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author | 2023-01-04 23:29:18 -0500 | |
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committer | 2023-01-04 23:29:18 -0500 | |
commit | 94b1e168b2b97b48b81f7a8f64406b0a6f64184e (patch) | |
tree | f57362a0fa01bfe8f0ad75a447c4c9e10bc15756 /3rdparty/bgfx/examples/common/bounds.cpp | |
parent | 5581eaa50a42256242f32569f59ce10d70ddd8c2 (diff) |
Revert "Update BGFX, BX and BIMG (#10750)" (#10787)
This reverts commit 5581eaa50a42256242f32569f59ce10d70ddd8c2 due to link failure on macOS.
Diffstat (limited to '3rdparty/bgfx/examples/common/bounds.cpp')
-rw-r--r-- | 3rdparty/bgfx/examples/common/bounds.cpp | 2104 |
1 files changed, 2104 insertions, 0 deletions
diff --git a/3rdparty/bgfx/examples/common/bounds.cpp b/3rdparty/bgfx/examples/common/bounds.cpp new file mode 100644 index 00000000000..7c92cb3da9f --- /dev/null +++ b/3rdparty/bgfx/examples/common/bounds.cpp @@ -0,0 +1,2104 @@ +/* + * Copyright 2011-2021 Branimir Karadzic. All rights reserved. + * License: https://github.com/bkaradzic/bgfx#license-bsd-2-clause + */ + +#include <bx/rng.h> +#include <bx/math.h> +#include "bounds.h" + +using namespace bx; + +Vec3 getCenter(const Aabb& _aabb) +{ + return mul(add(_aabb.min, _aabb.max), 0.5f); +} + +Vec3 getExtents(const Aabb& _aabb) +{ + return mul(sub(_aabb.max, _aabb.min), 0.5f); +} + +Vec3 getCenter(const Triangle& _triangle) +{ + return mul(add(add(_triangle.v0, _triangle.v1), _triangle.v2), 1.0f/3.0f); +} + +void toAabb(Aabb& _outAabb, const Vec3& _extents) +{ + _outAabb.min = neg(_extents); + _outAabb.max = _extents; +} + +void toAabb(Aabb& _outAabb, const Vec3& _center, const Vec3& _extents) +{ + _outAabb.min = sub(_center, _extents); + _outAabb.max = add(_center, _extents); +} + +void toAabb(Aabb& _outAabb, const Cylinder& _cylinder) +{ + // Reference(s): + // - https://web.archive.org/web/20181113055756/http://iquilezles.org/www/articles/diskbbox/diskbbox.htm + // + const Vec3 axis = sub(_cylinder.end, _cylinder.pos); + const Vec3 asq = mul(axis, axis); + const Vec3 nsq = mul(asq, 1.0f/dot(axis, axis) ); + const Vec3 tmp = sub(Vec3(1.0f), nsq); + + const float inv = 1.0f/(tmp.x*tmp.y*tmp.z); + + const Vec3 extent = + { + _cylinder.radius * tmp.x * bx::sqrt( (nsq.x + nsq.y * nsq.z) * inv), + _cylinder.radius * tmp.y * bx::sqrt( (nsq.y + nsq.z * nsq.x) * inv), + _cylinder.radius * tmp.z * bx::sqrt( (nsq.z + nsq.x * nsq.y) * inv), + }; + + const Vec3 minP = sub(_cylinder.pos, extent); + const Vec3 minE = sub(_cylinder.end, extent); + const Vec3 maxP = add(_cylinder.pos, extent); + const Vec3 maxE = add(_cylinder.end, extent); + + _outAabb.min = min(minP, minE); + _outAabb.max = max(maxP, maxE); +} + +void toAabb(Aabb& _outAabb, const Disk& _disk) +{ + // Reference(s): + // - https://web.archive.org/web/20181113055756/http://iquilezles.org/www/articles/diskbbox/diskbbox.htm + // + const Vec3 nsq = mul(_disk.normal, _disk.normal); + const Vec3 one = { 1.0f, 1.0f, 1.0f }; + const Vec3 tmp = sub(one, nsq); + const float inv = 1.0f / (tmp.x*tmp.y*tmp.z); + + const Vec3 extent = + { + _disk.radius * tmp.x * bx::sqrt( (nsq.x + nsq.y * nsq.z) * inv), + _disk.radius * tmp.y * bx::sqrt( (nsq.y + nsq.z * nsq.x) * inv), + _disk.radius * tmp.z * bx::sqrt( (nsq.z + nsq.x * nsq.y) * inv), + }; + + _outAabb.min = sub(_disk.center, extent); + _outAabb.max = add(_disk.center, extent); +} + +void toAabb(Aabb& _outAabb, const Obb& _obb) +{ + Vec3 xyz = { 1.0f, 1.0f, 1.0f }; + Vec3 tmp = mul(xyz, _obb.mtx); + + _outAabb.min = tmp; + _outAabb.max = tmp; + + for (uint32_t ii = 1; ii < 8; ++ii) + { + xyz.x = ii & 1 ? -1.0f : 1.0f; + xyz.y = ii & 2 ? -1.0f : 1.0f; + xyz.z = ii & 4 ? -1.0f : 1.0f; + tmp = mul(xyz, _obb.mtx); + + _outAabb.min = min(_outAabb.min, tmp); + _outAabb.max = max(_outAabb.max, tmp); + } +} + +void toAabb(Aabb& _outAabb, const Sphere& _sphere) +{ + const float radius = _sphere.radius; + _outAabb.min = sub(_sphere.center, radius); + _outAabb.max = add(_sphere.center, radius); +} + +void toAabb(Aabb& _outAabb, const Triangle& _triangle) +{ + _outAabb.min = min(_triangle.v0, _triangle.v1, _triangle.v2); + _outAabb.max = max(_triangle.v0, _triangle.v1, _triangle.v2); +} + +void aabbTransformToObb(Obb& _obb, const Aabb& _aabb, const float* _mtx) +{ + toObb(_obb, _aabb); + float result[16]; + mtxMul(result, _obb.mtx, _mtx); + memCopy(_obb.mtx, result, sizeof(result) ); +} + +void toAabb(Aabb& _outAabb, const void* _vertices, uint32_t _numVertices, uint32_t _stride) +{ + Vec3 mn(init::None); + Vec3 mx(init::None); + uint8_t* vertex = (uint8_t*)_vertices; + + mn = mx = load<Vec3>(vertex); + vertex += _stride; + + for (uint32_t ii = 1; ii < _numVertices; ++ii) + { + const Vec3 pos = load<Vec3>(vertex); + vertex += _stride; + + mn = min(pos, mn); + mx = max(pos, mx); + } + + _outAabb.min = mn; + _outAabb.max = mx; +} + +void toAabb(Aabb& _outAabb, const float* _mtx, const void* _vertices, uint32_t _numVertices, uint32_t _stride) +{ + Vec3 mn(init::None); + Vec3 mx(init::None); + uint8_t* vertex = (uint8_t*)_vertices; + mn = mx = mul(load<Vec3>(vertex), _mtx); + + vertex += _stride; + + for (uint32_t ii = 1; ii < _numVertices; ++ii) + { + Vec3 pos = mul(load<Vec3>(vertex), _mtx); + vertex += _stride; + + mn = min(pos, mn); + mx = max(pos, mx); + } + + _outAabb.min = mn; + _outAabb.max = mx; +} + +float calcAreaAabb(const Aabb& _aabb) +{ + const float ww = _aabb.max.x - _aabb.min.x; + const float hh = _aabb.max.y - _aabb.min.y; + const float dd = _aabb.max.z - _aabb.min.z; + return 2.0f * (ww*hh + ww*dd + hh*dd); +} + +void aabbExpand(Aabb& _outAabb, float _factor) +{ + _outAabb.min.x -= _factor; + _outAabb.min.y -= _factor; + _outAabb.min.z -= _factor; + _outAabb.max.x += _factor; + _outAabb.max.y += _factor; + _outAabb.max.z += _factor; +} + +void aabbExpand(Aabb& _outAabb, const Vec3& _pos) +{ + _outAabb.min = min(_outAabb.min, _pos); + _outAabb.max = max(_outAabb.max, _pos); +} + +void toObb(Obb& _outObb, const Aabb& _aabb) +{ + memSet(_outObb.mtx, 0, sizeof(_outObb.mtx) ); + _outObb.mtx[ 0] = (_aabb.max.x - _aabb.min.x) * 0.5f; + _outObb.mtx[ 5] = (_aabb.max.y - _aabb.min.y) * 0.5f; + _outObb.mtx[10] = (_aabb.max.z - _aabb.min.z) * 0.5f; + _outObb.mtx[12] = (_aabb.min.x + _aabb.max.x) * 0.5f; + _outObb.mtx[13] = (_aabb.min.y + _aabb.max.y) * 0.5f; + _outObb.mtx[14] = (_aabb.min.z + _aabb.max.z) * 0.5f; + _outObb.mtx[15] = 1.0f; +} + +void calcObb(Obb& _outObb, 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; + toObb(best, aabb); + + float angleStep = float(kPiHalf/_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) + { + mtxRotateXYZ(mtx, ax, ay, az); + + float mtxT[16]; + 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; + } + + memCopy(&_outObb, &best, sizeof(Obb) ); +} + +void calcMaxBoundingSphere(Sphere& _sphere, const void* _vertices, uint32_t _numVertices, uint32_t _stride) +{ + Aabb aabb; + toAabb(aabb, _vertices, _numVertices, _stride); + + Vec3 center = getCenter(aabb); + + float maxDistSq = 0.0f; + uint8_t* vertex = (uint8_t*)_vertices; + + for (uint32_t ii = 0; ii < _numVertices; ++ii) + { + const Vec3& pos = load<Vec3>(vertex); + vertex += _stride; + + const Vec3 tmp = sub(pos, center); + const float distSq = dot(tmp, tmp); + maxDistSq = max(distSq, maxDistSq); + } + + _sphere.center = center; + _sphere.radius = bx::sqrt(maxDistSq); +} + +void calcMinBoundingSphere(Sphere& _sphere, const void* _vertices, uint32_t _numVertices, uint32_t _stride, float _step) +{ + RngMwc rng; + + uint8_t* vertex = (uint8_t*)_vertices; + + Vec3 center(init::None); + float* position = (float*)&vertex[0]; + center.x = position[0]; + center.y = position[1]; + center.z = position[2]; + + position = (float*)&vertex[1*_stride]; + center.x += position[0]; + center.y += position[1]; + center.z += position[2]; + + center.x *= 0.5f; + center.y *= 0.5f; + center.z *= 0.5f; + + float xx = position[0] - center.x; + float yy = position[1] - center.y; + float zz = position[2] - center.z; + 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.x; + yy = position[1] - center.y; + zz = position[2] - center.z; + float distSq = xx*xx + yy*yy + zz*zz; + + if (distSq > maxDistSq) + { + done = false; + + center.x += xx * radiusStep; + center.y += yy * radiusStep; + center.z += zz * radiusStep; + maxDistSq = lerp(maxDistSq, distSq, _step); + + break; + } + } + + } while (!done); + + _sphere.center = center; + _sphere.radius = bx::sqrt(maxDistSq); +} + +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.normal.x = xw - xz; + near.normal.y = yw - yz; + near.normal.z = zw - zz; + near.dist = ww - wz; + + far.normal.x = xw + xz; + far.normal.y = yw + yz; + far.normal.z = zw + zz; + far.dist = ww + wz; + + const float xx = _viewProj[ 0]; + const float yx = _viewProj[ 4]; + const float zx = _viewProj[ 8]; + const float wx = _viewProj[12]; + + left.normal.x = xw - xx; + left.normal.y = yw - yx; + left.normal.z = zw - zx; + left.dist = ww - wx; + + right.normal.x = xw + xx; + right.normal.y = yw + yx; + right.normal.z = zw + zx; + right.dist = ww + wx; + + const float xy = _viewProj[ 1]; + const float yy = _viewProj[ 5]; + const float zy = _viewProj[ 9]; + const float wy = _viewProj[13]; + + top.normal.x = xw + xy; + top.normal.y = yw + yy; + top.normal.z = zw + zy; + top.dist = ww + wy; + + bottom.normal.x = xw - xy; + bottom.normal.y = yw - yy; + bottom.normal.z = zw - zy; + bottom.dist = ww - wy; + + Plane* plane = _result; + for (uint32_t ii = 0; ii < 6; ++ii) + { + const float invLen = 1.0f/length(plane->normal); + plane->normal = normalize(plane->normal); + plane->dist *= invLen; + ++plane; + } +} + +Ray makeRay(float _x, float _y, const float* _invVp) +{ + Ray ray; + + const Vec3 near = { _x, _y, 0.0f }; + ray.pos = mulH(near, _invVp); + + const Vec3 far = { _x, _y, 1.0f }; + Vec3 tmp = mulH(far, _invVp); + + const Vec3 dir = sub(tmp, ray.pos); + ray.dir = normalize(dir); + + return ray; +} + +inline Vec3 getPointAt(const Ray& _ray, float _t) +{ + return mad(_ray.dir, _t, _ray.pos); +} + +bool intersect(const Ray& _ray, const Aabb& _aabb, Hit* _hit) +{ + const Vec3 invDir = rcp(_ray.dir); + const Vec3 tmp0 = sub(_aabb.min, _ray.pos); + const Vec3 t0 = mul(tmp0, invDir); + const Vec3 tmp1 = sub(_aabb.max, _ray.pos); + const Vec3 t1 = mul(tmp1, invDir); + + const Vec3 mn = min(t0, t1); + const Vec3 mx = max(t0, t1); + + const float tmin = max(mn.x, mn.y, mn.z); + const float tmax = min(mx.x, mx.y, mx.z); + + if (0.0f > tmax + || tmin > tmax) + { + return false; + } + + if (NULL != _hit) + { + _hit->plane.normal.x = float( (t1.x == tmin) - (t0.x == tmin) ); + _hit->plane.normal.y = float( (t1.y == tmin) - (t0.y == tmin) ); + _hit->plane.normal.z = float( (t1.z == tmin) - (t0.z == tmin) ); + + _hit->plane.dist = tmin; + _hit->pos = getPointAt(_ray, tmin); + } + + return true; +} + +static constexpr Aabb kUnitAabb = +{ + { -1.0f, -1.0f, -1.0f }, + { 1.0f, 1.0f, 1.0f }, +}; + +bool intersect(const Ray& _ray, const Obb& _obb, Hit* _hit) +{ + Aabb aabb; + toAabb(aabb, _obb); + + if (!intersect(_ray, aabb) ) + { + return false; + } + + float mtxInv[16]; + mtxInverse(mtxInv, _obb.mtx); + + Ray obbRay; + obbRay.pos = mul(_ray.pos, mtxInv); + obbRay.dir = mulXyz0(_ray.dir, mtxInv); + + if (intersect(obbRay, kUnitAabb, _hit) ) + { + if (NULL != _hit) + { + _hit->pos = mul(_hit->pos, _obb.mtx); + + const Vec3 tmp = mulXyz0(_hit->plane.normal, _obb.mtx); + _hit->plane.normal = normalize(tmp); + } + + return true; + } + + return false; +} + +bool intersect(const Ray& _ray, const Disk& _disk, Hit* _hit) +{ + Plane plane(_disk.normal, -dot(_disk.center, _disk.normal) ); + + Hit tmpHit; + _hit = NULL != _hit ? _hit : &tmpHit; + + if (intersect(_ray, plane, _hit) ) + { + const Vec3 tmp = sub(_disk.center, _hit->pos); + return dot(tmp, tmp) <= square(_disk.radius); + } + + return false; +} + +static bool intersect(const Ray& _ray, const Cylinder& _cylinder, bool _capsule, Hit* _hit) +{ + Vec3 axis = sub(_cylinder.end, _cylinder.pos); + const Vec3 rc = sub(_ray.pos, _cylinder.pos); + const Vec3 dxa = cross(_ray.dir, axis); + + const float len = length(dxa); + const Vec3 normal = normalize(dxa); + const float dist = bx::abs(dot(rc, normal) ); + + if (dist > _cylinder.radius) + { + return false; + } + + Vec3 vo = cross(rc, axis); + const float t0 = -dot(vo, normal) / len; + + vo = normalize(cross(normal, axis) ); + + const float rsq = square(_cylinder.radius); + const float ddoto = dot(_ray.dir, vo); + const float ss = t0 - bx::abs(bx::sqrt(rsq - square(dist) ) / ddoto); + + if (0.0f > ss) + { + return false; + } + + const Vec3 point = getPointAt(_ray, ss); + + const float axisLen = length(axis); + axis = normalize(axis); + const float pdota = dot(_cylinder.pos, axis); + const float height = dot(point, axis) - pdota; + + if (0.0f < height + && axisLen > height) + { + if (NULL != _hit) + { + const float t1 = height / axisLen; + const Vec3 pointOnAxis = lerp(_cylinder.pos, _cylinder.end, t1); + + _hit->pos = point; + + const Vec3 tmp = sub(point, pointOnAxis); + _hit->plane.normal = normalize(tmp); + + _hit->plane.dist = ss; + } + + return true; + } + + if (_capsule) + { + const float rdota = dot(_ray.pos, axis); + const float pp = rdota - pdota; + const float t1 = pp / axisLen; + + const Vec3 pointOnAxis = lerp(_cylinder.pos, _cylinder.end, t1); + const Vec3 axisToRay = sub(_ray.pos, pointOnAxis); + + if (_cylinder.radius < length(axisToRay) + && 0.0f > ss) + { + return false; + } + + Sphere sphere; + sphere.radius = _cylinder.radius; + + sphere.center = 0.0f >= height + ? _cylinder.pos + : _cylinder.end + ; + + return intersect(_ray, sphere, _hit); + } + + Plane plane(init::None); + Vec3 pos(init::None); + + if (0.0f >= height) + { + plane.normal = neg(axis); + pos = _cylinder.pos; + } + else + { + plane.normal = axis; + pos = _cylinder.end; + } + + plane.dist = -dot(pos, plane.normal); + + Hit tmpHit; + _hit = NULL != _hit ? _hit : &tmpHit; + + if (intersect(_ray, plane, _hit) ) + { + const Vec3 tmp = sub(pos, _hit->pos); + return dot(tmp, tmp) <= rsq; + } + + return false; +} + +bool intersect(const Ray& _ray, const Cylinder& _cylinder, Hit* _hit) +{ + return intersect(_ray, _cylinder, false, _hit); +} + +bool intersect(const Ray& _ray, const Capsule& _capsule, Hit* _hit) +{ + BX_STATIC_ASSERT(sizeof(Capsule) == sizeof(Cylinder) ); + return intersect(_ray, *( (const Cylinder*)&_capsule), true, _hit); +} + +bool intersect(const Ray& _ray, const Cone& _cone, Hit* _hit) +{ + const Vec3 axis = sub(_cone.pos, _cone.end); + + const float len = length(axis); + const Vec3 normal = normalize(axis); + + Disk disk; + disk.center = _cone.pos; + disk.normal = normal; + disk.radius = _cone.radius; + + Hit tmpInt; + Hit* out = NULL != _hit ? _hit : &tmpInt; + bool hit = intersect(_ray, disk, out); + + const Vec3 ro = sub(_ray.pos, _cone.end); + + const float hyp = bx::sqrt(square(_cone.radius) + square(len) ); + const float cosaSq = square(len/hyp); + const float ndoto = dot(normal, ro); + const float ndotd = dot(normal, _ray.dir); + + const float aa = square(ndotd) - cosaSq; + const float bb = 2.0f * (ndotd*ndoto - dot(_ray.dir, ro)*cosaSq); + const float cc = square(ndoto) - dot(ro, ro)*cosaSq; + + float det = bb*bb - 4.0f*aa*cc; + + if (0.0f > det) + { + return hit; + } + + det = bx::sqrt(det); + const float invA2 = 1.0f / (2.0f*aa); + const float t1 = (-bb - det) * invA2; + const float t2 = (-bb + det) * invA2; + + float tt = t1; + if (0.0f > t1 + || (0.0f < t2 && t2 < t1) ) + { + tt = t2; + } + + if (0.0f > tt) + { + return hit; + } + + const Vec3 hitPos = getPointAt(_ray, tt); + const Vec3 point = sub(hitPos, _cone.end); + + const float hh = dot(normal, point); + + if (0.0f > hh + || len < hh) + { + return hit; + } + + if (NULL != _hit) + { + if (!hit + || tt < _hit->plane.dist) + { + _hit->plane.dist = tt; + _hit->pos = hitPos; + + const float scale = hh / dot(point, point); + const Vec3 pointScaled = mul(point, scale); + + const Vec3 tmp = sub(pointScaled, normal); + _hit->plane.normal = normalize(tmp); + } + } + + return true; +} + +bool intersect(const Ray& _ray, const Plane& _plane, Hit* _hit) +{ + const float dist = distance(_plane, _ray.pos); + if (0.0f > dist) + { + return false; + } + + const float ndotd = dot(_ray.dir, _plane.normal); + if (0.0f < ndotd) + { + return false; + } + + if (NULL != _hit) + { + _hit->plane.normal = _plane.normal; + + float tt = -dist/ndotd; + _hit->plane.dist = tt; + _hit->pos = getPointAt(_ray, tt); + } + + return true; +} + +bool intersect(const Ray& _ray, const Sphere& _sphere, Hit* _hit) +{ + const Vec3 rs = sub(_ray.pos, _sphere.center); + + const float bb = dot(rs, _ray.dir); + if (0.0f < bb) + { + return false; + } + + const float aa = dot(_ray.dir, _ray.dir); + const float cc = dot(rs, rs) - square(_sphere.radius); + + const float discriminant = bb*bb - aa*cc; + + if (0.0f >= discriminant) + { + return false; + } + + const float sqrtDiscriminant = bx::sqrt(discriminant); + const float invA = 1.0f / aa; + const float tt = -(bb + sqrtDiscriminant)*invA; + + if (0.0f >= tt) + { + return false; + } + + if (NULL != _hit) + { + _hit->plane.dist = tt; + + const Vec3 point = getPointAt(_ray, tt); + _hit->pos = point; + + const Vec3 tmp = sub(point, _sphere.center); + _hit->plane.normal = normalize(tmp); + } + + return true; +} + +bool intersect(const Ray& _ray, const Triangle& _triangle, Hit* _hit) +{ + const Vec3 edge10 = sub(_triangle.v1, _triangle.v0); + const Vec3 edge02 = sub(_triangle.v0, _triangle.v2); + const Vec3 normal = cross(edge02, edge10); + const Vec3 vo = sub(_triangle.v0, _ray.pos); + const Vec3 