/* * Copyright 2011-2017 Branimir Karadzic. All rights reserved. * License: https://github.com/bkaradzic/bgfx#license-bsd-2-clause */ #include #include #include "bounds.h" void aabbToObb(Obb& _obb, const Aabb& _aabb) { bx::memSet(_obb.m_mtx, 0, sizeof(_obb.m_mtx) ); _obb.m_mtx[ 0] = (_aabb.m_max[0] - _aabb.m_min[0]) * 0.5f; _obb.m_mtx[ 5] = (_aabb.m_max[1] - _aabb.m_min[1]) * 0.5f; _obb.m_mtx[10] = (_aabb.m_max[2] - _aabb.m_min[2]) * 0.5f; _obb.m_mtx[12] = (_aabb.m_min[0] + _aabb.m_max[0]) * 0.5f; _obb.m_mtx[13] = (_aabb.m_min[1] + _aabb.m_max[1]) * 0.5f; _obb.m_mtx[14] = (_aabb.m_min[2] + _aabb.m_max[2]) * 0.5f; _obb.m_mtx[15] = 1.0f; } void toAabb(Aabb& _aabb, const Sphere& _sphere) { float radius = _sphere.m_radius; bx::vec3Sub(_aabb.m_min, _sphere.m_center, radius); bx::vec3Add(_aabb.m_max, _sphere.m_center, radius); } void toAabb(Aabb& _aabb, const Disk& _disk) { // Reference: http://iquilezles.org/www/articles/diskbbox/diskbbox.htm float nsq[3]; bx::vec3Mul(nsq, _disk.m_normal, _disk.m_normal); float one[3] = { 1.0f, 1.0f, 1.0f }; float tmp[3]; bx::vec3Sub(tmp, one, nsq); const float inv = 1.0f / (tmp[0]*tmp[1]*tmp[2]); float extent[3]; extent[0] = _disk.m_radius * tmp[0] * bx::fsqrt( (nsq[0] + nsq[1] * nsq[2]) * inv); extent[1] = _disk.m_radius * tmp[1] * bx::fsqrt( (nsq[1] + nsq[2] * nsq[0]) * inv); extent[2] = _disk.m_radius * tmp[2] * bx::fsqrt( (nsq[2] + nsq[0] * nsq[1]) * inv); bx::vec3Sub(_aabb.m_min, _disk.m_center, extent); bx::vec3Add(_aabb.m_max, _disk.m_center, extent); } void toAabb(Aabb& _aabb, const Cylinder& _cylinder) { // Reference: http://iquilezles.org/www/articles/diskbbox/diskbbox.htm float axis[3]; bx::vec3Sub(axis, _cylinder.m_end, _cylinder.m_pos); float asq[3]; bx::vec3Mul(asq, axis, axis); float nsq[3]; bx::vec3Mul(nsq, asq, 1.0f/bx::vec3Dot(axis, axis) ); float one[3] = { 1.0f, 1.0f, 1.0f }; float tmp[3]; bx::vec3Sub(tmp, one, nsq); const float inv = 1.0f / (tmp[0]*tmp[1]*tmp[2]); float extent[3]; extent[0] = _cylinder.m_radius * tmp[0] * bx::fsqrt( (nsq[0] + nsq[1] * nsq[2]) * inv); extent[1] = _cylinder.m_radius * tmp[1] * bx::fsqrt( (nsq[1] + nsq[2] * nsq[0]) * inv); extent[2] = _cylinder.m_radius * tmp[2] * bx::fsqrt( (nsq[2] + nsq[0] * nsq[1]) * inv); float minP[3]; bx::vec3Sub(minP, _cylinder.m_pos, extent); float minE[3]; bx::vec3Sub(minE, _cylinder.m_end, extent); float maxP[3]; bx::vec3Add(maxP, _cylinder.m_pos, extent); float maxE[3]; bx::vec3Add(maxE, _cylinder.m_end, extent); bx::vec3Min(_aabb.m_min, minP, minE); bx::vec3Max(_aabb.m_max, maxP, maxE); } void aabbTransformToObb(Obb& _obb, const Aabb& _aabb, const float* _mtx) { aabbToObb(_obb, _aabb); float result[16]; bx::mtxMul(result, _obb.m_mtx, _mtx); bx::memCopy(_obb.m_mtx, result, sizeof(result) ); } void toAabb(Aabb& _aabb, const void* _vertices, uint32_t _numVertices, uint32_t _stride) { float min[3], max[3]; uint8_t* vertex = (uint8_t*)_vertices; float* position = (float*)vertex; min[0] = max[0] = position[0]; min[1] = max[1] = position[1]; min[2] = max[2] = position[2]; vertex += _stride; for (uint32_t ii = 1; ii < _numVertices; ++ii) { position = (float*)vertex; vertex += _stride; float xx = position[0]; float yy = position[1]; float zz = position[2]; min[0] = bx::fmin(xx, min[0]); min[1] = bx::fmin(yy, min[1]); min[2] = bx::fmin(zz, min[2]); max[0] = bx::fmax(xx, max[0]); max[1] = bx::fmax(yy, max[1]); max[2] = bx::fmax(zz, max[2]); } _aabb.m_min[0] = min[0]; _aabb.m_min[1] = min[1]; _aabb.m_min[2] = min[2]; _aabb.m_max[0] = max[0]; _aabb.m_max[1] = max[1]; _aabb.m_max[2] = max[2]; } void toAabb(Aabb& _aabb, const float* _mtx, const void* _vertices, uint32_t _numVertices, uint32_t _stride) { float min[3], max[3]; uint8_t* vertex = (uint8_t*)_vertices; float position[3]; bx::vec3MulMtx(position, (float*)vertex, _mtx); min[0] = max[0] = position[0]; min[1] = max[1] = position[1]; min[2] = max[2] = position[2]; vertex += _stride; for (uint32_t ii = 1; ii < _numVertices; ++ii) { bx::vec3MulMtx(position, (float*)vertex, _mtx); vertex += _stride; float xx = position[0]; float yy = position[1]; float zz = position[2]; min[0] = bx::fmin(xx, min[0]); min[1] = bx::fmin(yy, min[1]); min[2] = bx::fmin(zz, min[2]); max[0] = bx::fmax(xx, max[0]); max[1] = bx::fmax(yy, max[1]); max[2] = bx::fmax(zz, max[2]); } _aabb.m_min[0] = min[0]; _aabb.m_min[1] = min[1]; _aabb.m_min[2] = min[2]; _aabb.m_max[0] = max[0]; _aabb.m_max[1] = max[1]; _aabb.m_max[2] = max[2]; } float calcAreaAabb(const Aabb& _aabb) { float ww = _aabb.m_max[0] - _aabb.m_min[0]; float hh = _aabb.m_max[1] - _aabb.m_min[1]; float dd = _aabb.m_max[2] - _aabb.m_min[2]; return 2.0f * (ww*hh + ww*dd + hh*dd); } void aabbExpand(Aabb& _aabb, float _factor) { _aabb.m_min[0] -= _factor; _aabb.m_min[1] -= _factor; _aabb.m_min[2] -= _factor; _aabb.m_max[0] += _factor; _aabb.m_max[1] += _factor; _aabb.m_max[2] += _factor; } void aabbExpand(Aabb& _aabb, const float* _pos) { bx::vec3Min(_aabb.m_min, _aabb.m_min, _pos); bx::vec3Max(_aabb.m_max, _aabb.m_max, _pos); } uint32_t aabbOverlapTest(const Aabb& _aabb0, const Aabb& _aabb1) { const uint32_t ltMinX = _aabb0.m_max[0] < _aabb1.m_min[0]; const uint32_t gtMaxX = _aabb0.m_min[0] > _aabb1.m_max[0]; const uint32_t ltMinY = _aabb0.m_max[1] < _aabb1.m_min[1]; const uint32_t gtMaxY = _aabb0.m_min[1] > _aabb1.m_max[1]; const uint32_t ltMinZ = _aabb0.m_max[2] < _aabb1.m_min[2]; const uint32_t gtMaxZ = _aabb0.m_min[2] > _aabb1.m_max[2]; return 0 | (ltMinX<<0) | (gtMaxX<<1) | (ltMinY<<2) | (gtMaxY<<3) | (ltMinZ<<4) | (gtMaxZ<<5) ; } void calcObb(Obb& _obb, const void* _vertices, uint32_t _numVertices, uint32_t _stride, uint32_t _steps) { Aabb aabb; toAabb(aabb, _vertices, _numVertices, _stride); float minArea = calcAreaAabb(aabb); Obb