -1; int i=0; for (const CCollisionInfo& info : in) { float dot = info.GetNormalLeft().dot(norm); if (dot > maxDot) { maxDot = dot; idx = i; } ++i; } if (idx != -1) out.Add(in.GetItem(i), false); } static const zeus::CVector3f AABBNormalTable[] = { {-1.f, 0.f, 0.f}, {1.f, 0.f, 0.f}, {0.f, -1.f, 0.f}, {0.f, 1.f, 0.f}, {0.f, 0.f, -1.f}, {0.f, 0.f, 1.f} }; bool AABoxAABoxIntersection(const zeus::CAABox& aabb0, const CMaterialList& list0, const zeus::CAABox& aabb1, const CMaterialList& list1, CCollisionInfoList& infoList) { zeus::CVector3f maxOfMin(std::max(aabb0.min.x, aabb1.min.x), std::max(aabb0.min.y, aabb1.min.y), std::max(aabb0.min.z, aabb1.min.z)); zeus::CVector3f minOfMax(std::min(aabb0.max.x, aabb1.max.x), std::min(aabb0.max.y, aabb1.max.y), std::min(aabb0.max.z, aabb1.max.z)); if (maxOfMin.x >= minOfMax.x || maxOfMin.y >= minOfMax.y || maxOfMin.z >= minOfMax.z) return false; zeus::CAABox boolAABB(maxOfMin, minOfMax); int ineqFlags[] = { (aabb0.min.x <= aabb1.min.x ? 1 << 0 : 0) | (aabb0.min.x <= aabb1.max.x ? 1 << 1 : 0) | (aabb0.max.x <= aabb1.min.x ? 1 << 2 : 0) | (aabb0.max.x <= aabb1.max.x ? 1 << 3 : 0), (aabb0.min.y <= aabb1.min.y ? 1 << 0 : 0) | (aabb0.min.y <= aabb1.max.y ? 1 << 1 : 0) | (aabb0.max.y <= aabb1.min.y ? 1 << 2 : 0) | (aabb0.max.y <= aabb1.max.y ? 1 << 3 : 0), (aabb0.min.z <= aabb1.min.z ? 1 << 0 : 0) | (aabb0.min.z <= aabb1.max.z ? 1 << 1 : 0) | (aabb0.max.z <= aabb1.min.z ? 1 << 2 : 0) | (aabb0.max.z <= aabb1.max.z ? 1 << 3 : 0), }; for (int i=0 ; i<3 ; ++i) { switch (ineqFlags[i]) { case 0x2: // aabb0.min <= aabb1.max { CCollisionInfo info(boolAABB, list0, list1, AABBNormalTable[i*2+1], -AABBNormalTable[i*2+1]); infoList.Add(info, false); break; } case 0xB: // aabb0.min <= aabb1.min && aabb0.max <= aabb1.min && aabb0.max <= aabb1.max { CCollisionInfo info(boolAABB, list0, list1, AABBNormalTable[i*2], -AABBNormalTable[i*2]); infoList.Add(info, false); break; } default: break; } } if (infoList.GetCount()) return true; { CCollisionInfo info(boolAABB, list0, list1, AABBNormalTable[4], -AABBNormalTable[4]); infoList.Add(info, false); } { CCollisionInfo info(boolAABB, list0, list1, AABBNormalTable[5], -AABBNormalTable[5]); infoList.Add(info, false); } return true; } bool AABoxAABoxIntersection(const zeus::CAABox& aabb0, const zeus::CAABox& aabb1) { return aabb0.intersects(aabb1); } /* http://fileadmin.cs.lth.se/cs/Personal/Tomas_Akenine-Moller/code/tribox2.txt */ /********************************************************/ /* AABB-triangle overlap test code */ /* by Tomas Akenine-Möller */ /* Function: int triBoxOverlap(float boxcenter[3], */ /* float boxhalfsize[3],float triverts[3][3]); */ /* History: */ /* 2001-03-05: released the code in its first version */ /* 2001-06-18: changed the order of the tests, faster */ /* */ /* Acknowledgement: Many thanks to Pierre Terdiman for */ /* suggestions and discussions on how to optimize code. */ /* Thanks to David Hunt for finding a ">="-bug! */ /********************************************************/ #define FINDMINMAX(x0,x1,x2,min,max) \ min = max = x0; \ if (x1max) max = x1;\ if (x2max) max = x2; static bool planeBoxOverlap(const zeus::CVector3f& normal, float d, const zeus::CVector3f& maxbox) { zeus::CVector3f vmin, vmax; for (int q=0 ; q<=2 ; q++) { if (normal[q] > 0.0f) { vmin[q] = -maxbox[q]; vmax[q] = maxbox[q]; } else { vmin[q] = maxbox[q]; vmax[q] = -maxbox[q]; } } if (normal.dot(vmin) + d > 0.0f) return false; if (normal.dot(vmax) + d >= 0.0f) return true; return false; } /*======================== X-tests ========================*/ #define AXISTEST_X01(a, b, fa, fb) \ p0 = a*v0.y - b*v0.z; \ p2 = a*v2.y - b*v2.z; \ if(p0rad || max<-rad) return false; #define AXISTEST_X2(a, b, fa, fb) \ p0 = a*v0.y - b*v0.z; \ p1 = a*v1.y - b*v1.z; \ if(p0rad || max<-rad) return false; /*======================== Y-tests ========================*/ #define AXISTEST_Y02(a, b, fa, fb) \ p0 = -a*v0.x + b*v0.z; \ p2 = -a*v2.x + b*v2.z; \ if(p0rad || max<-rad) return false; #define AXISTEST_Y1(a, b, fa, fb) \ p0 = -a*v0.x + b*v0.z; \ p1 = -a*v1.x + b*v1.z; \ if(p0rad || max<-rad) return false; /*======================== Z-tests ========================*/ #define AXISTEST_Z12(a, b, fa, fb) \ p1 = a*v1.x - b*v1.y; \ p2 = a*v2.x - b*v2.y; \ if(p2rad || max<-rad) return false; #define AXISTEST_Z0(a, b, fa, fb) \ p0 = a*v0.x - b*v0.y; \ p1 = a*v1.x - b*v1.y; \ if(p0rad || max<-rad) return false; bool TriBoxOverlap(const zeus::CVector3f& boxcenter, const zeus::CVector3f& boxhalfsize, const zeus::CVector3f& trivert0, const zeus::CVector3f& trivert1, const zeus::CVector3f& trivert2) { /* use separating axis theorem to test overlap between triangle and box */ /* need to test for overlap in these directions: */ /* 1) the {x,y,z}-directions (actually, since we use the AABB of the triangle */ /* we do not even need to test these) */ /* 2) normal of the triangle */ /* 3) crossproduct(edge from tri, {x,y,z}-directin) */ /* this gives 3x3=9 more tests */ zeus::CVector3f v0, v1, v2; float min, max, d, p0, p1, p2, rad, fex, fey, fez; zeus::CVector3f normal, e0, e1, e2; /* This is the fastest branch on Sun */ /* move everything so that the boxcenter is in (0,0,0) */ v0 = trivert0 - boxcenter; v1 = trivert1 - boxcenter; v2 = trivert2 - boxcenter; /* compute triangle edges */ e0 = v1 - v0; /* tri edge 0 */ e1 = v2 - v1; /* tri edge 1 */ e2 = v0 - v2; /* tri edge 2 */ /* Bullet 3: */ /* test the 9 tests first (this was faster) */ fex = std::fabs(e0.x); fey = std::fabs(e0.y); fez = std::fabs(e0.z); AXISTEST_X01(e0.z, e0.y, fez, fey); AXISTEST_Y02(e0.z, e0.x, fez, fex); AXISTEST_Z12(e0.y, e0.x, fey, fex); fex = std::fabs(e1.x); fey = std::fabs(e1.y); fez = std::fabs(e1.z); AXISTEST_X01(e1.z, e1.y, fez, fey); AXISTEST_Y02(e1.z, e1.x, fez, fex); AXISTEST_Z0(e1.y, e1.x, fey, fex); fex = std::fabs(e2.x); fey = std::fabs(e2.y); fez = std::fabs(e2.z); AXISTEST_X2(e2.z, e2.y, fez, fey); AXISTEST_Y1(e2.z, e2.x, fez, fex); AXISTEST_Z12(e2.y, e2.x, fey, fex); /* Bullet 1: */ /* first test overlap in the {x,y,z}-directions */ /* find min, max of the triangle each direction, and test for overlap in */ /* that direction -- this is equivalent to testing a minimal AABB around */ /* the triangle against the AABB */ /* test in X-direction */ FINDMINMAX(v0.x, v1.x, v2.x, min, max); if (min>boxhalfsize.x || max<-boxhalfsize.x) return false; /* test in Y-direction */ FINDMINMAX(v0.y, v1.y, v2.y, min, max); if (min>boxhalfsize.y || max<-boxhalfsize.y) return