dxo = cross(_ray.dir, vo); + const float det = dot(normal, _ray.dir); + + if (0.0f < det) + { + return false; + } + + const float invDet = 1.0f/det; + const float bz = dot(dxo, edge02) * invDet; + const float by = dot(dxo, edge10) * invDet; + const float bx = 1.0f - by - bz; + + if (0.0f > bx + || 0.0f > by + || 0.0f > bz) + { + return false; + } + + if (NULL != _hit) + { + _hit->plane.normal = normalize(normal); + + const float tt = dot(normal, vo) * invDet; + _hit->plane.dist = tt; + _hit->pos = getPointAt(_ray, tt); + } + + return true; +} + +Vec3 barycentric(const Triangle& _triangle, const Vec3& _pos) +{ + const Vec3 v0 = sub(_triangle.v1, _triangle.v0); + const Vec3 v1 = sub(_triangle.v2, _triangle.v0); + const Vec3 v2 = sub(_pos, _triangle.v0); + + const float dot00 = dot(v0, v0); + const float dot01 = dot(v0, v1); + const float dot02 = dot(v0, v2); + const float dot11 = dot(v1, v1); + const float dot12 = dot(v1, v2); + + const float invDenom = 1.0f/(dot00*dot11 - square(dot01) ); + + const float vv = (dot11*dot02 - dot01*dot12)*invDenom; + const float ww = (dot00*dot12 - dot01*dot02)*invDenom; + const float uu = 1.0f - vv - ww; + + return { uu, vv, ww }; +} + +Vec3 cartesian(const Triangle& _triangle, const Vec3& _uvw) +{ + const Vec3 b0 = mul(_triangle.v0, _uvw.x); + const Vec3 b1 = mul(_triangle.v1, _uvw.y); + const Vec3 b2 = mul(_triangle.v2, _uvw.z); + + return add(add(b0, b1), b2); +} + +void calcPlane(Plane& _outPlane, const Disk& _disk) +{ + calcPlane(_outPlane, _disk.normal, _disk.center); +} + +void calcPlane(Plane& _outPlane, const Triangle& _triangle) +{ + calcPlane(_outPlane, _triangle.v0, _triangle.v1, _triangle.v2); +} + +struct Interval +{ + Interval(float _val) + : start(_val) + , end(_val) + { + } + + Interval(float _start, float _end) + : start(_start) + , end(_end) + { + } + + void set(float _val) + { + start = _val; + end = _val; + } + + void expand(float _val) + { + start = min(_val, start); + end = max(_val, end); + } + + float start; + float end; +}; + +bool overlap(const Interval& _a, const Interval& _b) +{ + return _a.end > _b.start + && _b.end > _a.start + ; +} + +float projectToAxis(const Vec3& _axis, const Vec3& _point) +{ + return dot(_axis, _point); +} + +Interval projectToAxis(const Vec3& _axis, const Vec3* _points, uint32_t _num) +{ + Interval interval(projectToAxis(_axis, _points[0]) ); + + for (uint32_t ii = 1; ii < _num; ++ii) + { + interval.expand(projectToAxis(_axis, _points[ii]) ); + } + + return interval; +} + +Interval projectToAxis(const Vec3& _axis, const Aabb& _aabb) +{ + const float extent = bx::abs(projectToAxis(abs(_axis), getExtents(_aabb) ) ); + const float center = projectToAxis( _axis , getCenter (_aabb) ); + return + { + center - extent, + center + extent, + }; +} + +Interval projectToAxis(const Vec3& _axis, const Triangle& _triangle) +{ + const float a0 = projectToAxis(_axis, _triangle.v0); + const float a1 = projectToAxis(_axis, _triangle.v1); + const float a2 = projectToAxis(_axis, _triangle.v2); + return + { + min(a0, a1, a2), + max(a0, a1, a2), + }; +} + +struct Srt +{ + Quaternion rotation = init::Identity; + Vec3 translation = init::Zero; + Vec3 scale = init::Zero; +}; + +Srt toSrt(const Aabb& _aabb) +{ + return { init::Identity, getCenter(_aabb), getExtents(_aabb) }; +} + +Srt toSrt(const void* _mtx) +{ + Srt result; + + const float* mtx = (const float*)_mtx; + + result.translation = { mtx[12], mtx[13], mtx[14] }; + + float xx = mtx[ 0]; + float xy = mtx[ 1]; + float xz = mtx[ 2]; + float yx = mtx[ 4]; + float yy = mtx[ 5]; + float yz = mtx[ 6]; + float zx = mtx[ 8]; + float zy = mtx[ 9]; + float zz = mtx[10]; + + result.scale = + { + bx::sqrt(xx*xx + xy*xy + xz*xz), + bx::sqrt(yx*yx + yy*yy + yz*yz), + bx::sqrt(zx*zx + zy*zy + zz*zz), + }; + + const Vec3 invScale = rcp(result.scale); + + xx *= invScale.x; + xy *= invScale.x; + xz *= invScale.x; + yx *= invScale.y; + yy *= invScale.y; + yz *= invScale.y; + zx *= invScale.z; + zy *= invScale.z; + zz *= invScale.z; + + const float trace = xx + yy + zz; + + if (0.0f < trace) + { + const float invS = 0.5f * rsqrt(trace + 1.0f); + result.rotation = + { + (yz - zy) * invS, + (zx - xz) * invS, + (xy - yx) * invS, + 0.25f / invS, + }; + } + else + { + if (xx > yy + && xx > zz) + { + const float invS = 0.5f * bx::sqrt(max(1.0f + xx - yy - zz, 1e-8f) ); + result.rotation = + { + 0.25f / invS, + (xy + yx) * invS, + (xz + zx) * invS, + (yz - zy) * invS, + }; + } + else if (yy > zz) + { + const float invS = 0.5f * bx::sqrt(max(1.0f + yy - xx - zz, 1e-8f) ); + result.rotation = + { + (xy + yx) * invS, + 0.25f / invS, + (yz + zy) * invS, + (zx - xz) * invS, + }; + } + else + { + const float invS = 0.5f * bx::sqrt(max(1.0f + zz - xx - yy, 1e-8f) ); + result.rotation = + { + (xz + zx) * invS, + (yz + zy) * invS, + 0.25f / invS, + (xy - yx) * invS, + }; + } + } + + return result; +} + +void mtxFromSrt(float* _outMtx, const Srt& _srt) +{ + mtxQuat(_outMtx, _srt.rotation); + + store<Vec3>(&_outMtx[0], mul(load<Vec3>(&_outMtx[0]), _srt.scale.x) ); + store<Vec3>(&_outMtx[4], mul(load<Vec3>(&_outMtx[4]), _srt.scale.y) ); + store<Vec3>(&_outMtx[8], mul(load<Vec3>(&_outMtx[8]), _srt.scale.z) ); + + store<Vec3>(&_outMtx[12], _srt.translation); +} + +bool isNearZero(float _v) +{ + return equal(_v, 0.0f, 0.00001f); +} + +bool isNearZero(const Vec3& _v) +{ + return isNearZero(dot(_v, _v) ); +} + +struct Line +{ + Vec3 pos = init::None; + Vec3 dir = init::None; +}; + +inline Vec3 getPointAt(const Line& _line, float _t) +{ + return mad(_line.dir, _t, _line.pos); +} + +bool intersect(Line& _outLine, const Plane& _planeA, const Plane& _planeB) +{ + const Vec3 axb = cross(_planeA.normal, _planeB.normal); + const float denom = dot(axb, axb); + + if (isNearZero(denom) ) + { + return false; + } + + const Vec3 bxaxb = cross(_planeB.normal, axb); + const Vec3 axbxa = cross(axb, _planeA.normal); + const Vec3 tmp0 = mul(bxaxb, _planeA.dist); + const Vec3 tmp1 = mul(axbxa, _planeB.dist); + const Vec3 tmp2 = add(tmp0, tmp1); + + _outLine.pos = mul(tmp2, -1.0f/denom); + _outLine.dir = normalize(axb); + + return true; +} + +Vec3 intersectPlanes(const Plane& _pa, const Plane& _pb, const Plane& _pc) +{ + const Vec3 axb = cross(_pa.normal, _pb.normal); + const Vec3 bxc = cross(_pb.normal, _pc.normal); + const Vec3 cxa = cross(_pc.normal, _pa.normal); + const Vec3 tmp0 = mul(bxc, _pa.dist); + const Vec3 tmp1 = mul(cxa, _pb.dist); + const Vec3 tmp2 = mul(axb, _pc.dist); + const Vec3 tmp3 = add(tmp0, tmp1); + const Vec3 tmp4 = add(tmp3, tmp2); + + const float denom = dot(_pa.normal, bxc); + const Vec3 result = mul(tmp4, -1.0f/denom); + + return result; +} + +struct LineSegment +{ + Vec3 pos; + Vec3 end; +}; + +inline Vec3 getPointAt(const LineSegment& _line, float _t) +{ + return lerp(_line.pos, _line.end, _t); +} + +bool intersect(float& _outTa, float& _outTb, const LineSegment& _a, const LineSegment& _b) +{ + // Reference(s): + // + // - The shortest line between two lines in 3D + // https://web.archive.org/web/20120309093234/http://paulbourke.net/geometry/lineline3d/ + + const Vec3 bd = sub(_b.end, _b.pos); + if (isNearZero(bd) ) + { + return false; + } + + const Vec3 ad = sub(_a.end, _a.pos); + if (isNearZero(ad) ) + { + return false; + } + + const Vec3 ab = sub(_a.pos, _b.pos); + + const float d0 = projectToAxis(ab, bd); + const float d1 = projectToAxis(ad, bd); + const float d2 = projectToAxis(ab, ad); + const float d3 = projectToAxis(bd, bd); + const float d4 = projectToAxis(ad, ad); + + const float denom = d4*d3 - square(d1); + + float ta = 0.0f; + + if (!isNearZero(denom) ) + { + ta = (d0*d1 - d2*d3)/denom; + } + + _outTa = ta; + _outTb = (d0+d1*ta)/d3; + + return true; +} + +bool intersect(const LineSegment& _a, const LineSegment& _b) +{ + float ta, tb; + if (!intersect(ta, tb, _a, _b) ) + { + return false; + } + + return 0.0f >= ta + && 1.0f <= ta + && 0.0f >= tb + && 1.0f <= tb + ; +} + +bool intersect(const LineSegment& _line, const Plane& _plane, Hit* _hit) +{ + const float dist = distance(_plane, _line.pos); + const float flip = sign(dist); + const Vec3 dir = normalize(sub(_line.end, _line.pos) ); + const float ndotd = dot(dir, _plane.normal); + const float tt = -dist/ndotd; + const float len = length(sub(_line.end, _line.pos) ); + + if (tt < 0.0f || tt > len) + { + return false; + } + + if (NULL != _hit) + { + _hit->pos = mad(dir, tt, _line.pos); + + _hit->plane.normal = mul(_plane.normal, flip); + _hit->plane.dist = -dot(_hit->plane.normal, _hit->pos); + } + + return true; +} + +float distance(const Plane& _plane, const LineSegment& _line) +{ + const float pd = distance(_plane, _line.pos); + const float ed = distance(_plane, _line.end); + return min(max(pd*ed, 0.0f), bx::abs(pd), bx::abs(ed) ); +} + +Vec3 closestPoint(const Line& _line, const Vec3& _point) +{ + const float tt = projectToAxis(_line.dir, sub(_point, _line.pos) ); + return getPointAt(_line, tt); +} + +Vec3 closestPoint(const LineSegment& _line, const Vec3& _point, float& _outT) +{ + const Vec3 axis = sub(_line.end, _line.pos); + const float lengthSq = dot(axis, axis); + const float tt = clamp(projectToAxis(axis, sub(_point, _line.pos) ) / lengthSq, 0.0f, 1.0f); + _outT = tt; + return mad(axis, tt, _line.pos); +} + +Vec3 closestPoint(const LineSegment& _line, const Vec3& _point) +{ + float ignored; + return closestPoint(_line, _point, ignored); +} + +Vec3 closestPoint(const Plane& _plane, const Vec3& _point) +{ + const float dist = distance(_plane, _point); + return sub(_point, mul(_plane.normal, dist) ); +} + +Vec3 closestPoint(const Aabb& _aabb, const Vec3& _point) +{ + return clamp(_point, _aabb.min, _aabb.max); +} + +Vec3 closestPoint(const Obb& _obb, const Vec3& _point) +{ + const Srt srt = toSrt(_obb.mtx); + + Aabb aabb; + toAabb(aabb, srt.scale); + + const Quaternion invRotation = invert(srt.rotation); + const Vec3 obbSpacePos = mul(sub(_point, srt.translation), srt.rotation); + const Vec3 pos = closestPoint(aabb, obbSpacePos); + + return add(mul(pos, invRotation), srt.translation); +} + +Vec3 closestPoint(const Triangle& _triangle, const Vec3& _point) +{ + Plane plane(init::None); + calcPlane(plane, _triangle); + + const Vec3 pos = closestPoint(plane, _point); + const Vec3 uvw = barycentric(_triangle, pos); + + return cartesian(_triangle, clamp<Vec3>(uvw, Vec3(0.0f), Vec3(1.0f) ) ); +} + +bool overlap(const Aabb& _aabb, const Vec3& _pos) +{ + const Vec3 ac = getCenter(_aabb); + const Vec3 ae = getExtents(_aabb); + const Vec3 abc = bx::abs(sub(ac, _pos) ); + + return abc.x <= ae.x + && abc.y <= ae.y + && abc.z <= ae.z + ; +} + +bool overlap(const Aabb& _aabbA, const Aabb& _aabbB) +{ + return true + && overlap(Interval{_aabbA.min.x, _aabbA.max.x}, Interval{_aabbB.min.x, _aabbB.max.x}) + && overlap(Interval{_aabbA.min.y, _aabbA.max.y}, Interval{_aabbB.min.y, _aabbB.max.y}) + && overlap(Interval{_aabbA.min.z, _aabbA.max.z}, Interval{_aabbB.min.z, _aabbB.max.z}) + ; +} + +bool overlap(const Aabb& _aabb, const Plane& _plane) +{ + const Vec3 center = getCenter(_aabb); + const float dist = distance(_plane, center); + + const Vec3 extents = getExtents(_aabb); + const Vec3 normal = bx::abs(_plane.normal); + const float radius = dot(extents, normal); + + return bx::abs(dist) <= radius; +} + +static constexpr Vec3 kAxis[] = +{ + { 1.0f, 0.0f, 0.0f }, + { 0.0f, 1.0f, 0.0f }, + { 0.0f, 0.0f, 1.0f }, +}; + +bool overlap(const Aabb& _aabb, const Triangle& _triangle) +{ + Aabb triAabb; + toAabb(triAabb, _triangle); + + if (!overlap(_aabb, triAabb) ) + { + return false; + } + + Plane plane(init::None); + calcPlane(plane, _triangle); + + if (!overlap(_aabb, plane) ) + { + return false; + } + + const Vec3 center = getCenter(_aabb); + const Vec3 v0 = sub(_triangle.v0, center); + const