best; aabbToObb(best, aabb); float angleStep = float(bx::piHalf/_steps); float ax = 0.0f; float mtx[16]; for (uint32_t ii = 0; ii < _steps; ++ii) { float ay = 0.0f; for (uint32_t jj = 0; jj < _steps; ++jj) { float az = 0.0f; for (uint32_t kk = 0; kk < _steps; ++kk) { bx::mtxRotateXYZ(mtx, ax, ay, az); float mtxT[16]; bx::mtxTranspose(mtxT, mtx); toAabb(aabb, mtxT, _vertices, _numVertices, _stride); float area = calcAreaAabb(aabb); if (area < minArea) { minArea = area; aabbTransformToObb(best, aabb, mtx); } az += angleStep; } ay += angleStep; } ax += angleStep; } bx::memCopy(&_obb, &best, sizeof(Obb) ); } void calcMaxBoundingSphere(Sphere& _sphere, const void* _vertices, uint32_t _numVertices, uint32_t _stride) { Aabb aabb; toAabb(aabb, _vertices, _numVertices, _stride); float center[3]; center[0] = (aabb.m_min[0] + aabb.m_max[0]) * 0.5f; center[1] = (aabb.m_min[1] + aabb.m_max[1]) * 0.5f; center[2] = (aabb.m_min[2] + aabb.m_max[2]) * 0.5f; float maxDistSq = 0.0f; uint8_t* vertex = (uint8_t*)_vertices; for (uint32_t ii = 0; ii < _numVertices; ++ii) { float* position = (float*)vertex; vertex += _stride; float xx = position[0] - center[0]; float yy = position[1] - center[1]; float zz = position[2] - center[2]; float distSq = xx*xx + yy*yy + zz*zz; maxDistSq = bx::fmax(distSq, maxDistSq); } bx::vec3Move(_sphere.m_center, center); _sphere.m_radius = bx::fsqrt(maxDistSq); } void calcMinBoundingSphere(Sphere& _sphere, const void* _vertices, uint32_t _numVertices, uint32_t _stride, float _step) { bx::RngMwc rng; uint8_t* vertex = (uint8_t*)_vertices; float center[3]; float* position = (float*)&vertex[0]; bx::vec3Move(center, position); position = (float*)&vertex[1*_stride]; center[0] += position[0]; center[1] += position[1]; center[2] += position[2]; center[0] *= 0.5f; center[1] *= 0.5f; center[2] *= 0.5f; float xx = position[0] - center[0]; float yy = position[1] - center[1]; float zz = position[2] - center[2]; float maxDistSq = xx*xx + yy*yy + zz*zz; float radiusStep = _step * 0.37f; bool done; do { done = true; for (uint32_t ii = 0, index = rng.gen()%_numVertices; ii < _numVertices; ++ii, index = (index + 1)%_numVertices) { position = (float*)&vertex[index*_stride]; xx = position[0] - center[0]; yy = position[1] - center[1]; zz = position[2] - center[2]; float distSq = xx*xx + yy*yy + zz*zz; if (distSq > maxDistSq) { done = false; center[0] += xx * radiusStep; center[1] += yy * radiusStep; center[2] += zz * radiusStep; maxDistSq = bx::flerp(maxDistSq, distSq, _step); break; } } } while (!done); bx::vec3Move(_sphere.m_center, center); _sphere.m_radius = bx::fsqrt(maxDistSq); } void calcPlaneUv(const Plane& _plane, float* _udir, float* _vdir) { bx::vec3TangentFrame(_plane.m_normal, _udir, _vdir); } void buildFrustumPlanes(Plane* _result, const float* _viewProj) { const float xw = _viewProj[ 3]; const float yw = _viewProj[ 