false; /* test in Z-direction */ FINDMINMAX(v0.z, v1.z, v2.z, min, max); if (min>boxhalfsize.z || max<-boxhalfsize.z) return false; /* Bullet 2: */ /* test if the box intersects the plane of the triangle */ /* compute plane equation of triangle: normal*x+d=0 */ normal = e0.cross(e1); d = -normal.dot(v0); /* plane eq: normal.x+d=0 */ if (!planeBoxOverlap(normal, d, boxhalfsize)) return false; return true; /* box and triangle overlaps */ } double TriPointSqrDist(const zeus::CVector3f& point, const zeus::CVector3f& trivert0, const zeus::CVector3f& trivert1, const zeus::CVector3f& trivert2, float* baryX, float* baryY) { zeus::CVector3d A = trivert0 - point; zeus::CVector3d B = trivert1 - trivert0; zeus::CVector3d C = trivert2 - trivert0; double bMag = B.magSquared(); double cMag = C.magSquared(); double bDotC = B.dot(C); double aDotB = A.dot(B); double aDotC = A.dot(C); double ret = A.magSquared(); double rej = std::fabs(bMag * cMag - bDotC * bDotC); double retB = bDotC * aDotC - cMag * aDotB; double retA = bDotC * aDotB - bMag * aDotC; if (retB + retA <= rej) { if (retB < 0.0) { if (retA < 0.0) { if (aDotB < 0.0) { retA = 0.0; if (-aDotB >= bMag) { retB = 1.0; ret += 2.0 * aDotB + bMag; } else { retB = -aDotB / bMag; ret += aDotB * retB; } } else { retB = 0.0; if (aDotC >= 0.0) { retA = 0.0; } else if (-aDotC >= cMag) { retA = 1.0; ret += 2.0 * aDotC + cMag; } else { retA = -aDotC / cMag; ret += aDotC * retA; } } } else { retB = 0.0; if (aDotC >= 0.0) { retA = 0.0; } else if (-aDotC >= cMag) { retA = 1.0; ret += 2.0 * aDotC + cMag; } else { retA = -aDotC / cMag; ret += aDotC * retA; } } } else if (retA < 0.0) { retA = 0.0; if (aDotB >= 0.0) { retB = 0.0; } else if (-aDotB >= bMag) { retB = 1.0; ret += 2.0 * aDotB + bMag; } else { retB = -aDotB / bMag; ret += aDotB * retB; } } else { float f3 = 1.0 / rej; retA *= f3; retB *= f3; ret += retB * (2.0 * aDotB + (bMag * retB + bDotC * retA)) + retA * (2.0 * aDotC + (bDotC * retB + cMag * retA)); } } else if (retB < 0.0) { retB = bDotC + aDotB; retA = cMag + aDotC; if (retA > retB) { retA -= retB; retB = bMag - 2.0 * bDotC; retB += cMag; if (retA >= retB) { retB = 1.0; retA = 0.0; ret += 2.0 * aDotB + bMag; } else { retB = retA / retB; retA = 1.0 - retB; ret += retB * (2.0 * aDotB + (bMag * retB + bDotC * retA)) + retA * (2.0 * aDotC + (bDotC * retB + cMag * retA)); } } else { retB = 0.0; if (retA <= 0.0) { retA = 1.0; ret += 2.0 * aDotC + cMag; } else if (aDotC >= 0.0) { retA = 0.0; } else { retA = -aDotC / cMag; ret += aDotC * retA; } } } else { if (retA < 0.0) { retB = bDotC + aDotC; retA = bMag + aDotB; if (retA > retB) { retA -= retB; retB = bMag - 2.0 * bDotC; retB += cMag; if (retA >= retB) { retA = 1.0; retB = 0.0; ret += 2.0 * aDotC + cMag; } else { retA /= retB; retB = 1.0 - retA; ret += retB * (2.0 * aDotB + (bMag * retB + bDotC * retA)) + retA * (2.0 * aDotC + (bDotC * retB + cMag * retA)); } } else { retA = 0.0; if (retA <= 0.0) { retB = 1.0; ret += 2.0 * aDotB + bMag; } else if (aDotB >= 0.0) { retB = 0.0; } else { retB = -aDotB / bMag; ret += aDotB * retB; } } } else { retB = cMag + aDotC; retB -= bDotC; retA = retB - aDotB; if (retA <= 0.0) { retB = 0.0; retA = 1.0; ret += 2.0 * aDotC + cMag; } else { retB = bMag - 2.0 * bDotC; retB += cMag; if (retA >= retB) { retB = 1.0; retA = 0.0; ret += 2.0 * aDotB + bMag; } else { retB = retA / retB; retA = 1.0 - retB; ret += retB * (2.0 * aDotB + (bMag * retB + bDotC * retA)) + retA * (2.0 * aDotC + (bDotC * retB + cMag * retA)); } } } } if (baryX) *baryX = retA; if (baryY) *baryY = retB; return ret; } bool TriSphereOverlap(const zeus::CSphere& sphere, const zeus::CVector3f& trivert0, const zeus::CVector3f& trivert1, const zeus::CVector3f& trivert2) { return TriPointSqrDist(sphere.position, trivert0, trivert1, trivert2, nullptr, nullptr) <= sphere.radius * sphere.radius; } bool TriSphereIntersection(const zeus::CSphere& sphere, const zeus::CVector3f& trivert0, const zeus::CVector3f& trivert1, const zeus::CVector3f& trivert2, zeus::CVector3f& point, zeus::CVector3f& normal) { float baryX, baryY; if (TriPointSqrDist(sphere.position, trivert0, trivert1, trivert2, &baryX, &baryY) > sphere.radius * sphere.radius) return false; zeus::CVector3f barys(baryX, baryY, 1.f - (baryX + baryY)); point = zeus::baryToWorld(trivert2, trivert1, trivert0, barys); if (baryX == 0.f || baryX == 1.f || baryY == 0.f || baryY == 1.f || barys.z == 0.f || barys.z == 1.f) normal = -sphere.getSurfaceNormal(point); else normal = (trivert1 - trivert0).cross(trivert2 - trivert0).normalized(); return true; } bool BoxLineTest(const zeus::CAABox& aabb, const zeus::CVector3f& point, const zeus::CVector3f& dir, float& tMin, float& tMax, int& axis, bool& sign) { tMin = -999999.f; tMax = 999999.f; for (int i=0 ; i<3 ; ++i) { if (dir[i] == 0.f) if (point[i] < aabb.min[i] || point[i] > aabb.max[i]) return false; float dirRecip = 1.f / dir[i]; float tmpMin, tmpMax; if (dir[i] < 0.f) { tmpMin = (aabb.max[i] - point[i]) * dirRecip; tmpMax = (aabb.min[i] - point[i]) * dirRecip; } else { tmpMin = (aabb.min[i] - point[i]) * dirRecip; tmpMax = (aabb.max[i] - point[i]) * dirRecip; } if (tmpMin > tMin) { sign = dir[i] < 0.f; axis = i; tMin = tmpMin; } if (tmpMax < tMax) tMax = tmpMax; } return tMin <= tMax; } bool LineCircleIntersection2d(const zeus::CVector3f& point, const zeus::CVector3f& dir, const zeus::CSphere& sphere, int axis1, int axis2, float& d) { zeus::CVector3f delta = sphere.position - point; zeus::CVector2f deltaVec(delta[axis1], delta[axis2]); zeus::CVector2f dirVec(dir[axis1], dir[axis2]); float dirVecMag = dirVec.magnitude(); if (dirVecMag < FLT_EPSILON) return false; float deltaVecDot = deltaVec.dot(dirVec / dirVecMag); float deltaVecMagSq = deltaVec.magSquared(); float sphereRadSq = sphere.radius * sphere.radius; if (deltaVecDot < 0.f && deltaVecMagSq > sphereRadSq) return false; float tSq = sphereRadSq - (deltaVecMagSq - deltaVecDot * deltaVecDot); if (tSq < 0.f) return false; float t = std::sqrt(tSq); d = (deltaVecMagSq > sphereRadSq) ? deltaVecDot - t : deltaVecDot + t; d /= dirVecMag; return true; } bool MovingSphereAABox(const zeus::CSphere& sphere, const zeus::CAABox& aabb, const zeus::CVector3f& dir, double& dOut, zeus::CVector3f& point, zeus::CVector3f& normal) { zeus::CAABox expAABB(aabb.min - sphere.radius, aabb.max + sphere.radius); float tMin, tMax; int axis; bool sign; if (!BoxLineTest(expAABB, sphere.position, dir, tMin, tMax, axis, sign)) return false; point = sphere.position + tMin * dir; int nextAxis1 = (axis+1) % 3; // r0 int nextAxis2 = (axis+2) % 3; // r5 bool inMin1 = point[nextAxis1] >= aabb.min[nextAxis1]; // r6 bool inMax1 = point[nextAxis1] <= aabb.max[nextAxis1]; // r8 bool inBounds1 = inMin1 && inMax1; // r9 bool inMin2 = point[nextAxis2] >= aabb.min[nextAxis2]; // r7 bool inMax2 = point[nextAxis2] <= aabb.max[nextAxis2]; // r4 bool inBounds2 = inMin2 && inMax2; // r8 if (inBounds1 && inBounds2) { if (tMin < 0.f || tMin > dOut) return false; normal[axis] = sign ? 