Vec3 v1 = sub(_triangle.v1, center); + const Vec3 v2 = sub(_triangle.v2, center); + + const Vec3 edge[] = + { + sub(v1, v0), + sub(v2, v1), + sub(v0, v2), + }; + + for (uint32_t ii = 0; ii < 3; ++ii) + { + for (uint32_t jj = 0; jj < 3; ++jj) + { + const Vec3 axis = cross(kAxis[ii], edge[jj]); + + const Interval aabbR = projectToAxis(axis, _aabb); + const Interval triR = projectToAxis(axis, _triangle); + + if (!overlap(aabbR, triR) ) + { + return false; + } + } + } + + return true; +} + +bool overlap(const Aabb& _aabb, const Capsule& _capsule) +{ + const Vec3 pos = closestPoint(LineSegment{_capsule.pos, _capsule.end}, getCenter(_aabb) ); + return overlap(_aabb, Sphere{pos, _capsule.radius}); +} + +bool overlap(const Aabb& _aabb, const Cone& _cone) +{ + float tt; + const Vec3 pos = closestPoint(LineSegment{_cone.pos, _cone.end}, getCenter(_aabb), tt); + return overlap(_aabb, Sphere{pos, lerp(_cone.radius, 0.0f, tt)}); +} + +bool overlap(const Aabb& _aabb, const Disk& _disk) +{ + if (!overlap(_aabb, Sphere{_disk.center, _disk.radius}) ) + { + return false; + } + + Plane plane(init::None); + calcPlane(plane, _disk.normal, _disk.center); + + return overlap(_aabb, plane); +} + +static void calcObbVertices( + bx::Vec3* _outVertices + , const bx::Vec3& _axisX + , const bx::Vec3& _axisY + , const bx::Vec3& _axisZ + , const bx::Vec3& _pos + , const bx::Vec3& _scale + ) +{ + const Vec3 ax = mul(_axisX, _scale.x); + const Vec3 ay = mul(_axisY, _scale.y); + const Vec3 az = mul(_axisZ, _scale.z); + + const Vec3 ppx = add(_pos, ax); + const Vec3 pmx = sub(_pos, ax); + const Vec3 ypz = add(ay, az); + const Vec3 ymz = sub(ay, az); + + _outVertices[0] = sub(pmx, ymz); + _outVertices[1] = sub(ppx, ymz); + _outVertices[2] = add(ppx, ymz); + _outVertices[3] = add(pmx, ymz); + _outVertices[4] = sub(pmx, ypz); + _outVertices[5] = sub(ppx, ypz); + _outVertices[6] = add(ppx, ypz); + _outVertices[7] = add(pmx, ypz); +} + +static bool overlaps(const Vec3& _axis, const Vec3* _vertsA, const Vec3* _vertsB) +{ + Interval ia = projectToAxis(_axis, _vertsA, 8); + Interval ib = projectToAxis(_axis, _vertsB, 8); + + return overlap(ia, ib); +} + +static bool overlap(const Srt& _srtA, const Srt& _srtB) +{ + const Vec3 ax = toXAxis(_srtA.rotation); + const Vec3 ay = toYAxis(_srtA.rotation); + const Vec3 az = toZAxis(_srtA.rotation); + + const Vec3 bx = toXAxis(_srtB.rotation); + const Vec3 by = toYAxis(_srtB.rotation); + const Vec3 bz = toZAxis(_srtB.rotation); + + Vec3 vertsA[8] = { init::None, init::None, init::None, init::None, init::None, init::None, init::None, init::None }; + calcObbVertices(vertsA, ax, ay, az, init::Zero, _srtA.scale); + + Vec3 vertsB[8] = { init::None, init::None, init::None, init::None, init::None, init::None, init::None, init::None }; + calcObbVertices(vertsB, bx, by, bz, sub(_srtB.translation, _srtA.translation), _srtB.scale); + + return overlaps(ax, vertsA, vertsB) + && overlaps(ay, vertsA, vertsB) + && overlaps(az, vertsA, vertsB) + && overlaps(bx, vertsA, vertsB) + && overlaps(by, vertsA, vertsB) + && overlaps(bz, vertsA, vertsB) + && overlaps(cross(ax, bx), vertsA, vertsB) + && overlaps(cross(ax, by), vertsA, vertsB) + && overlaps(cross(ax, bz), vertsA, vertsB) + && overlaps(cross(ay, bx), vertsA, vertsB) + && overlaps(cross(ay, by), vertsA, vertsB) + && overlaps(cross(ay, bz), vertsA, vertsB) + && overlaps(cross(az, bx), vertsA, vertsB) + && overlaps(cross(az, by), vertsA, vertsB) + && overlaps(cross(az, bz), vertsA, vertsB) + ; +} + +bool overlap(const Aabb& _aabb, const Obb& _obb) +{ + const Srt srtA = toSrt(_aabb); + const Srt srtB = toSrt(_obb.mtx); + + return overlap(srtA, srtB); +} + +bool overlap(const Capsule& _capsule, const Vec3& _pos) +{ + const Vec3 pos = closestPoint(LineSegment{_capsule.pos, _capsule.end}, _pos); + return overlap(Sphere{pos, _capsule.radius}, _pos); +} + +bool overlap(const Capsule& _capsule, const Plane& _plane) +{ + return distance(_plane, LineSegment{_capsule.pos, _capsule.end}) <= _capsule.radius; +} + +bool overlap(const Capsule& _capsuleA, const Capsule& _capsuleB) +{ + float ta, tb; + if (!intersect(ta, tb, {_capsuleA.pos, _capsuleA.end}, {_capsuleB.pos, _capsuleB.end}) ) + { + return false; + } + + if (0.0f <= ta + && 1.0f >= ta + && 0.0f <= tb + && 1.0f >= tb) + { + const Vec3 ad = sub(_capsuleA.end, _capsuleA.pos); + const Vec3 bd = sub(_capsuleB.end, _capsuleB.pos); + + return overlap( + Sphere{mad(ad, ta, _capsuleA.pos), _capsuleA.radius} + , Sphere{mad(bd, tb, _capsuleB.pos), _capsuleB.radius} + ); + } + + if (0.0f <= ta + && 1.0f >= ta) + { + return overlap(_capsuleA, Sphere{0.0f >= tb ? _capsuleB.pos : _capsuleB.end, _capsuleB.radius}); + } + + if (0.0f <= tb + && 1.0f >= tb) + { + return overlap(_capsuleB, Sphere{0.0f >= ta ? _capsuleA.pos : _capsuleA.end, _capsuleA.radius}); + } + + const Vec3 pa = 0.0f > ta ? _capsuleA.pos : _capsuleA.end; + const Vec3 pb = 0.0f > tb ? _capsuleB.pos : _capsuleB.end; + const Vec3 closestA = closestPoint(LineSegment{_capsuleA.pos, _capsuleA.end}, pb); + const Vec3 closestB = closestPoint(LineSegment{_capsuleB.pos, _capsuleB.end}, pa); + + if (dot(closestA, pb) <= dot(closestB, pa) ) + { + return overlap(_capsuleA, Sphere{closestB, _capsuleB.radius}); + } + + return overlap(_capsuleB, Sphere{closestA, _capsuleA.radius}); +} + +bool overlap(const Cone& _cone, const Vec3& _pos) +{ + float tt; + const Vec3 pos = closestPoint(LineSegment{_cone.pos, _cone.end}, _pos, tt); + return overlap(Disk{pos, normalize(sub(_cone.end, _cone.pos) ), lerp(_cone.radius, 0.0f, tt)}, _pos); +} + +bool overlap(const Cone& _cone, const Cylinder& _cylinder) +{ + BX_UNUSED(_cone, _cylinder); + return false; +} + +bool overlap(const Cone& _cone, const Capsule& _capsule) +{ + BX_UNUSED(_cone, _capsule); + return false; +} + +bool overlap(const Cone& _coneA, const Cone& _coneB) +{ + BX_UNUSED(_coneA, _coneB); + return false; +} + +bool overlap(const Cone& _cone, const Disk& _disk) +{ + BX_UNUSED(_cone, _disk); + return false; +} + +bool overlap(const Cone& _cone, const Obb& _obb) +{ + BX_UNUSED(_cone, _obb); + return false; +} + +bool overlap(const Cylinder& _cylinder, const Vec3& _pos) +{ + const Vec3 pos = closestPoint(LineSegment{_cylinder.pos, _cylinder.end}, _pos); + return overlap(Disk{pos, normalize(sub(_cylinder.end, _cylinder.pos) ), _cylinder.radius}, _pos); +} + +bool overlap(const Cylinder& _cylinder, const Sphere& _sphere) +{ + const Vec3 pos = closestPoint(LineSegment{_cylinder.pos, _cylinder.end}, _sphere.center); + return overlap(Disk{pos, normalize(sub(_cylinder.end, _cylinder.pos) ), _cylinder.radius}, _sphere); +} + +bool overlap(const Cylinder& _cylinder, const Aabb& _aabb) +{ + const Vec3 pos = closestPoint(LineSegment{_cylinder.pos, _cylinder.end}, getCenter(_aabb) ); + return overlap(Disk{pos, normalize(sub(_cylinder.end, _cylinder.pos) ), _cylinder.radius}, _aabb); +} + +bool overlap(const Cylinder& _cylinder, const Plane& _plane) +{ + BX_UNUSED(_cylinder, _plane); + return false; +} + +bool overlap(const Cylinder& _cylinderA, const Cylinder& _cylinderB) +{ + BX_UNUSED(_cylinderA, _cylinderB); + return false; +} + +bool overlap(const Cylinder& _cylinder, const Capsule& _capsule) +{ + BX_UNUSED(_cylinder, _capsule); + return false; +} + +bool overlap(const Cylinder& _cylinder, const Disk& _disk) +{ + BX_UNUSED(_cylinder, _disk); + return false; +} + +bool overlap(const Cylinder& _cylinder, const Obb& _obb) +{ + BX_UNUSED(_cylinder, _obb); + return false; +} + +bool overlap(const Disk& _disk, const Vec3& _pos) +{ + Plane plane(init::None); + calcPlane(plane, _disk.normal, _disk.center); + + if (!isNearZero(distance(plane, _pos) ) ) + { + return false; + } + + return distanceSq(_disk.center, _pos) <= square(_disk.radius); +} + +bool overlap(const Disk& _disk, const Plane& _plane) +{ + Plane plane(init::None); + calcPlane(plane, _disk.normal, _disk.center); + + if (!overlap(plane, _plane) ) + { + return false; + } + + return overlap(_plane, Sphere{_disk.center, _disk.radius}); +} + +bool overlap(const Disk& _disk, const Capsule& _capsule) +{ + if (!overlap(_capsule, Sphere{_disk.center, _disk.radius}) ) + { + return false; + } + + Plane plane(init::None); + calcPlane(plane, _disk.normal, _disk.center); + + return overlap(_capsule, plane); +} + +bool overlap(const Disk& _diskA, const Disk& _diskB) +{ + Plane planeA(init::None); + calcPlane(planeA, _diskA.normal, _diskA.center); + + Plane planeB(init::None); + calcPlane(planeB, _diskB); + + Line line; + + if (!intersect(line, planeA, planeB) ) + { + return false; + } + + const Vec3 pa = closestPoint(line, _diskA.center); + const Vec3 pb = closestPoint(line, _diskB.center); + + const float lenA = distance(pa, _diskA.center); + const float lenB = distance(pb, _diskB.center); + + return bx::sqrt(square(_diskA.radius) - square(lenA) ) + + bx::sqrt(square(_diskB.radius) - square(lenB) ) + >= distance(pa, pb) + ; +} + +bool overlap(const Disk& _disk, const Obb& _obb) +{ + if (!overlap(_obb, Sphere{_disk.center, _disk.radius}) ) + { + return false; + } + + Plane plane(init::None); + calcPlane(plane, _disk.normal, _disk.center); + + return overlap(_obb, plane); +} + +bool overlap(const Obb& _obb, const Vec3& _pos) +{ + const Srt srt = toSrt(_obb.mtx); + + Aabb aabb; + toAabb(aabb, srt.scale); + + const Quaternion invRotation = invert(srt.rotation); + const Vec3 pos = mul(sub(_pos, srt.translation), invRotation); + + return overlap(aabb, pos); +} + +bool overlap(const Obb& _obb, const Plane& _plane) +{ + const Srt srt = toSrt(_obb.mtx); + + const Quaternion invRotation = invert(srt.rotation); + const Vec3 axis = + { + projectToAxis(_plane.normal, mul(Vec3{1.0f, 0.0f, 0.0f}, invRotation) ), + projectToAxis(_plane.normal, mul(Vec3{0.0f, 1.0f, 0.0f}, invRotation) ), + projectToAxis(_plane.normal, mul(Vec3{0.0f, 0.0f, 1.0f}, invRotation) ), + }; + + const float dist = bx::abs(distance(_plane, srt.translation) ); + const float radius = dot(srt.scale, bx::abs(axis) ); + + return dist <= radius; +} + +bool overlap(const Obb& _obb, const Capsule& _capsule) +{ + const Srt srt = toSrt(_obb.mtx); + + Aabb aabb; + toAabb(aabb, srt.scale); + + const Quaternion invRotation = invert(srt.rotation); + + const Capsule capsule = + { + mul(sub(_capsule.pos, srt.translation), invRotation), + mul(sub(_capsule.end, srt.translation), invRotation), + _capsule.radius, + }; + + return overlap(aabb, capsule); +} + +bool overlap(const Obb& _obbA, const Obb& _obbB) +{ + const Srt srtA = toSrt(_obbA.mtx); + const Srt srtB = toSrt(_obbB.mtx); + + return overlap(srtA, srtB); +} + +bool overlap(const Plane& _plane, const LineSegment& _line) +{ + return isNearZero(distance(_plane, _line) ); +} + +bool overlap(const Plane& _plane, const Vec3& _pos) +{ + return isNearZero(distance(_plane, _pos) ); +} + +bool overlap(const Plane& _planeA, const Plane& _planeB) +{ + const Vec3 dir = cross(_planeA.normal, _planeB.normal); + const float len = length(dir); + + return !isNearZero(len); +} + +bool overlap(const Plane& _plane, const Cone& _cone) +{ + const Vec3 axis = sub(_cone.pos, _cone.end); + const float len = length(axis); + const Vec3 dir = normalize(axis); + + const Vec3 v1 = cross(_plane.normal, dir); + const Vec3 v2 = cross(v1, dir); + + const float bb = len; + const float aa = _cone.radius; + const float cc = bx::sqrt(square(aa) + square(bb) ); + + const Vec3 pos = add(add(_cone.end + , mul(dir, len * bb/cc) ) + , mul(v2, len * aa/cc) + ); + + return overlap(_plane, LineSegment{pos, _cone.end}); +} + +bool overlap(const Sphere& _sphere, const Vec3& _pos) +{ + const float distSq = distanceSq(_sphere.center, _pos); + const float radiusSq = square(_sphere.radius); + return distSq <= radiusSq; +} + +bool overlap(const