7]; const float zw = _viewProj[11]; const float ww = _viewProj[15]; const float xz = _viewProj[ 2]; const float yz = _viewProj[ 6]; const float zz = _viewProj[10]; const float wz = _viewProj[14]; Plane& near = _result[0]; Plane& far = _result[1]; Plane& left = _result[2]; Plane& right = _result[3]; Plane& top = _result[4]; Plane& bottom = _result[5]; near.m_normal[0] = xw - xz; near.m_normal[1] = yw - yz; near.m_normal[2] = zw - zz; near.m_dist = ww - wz; far.m_normal[0] = xw + xz; far.m_normal[1] = yw + yz; far.m_normal[2] = zw + zz; far.m_dist = ww + wz; const float xx = _viewProj[ 0]; const float yx = _viewProj[ 4]; const float zx = _viewProj[ 8]; const float wx = _viewProj[12]; left.m_normal[0] = xw - xx; left.m_normal[1] = yw - yx; left.m_normal[2] = zw - zx; left.m_dist = ww - wx; right.m_normal[0] = xw + xx; right.m_normal[1] = yw + yx; right.m_normal[2] = zw + zx; right.m_dist = ww + wx; const float xy = _viewProj[ 1]; const float yy = _viewProj[ 5]; const float zy = _viewProj[ 9]; const float wy = _viewProj[13]; top.m_normal[0] = xw + xy; top.m_normal[1] = yw + yy; top.m_normal[2] = zw + zy; top.m_dist = ww + wy; bottom.m_normal[0] = xw - xy; bottom.m_normal[1] = yw - yy; bottom.m_normal[2] = zw - zy; bottom.m_dist = ww - wy; Plane* plane = _result; for (uint32_t ii = 0; ii < 6; ++ii) { float invLen = 1.0f / bx::vec3Norm(plane->m_normal, plane->m_normal); plane->m_dist *= invLen; ++plane; } } void intersectPlanes(float _result[3], const Plane& _pa, const Plane& _pb, const Plane& _pc) { float axb[3]; bx::vec3Cross(axb, _pa.m_normal, _pb.m_normal); float bxc[3]; bx::vec3Cross(bxc, _pb.m_normal, _pc.m_normal); float cxa[3]; bx::vec3Cross(cxa, _pc.m_normal, _pa.m_normal); float tmp0[3]; bx::vec3Mul(tmp0, bxc, _pa.m_dist); float tmp1[3]; bx::vec3Mul(tmp1, cxa, _pb.m_dist); float tmp2[3]; bx::vec3Mul(tmp2, axb, _pc.m_dist); float tmp[3]; bx::vec3Add(tmp, tmp0, tmp1); bx::vec3Add(tmp0, tmp, tmp2); float denom = bx::vec3Dot(_pa.m_normal, bxc); bx::vec3Mul(_result, tmp0, -1.0f/denom); } Ray makeRay(float _x, float _y, const float* _invVp) { Ray ray; const float near[3] = { _x, _y, 0.0f }; bx::vec3MulMtxH(ray.m_pos, near, _invVp); float tmp[3]; const float far[3] = { _x, _y, 1.0f }; bx::vec3MulMtxH(tmp, far, _invVp); float dir[3]; bx::vec3Sub(dir, tmp, ray.m_pos); bx::vec3Norm(ray.m_dir, dir); return ray; } inline void getPointAt(float* _result, const Ray& _ray, float _t) { float tmp[3]; bx::vec3Mul(tmp, _ray.m_dir, _t); bx::vec3Add(_result, _ray.m_pos, tmp); } bool intersect(const Ray& _ray, const Aabb& _aabb, Intersection* _intersection) { float invDir[3]; bx::vec3Rcp(invDir, _ray.m_dir); float tmp[3]; float t0[3]; bx::vec3Sub(tmp, _aabb.m_min, _ray.m_pos); bx::vec3Mul(t0, tmp, invDir); float t1[3]; bx::vec3Sub(tmp, _aabb.m_max, _ray.m_pos); bx::vec3Mul(t1, tmp, invDir); float min[3]; bx::vec3Min(min, t0, t1); float