1.f : -1.f; dOut = tMin; point -= normal * sphere.radius; return true; } else if (!inBounds1 && !inBounds2) { int pointFlags = (1 << axis) * sign | (1 << nextAxis1) * inMin1 | (1 << nextAxis2) * inMin2; zeus::CVector3f aabbPoint = aabb.getPoint(pointFlags); float d; if (CollisionUtil::RaySphereIntersection(zeus::CSphere(aabbPoint, sphere.radius), sphere.position, dir, dOut, d, point)) { int useAxis = -1; for (int i=0 ; i<3 ; ++i) { if ((pointFlags & (1 << i)) ? aabbPoint[i] > point[i] : aabbPoint[i] < point[i]) { useAxis = i; break; } } if (useAxis == -1) { normal = (point - aabbPoint).normalized(); point -= sphere.radius * normal; return true; } int useAxisNext1 = (useAxis+1) % 3; int useAxisNext2 = (useAxis+2) % 3; float d; if (CollisionUtil::LineCircleIntersection2d(sphere.position, dir, zeus::CSphere(aabbPoint, sphere.radius), useAxisNext1, useAxisNext2, d) && d > 0.f && d < dOut) { if (point[useAxis] > aabb.max[useAxis]) { int useAxisBit = 1 << useAxis; if (pointFlags & useAxisBit) return false; zeus::CVector3f aabbPoint1 = aabb.getPoint(pointFlags | useAxisBit); if (CollisionUtil::RaySphereIntersection(zeus::CSphere(aabbPoint1, sphere.radius), sphere.position, dir, dOut, d, point)) { dOut = d; normal = (point - aabbPoint1).normalized(); point -= normal * sphere.radius; return true; } else { return false; } } else if (point[useAxis] < aabb.min[useAxis]) { int useAxisBit = 1 << useAxis; if (!(pointFlags & useAxisBit)) return false; zeus::CVector3f aabbPoint1 = aabb.getPoint(pointFlags ^ useAxisBit); if (CollisionUtil::RaySphereIntersection(zeus::CSphere(aabbPoint1, sphere.radius), sphere.position, dir, dOut, d, point)) { dOut = d; normal = (point - aabbPoint1).normalized(); point -= normal * sphere.radius; return true; } else { return false; } } else { normal = point - aabbPoint; normal.normalize(); point -= normal * sphere.radius; return true; } } } else { int reverseCount = 0; float dMin = 1.0e10f; int minAxis = 0; for (int i=0 ; i<3 ; ++i) { if (std::fabs(dir[i]) > FLT_EPSILON) { bool pointMax = pointFlags & (1 << i); if (pointMax != dir[i] > 0.f) { ++reverseCount; float d = 1.f / dir[i] * ((pointMax ? aabb.max[i] : aabb.min[i]) - sphere.position[i]); if (d < 0.f) return false; if (d < dMin) { dMin = d; minAxis = i; } } } } if (reverseCount < 2) return false; int useAxisNext1 = (minAxis+1) % 3; int useAxisNext2 = (minAxis+2) % 3; float d; if (CollisionUtil::LineCircleIntersection2d(sphere.position, dir, zeus::CSphere(aabbPoint, sphere.radius), useAxisNext1, useAxisNext2, d) && d > 0.f && d < dOut) { point = sphere.position + d * dir; if (point[minAxis] > aabb.max[minAxis]) return false; if (point[minAxis] < aabb.min[minAxis]) return false; dOut = d; normal = point - aabbPoint; normal.normalize(); point -= sphere.radius * normal; return true; } else { return false; } } } bool useNextAxis1 = inBounds1 ? nextAxis2 : nextAxis1; bool useNextAxis2 = inBounds1 ? nextAxis1 : nextAxis2; int pointFlags = ((1 << int(useNextAxis1)) * (inBounds1 ? inMin2 : inMin1)) | ((1 << axis) * sign); zeus::CVector3f aabbPoint2 = aabb.getPoint(pointFlags); float d; if (LineCircleIntersection2d(sphere.position, dir, zeus::CSphere(aabbPoint2, sphere.radius), axis, useNextAxis1, d) && d > 0.f && d < dOut) { point = sphere.position + d * dir; if (point[useNextAxis2] > aabb.max[useNextAxis2]) { zeus::CVector3f aabbPoint3 = aabb.getPoint(pointFlags | (1 << int(useNextAxis2))); if (point[useNextAxis2] < expAABB.max[useNextAxis2]) { if (RaySphereIntersection(zeus::CSphere(aabbPoint3, sphere.radius), sphere.position, dir, dOut, d, point)) { dOut = d; normal = (point - aabbPoint3).normalized(); point -= sphere.radius * normal; return true; } } return false; } else if (point[useNextAxis2] < aabb.min[useNextAxis2]) { if (point[useNextAxis2] > expAABB.min[useNextAxis2]) { if (RaySphereIntersection(zeus::CSphere(aabbPoint2, sphere.radius), sphere.position, dir, dOut, d, point)) { dOut = d; normal = (point - aabbPoint2).normalized(); point -= sphere.radius * normal; return true; } } return false; } else { dOut = d; normal = point - aabbPoint2; normal.normalize(); point -= sphere.radius * normal; return true; } } return false; } bool AABox_AABox_Moving(const zeus::CAABox& aabb0, const zeus::CAABox& aabb1, const zeus::CVector3f& dir, double& d, zeus::CVector3f& point, zeus::CVector3f& normal) { zeus::CVector3d vecMin(-FLT_MAX); zeus::CVector3d vecMax(FLT_MAX); for (int i=0 ; i<3 ; ++i) { if (std::fabs(dir[i]) < FLT_EPSILON) { if (aabb0.min[i] >= aabb1.min[i] && aabb0.min[i] <= aabb1.max[i]) continue; if (aabb0.max[i] >= aabb1.min[i] && aabb0.max[i] <= aabb1.max[i]) continue; if (aabb0.min[i] < aabb1.min[i] && aabb0.max[i] > aabb1.max[i]) continue; return false; } else { if (aabb0.max[i] < aabb1.min[i] && dir[i] > 0.f) vecMin[i] = (aabb1.min[i] - aabb0.max[i]) / dir[i]; else if (aabb1.max[i] < aabb0.min[i] && dir[i] < 0.f) vecMin[i] = (aabb1.max[i] - aabb0.min[i]) / dir[i]; else if (aabb1.max[i] > aabb0.min[i] && dir[i] < 0.f) vecMin[i] = (aabb1.max[i] - aabb0.min[i]) / dir[i]; else if (aabb0.max[i] > aabb1.min[i] && dir[i] > 0.f) vecMin[i] = (aabb1.min[i] - aabb0.max[i]) / dir[i]; if (aabb1.max[i] > aabb0.min[i] && dir[i] > 0.f) vecMax[i] = (aabb1.max[i] - aabb0.min[i]) / dir[i]; else if (aabb0.max[i] > aabb1.min[i] && dir[i] < 0.f) vecMax[i] = (aabb1.min[i] - aabb0.max[i]) / dir[i]; else if (aabb0.max[i] < aabb1.min[i] && dir[i] < 0.f) vecMax[i] = (aabb1.min[i] - aabb0.max[i]) / dir[i]; else if (aabb1.max[i] < aabb0.min[i] && dir[i] > 0.f) vecMax[i] = (aabb1.max[i] - aabb0.min[i]) / dir[i]; } } int maxAxis = 0; if (vecMin[1] > vecMin[0]) maxAxis = 1; if (vecMin[2] > vecMin[maxAxis]) maxAxis = 2; double minMax = std::min(std::min(vecMax[2], vecMax[1]), vecMax[0]); if (vecMin[maxAxis] > minMax) return false; d = vecMin[maxAxis]; normal = zeus::CVector3f::skZero; normal[maxAxis] = dir[maxAxis] > 0.f ? -1.f : 1.f; for (int i=0 ; i<3 ; ++i) point[i] = dir[i] > 0.f ? aabb0.max[i] : aabb0.min[i]; point += float(d) * dir; return true; } }