max[3]; bx::vec3Max(max, t0, t1); const float tmin = bx::fmax3(min[0], min[1], min[2]); const float tmax = bx::fmin3(max[0], max[1], max[2]); if (tmax < 0.0f || tmin > tmax) { return false; } if (NULL != _intersection) { _intersection->m_normal[0] = float( (min[0] == tmin) - (max[0] == tmin) ); _intersection->m_normal[1] = float( (min[1] == tmin) - (max[1] == tmin) ); _intersection->m_normal[2] = float( (min[2] == tmin) - (max[2] == tmin) ); _intersection->m_dist = tmin; getPointAt(_intersection->m_pos, _ray, tmin); } return true; } bool intersect(const Ray& _ray, const Disk& _disk, Intersection* _intersection) { Plane plane; bx::vec3Move(plane.m_normal, _disk.m_normal); plane.m_dist = -bx::vec3Dot(_disk.m_center, _disk.m_normal); Intersection tmpIntersection; _intersection = NULL != _intersection ? _intersection : &tmpIntersection; if (intersect(_ray, plane, _intersection) ) { float tmp[3]; bx::vec3Sub(tmp, _disk.m_center, _intersection->m_pos); return bx::vec3Dot(tmp, tmp) <= bx::fsq(_disk.m_radius); } return false; } bool intersect(const Ray& _ray, const Cylinder& _cylinder, bool _capsule, Intersection* _intersection) { float axis[3]; bx::vec3Sub(axis, _cylinder.m_end, _cylinder.m_pos); float rc[3]; bx::vec3Sub(rc, _ray.m_pos, _cylinder.m_pos); float normal[3]; bx::vec3Cross(normal, _ray.m_dir, axis); const float len = bx::vec3Norm(normal, normal); const float dist = bx::fabsolute(bx::vec3Dot(rc, normal) ); if (dist > _cylinder.m_radius) { return false; } float vo[3]; bx::vec3Cross(vo, rc, axis); const float t0 = -bx::vec3Dot(vo, normal) / len; bx::vec3Cross(vo, normal, axis); bx::vec3Norm(vo, vo); const float rsq = bx::fsq(_cylinder.m_radius); const float ddoto = bx::vec3Dot(_ray.m_dir, vo); const float ss = t0 - bx::fabsolute(bx::fsqrt(rsq - bx::fsq(dist) ) / ddoto); float point[3]; getPointAt(point, _ray, ss); const float axisLen = bx::vec3Norm(axis, axis); const float pdota = bx::vec3Dot(_cylinder.m_pos, axis); const float height = bx::vec3Dot(point, axis) - pdota; if (height > 0.0f && height < axisLen) { if (NULL != _intersection) { const float t1 = height / axisLen; float pointOnAxis[3]; bx::vec3Lerp(pointOnAxis, _cylinder.m_pos, _cylinder.m_end, t1); bx::vec3Move(_intersection->m_pos, point); float tmp[3]; bx::vec3Sub(tmp, point, pointOnAxis); bx::vec3Norm(_intersection->m_normal, tmp); _intersection->m_dist = ss; } return true; } if (_capsule) { const float rdota = bx::vec3Dot(_ray.m_pos, axis); const float pp = rdota - pdota; const float t1 = pp / axisLen; float pointOnAxis[3]; bx::vec3Lerp(pointOnAxis, _cylinder.m_pos, _cylinder.m_end, t1); float axisToRay[3]; bx::vec3Sub(axisToRay, _ray.m_pos, pointOnAxis); if (_cylinder.m_radius < bx::vec3Length(axisToRay) && 0.0f > ss) { return false; } Sphere sphere; sphere.m_radius = _cylinder.m_radius; bx::vec3Move(sphere.m_center, 0.0f >= height ? _cylinder.m_pos : _cylinder.m_end ); return intersect(_ray, sphere, _intersection); } Plane plane; float pos[3]; if (0.0f >= height) { bx::vec3Neg(plane.m_normal, axis); bx::vec3Move(pos, _cylinder.m_pos); } else { bx::vec3Move(plane.m_normal, axis); bx::vec3Move(pos, _cylinder.m_end); } plane.m_dist = -bx::vec3Dot(pos, plane.m_normal); Intersection tmpIntersection; _intersection = NULL != _intersection ? _intersection : &tmpIntersection; if (intersect(_ray, plane, _intersection) ) { float tmp[3]; bx::vec3Sub(tmp, pos, _intersection->m_pos); return bx::vec3Dot(tmp, tmp) <= rsq; } return false; } bool intersect(const Ray& _ray, const Plane& _plane, Intersection* _intersection) { float equation = bx::vec3Dot(_ray.m_pos, _plane.m_normal) + _plane.m_dist; if (0.0f > equation) { return false; } float ndotd = bx::vec3Dot(_ray.m_dir, _plane.m_normal); if (0.0f < ndotd) { return false; } if (NULL != _intersection) { bx::vec3Move(_intersection->m_normal, _plane.m_normal); float tt = -equation/ndotd; _intersection->m_dist = tt; getPointAt(_intersection->m_pos, _ray, tt); } return true; } bool intersect(const Ray& _ray, const Sphere& _sphere, Intersection* _intersection) { float rs[3]; bx::vec3Sub(rs, _ray.m_pos, _sphere.m_center); const float bb = bx::vec3Dot(rs, _ray.m_dir); if (0.0f < bb) { return false; } const float aa = bx::vec3Dot(_ray.m_dir, _ray.m_dir); const float cc = bx::vec3Dot(rs, rs) - bx::fsq(_sphere.m_radius); const float discriminant = bb*bb - aa*cc; if (0.0f >= discriminant) { return false; } const float sqrtDiscriminant = bx::fsqrt(discriminant); const float invA = 1.0f / aa; const float tt = -(bb + sqrtDiscriminant)*invA; if (0.0f >= tt) { return false; } if (NULL != _intersection) { _intersection->m_dist = tt; float point[3]; getPointAt(point, _ray, tt); bx::vec3Move(_intersection->m_pos, point); float tmp[3]; bx::vec3Sub(tmp, point, _sphere.m_center); bx::vec3Norm(_intersection->m_normal, tmp); } return true; } bool intersect(const Ray& _ray, const Tris& _triangle, Intersection* _intersection) { float edge10[3]; bx::vec3Sub(edge10, _triangle.m_v1, _triangle.m_v0); float edge02[3]; bx::vec3Sub(edge02, _triangle.m_v0, _triangle.m_v2); float normal[3]; bx::vec3Cross(normal, edge02, edge10); float vo[3]; bx::vec3Sub(vo, _triangle.m_v0, _ray.m_pos); float dxo[3]; bx::vec3Cross(dxo, _ray.m_dir, vo); const float det = bx::vec3Dot(normal, _ray.m_dir); if (det > 0.0f) { return false; } const float invDet = 1.0f/det; const float bz = bx::vec3Dot(dxo, edge02) * invDet; const float by = bx::vec3Dot(dxo, edge10) * invDet; const float bx = 1.0f - by - bz; if (bx < 0.0f || by < 0.0f || bz < 0.0f) { return false; } if (NULL != _intersection) { bx::vec3Norm(_intersection->m_normal, normal); const float tt = bx::vec3Dot(normal, vo) * invDet; _intersection->m_dist = tt; getPointAt(_intersection->m_pos, _ray, tt); } return true; }