Sphere& _sphereA, const Sphere& _sphereB) +{ + const float distSq = distanceSq(_sphereA.center, _sphereB.center); + const float radiusSq = square(_sphereA.radius + _sphereB.radius); + return distSq <= radiusSq; +} + +bool overlap(const Sphere& _sphere, const Aabb& _aabb) +{ + const Vec3 pos = closestPoint(_aabb, _sphere.center); + return overlap(_sphere, pos); +} + +bool overlap(const Sphere& _sphere, const Plane& _plane) +{ + return bx::abs(distance(_plane, _sphere.center) ) <= _sphere.radius; +} + +bool overlap(const Sphere& _sphere, const Triangle& _triangle) +{ + Plane plane(init::None); + calcPlane(plane, _triangle); + + if (!overlap(_sphere, plane) ) + { + return false; + } + + const Vec3 pos = closestPoint(plane, _sphere.center); + const Vec3 uvw = barycentric(_triangle, pos); + const float nr = -_sphere.radius; + + return uvw.x >= nr + && uvw.y >= nr + && uvw.z >= nr + ; +} + +bool overlap(const Sphere& _sphere, const Capsule& _capsule) +{ + const Vec3 pos = closestPoint(LineSegment{_capsule.pos, _capsule.end}, _sphere.center); + return overlap(_sphere, Sphere{pos, _capsule.radius}); +} + +bool overlap(const Sphere& _sphere, const Cone& _cone) +{ + float tt; + const Vec3 pos = closestPoint(LineSegment{_cone.pos, _cone.end}, _sphere.center, tt); + return overlap(_sphere, Sphere{pos, lerp(_cone.radius, 0.0f, tt)}); +} + +bool overlap(const Sphere& _sphere, const Disk& _disk) +{ + if (!overlap(_sphere, Sphere{_disk.center, _disk.radius}) ) + { + return false; + } + + Plane plane(init::None); + calcPlane(plane, _disk.normal, _disk.center); + + return overlap(_sphere, plane); +} + +bool overlap(const Sphere& _sphere, const Obb& _obb) +{ + const Vec3 pos = closestPoint(_obb, _sphere.center); + return overlap(_sphere, pos); +} + +bool overlap(const Triangle& _triangle, const Vec3& _pos) +{ + const Vec3 uvw = barycentric(_triangle, _pos); + + return uvw.x >= 0.0f + && uvw.y >= 0.0f + && uvw.z >= 0.0f + ; +} + +bool overlap(const Triangle& _triangle, const Plane& _plane) +{ + const float dist0 = distance(_plane, _triangle.v0); + const float dist1 = distance(_plane, _triangle.v1); + const float dist2 = distance(_plane, _triangle.v2); + + const float minDist = min(dist0, dist1, dist2); + const float maxDist = max(dist0, dist1, dist2); + + return 0.0f > minDist + && 0.0f < maxDist + ; +} + +inline bool overlap(const Triangle& _triangleA, const Triangle& _triangleB, const Vec3& _axis) +{ + const Interval ia = projectToAxis(_axis, _triangleA); + const Interval ib = projectToAxis(_axis, _triangleB); + return overlap(ia, ib); +} + +bool overlap(const Triangle& _triangleA, const Triangle& _triangleB) +{ + const Vec3 baA = sub(_triangleA.v1, _triangleA.v0); + const Vec3 cbA = sub(_triangleA.v2, _triangleA.v1); + const Vec3 acA = sub(_triangleA.v0, _triangleA.v2); + + const Vec3 baB = sub(_triangleB.v1, _triangleB.v0); + const Vec3 cbB = sub(_triangleB.v2, _triangleB.v1); + const Vec3 acB = sub(_triangleB.v0, _triangleB.v2); + + return overlap(_triangleA, _triangleB, cross(baA, cbA) ) + && overlap(_triangleA, _triangleB, cross(baB, cbB) ) + && overlap(_triangleA, _triangleB, cross(baB, baA) ) + && overlap(_triangleA, _triangleB, cross(baB, cbA) ) + && overlap(_triangleA, _triangleB, cross(baB, acA) ) + && overlap(_triangleA, _triangleB, cross(cbB, baA) ) + && overlap(_triangleA, _triangleB, cross(cbB, cbA) ) + && overlap(_triangleA, _triangleB, cross(cbB, acA) ) + && overlap(_triangleA, _triangleB, cross(acB, baA) ) + && overlap(_triangleA, _triangleB, cross(acB, cbA) ) + && overlap(_triangleA, _triangleB, cross(acB, acA) ) + ; +} + +template<typename Ty> +bool overlap(const Triangle& _triangle, const Ty& _ty) +{ + Plane plane(init::None); + calcPlane(plane, _triangle); + + plane.normal = neg(plane.normal); + plane.dist = -plane.dist; + + const LineSegment line = + { + _ty.pos, + _ty.end, + }; + + Hit hit; + if (intersect(line, plane, &hit) ) + { + return true; + } + + const Vec3 pos = closestPoint(plane, hit.pos); + const Vec3 uvw = barycentric(_triangle, pos); + + const float nr = -_ty.radius; + + if (uvw.x >= nr + && uvw.y >= nr + && uvw.z >= nr) + { + return true; + } + + const LineSegment ab = LineSegment{_triangle.v0, _triangle.v1}; + const LineSegment bc = LineSegment{_triangle.v1, _triangle.v2}; + const LineSegment ca = LineSegment{_triangle.v2, _triangle.v0}; + + float ta0 = 0.0f, tb0 = 0.0f; + const bool i0 = intersect(ta0, tb0, ab, line); + + float ta1, tb1; + const bool i1 = intersect(ta1, tb1, bc, line); + + float ta2, tb2; + const bool i2 = intersect(ta2, tb2, ca, line); + + if (!i0 + || !i1 + || !i2) + { + return false; + } + + ta0 = clamp(ta0, 0.0f, 1.0f); + ta1 = clamp(ta1, 0.0f, 1.0f); + ta2 = clamp(ta2, 0.0f, 1.0f); + tb0 = clamp(tb0, 0.0f, 1.0f); + tb1 = clamp(tb1, 0.0f, 1.0f); + tb2 = clamp(tb2, 0.0f, 1.0f); + + const Vec3 pa0 = getPointAt(ab, ta0); + const Vec3 pa1 = getPointAt(bc, ta1); + const Vec3 pa2 = getPointAt(ca, ta2); + + const Vec3 pb0 = getPointAt(line, tb0); + const Vec3 pb1 = getPointAt(line, tb1); + const Vec3 pb2 = getPointAt(line, tb2); + + const float d0 = distanceSq(pa0, pb0); + const float d1 = distanceSq(pa1, pb1); + const float d2 = distanceSq(pa2, pb2); + + if (d0 <= d1 + && d0 <= d2) + { + return overlap(_ty, pa0); + } + else if (d1 <= d2) + { + return overlap(_ty, pa1); + } + + return overlap(_ty, pa2); +} + +bool overlap(const Triangle& _triangle, const Cylinder& _cylinder) +{ + return overlap<Cylinder>(_triangle, _cylinder); +} + +bool overlap(const Triangle& _triangle, const Capsule& _capsule) +{ + return overlap<Capsule>(_triangle, _capsule); +} + +bool overlap(const Triangle& _triangle, const Cone& _cone) +{ + const LineSegment ab = LineSegment{_triangle.v0, _triangle.v1}; + const LineSegment bc = LineSegment{_triangle.v1, _triangle.v2}; + const LineSegment ca = LineSegment{_triangle.v2, _triangle.v0}; + + const LineSegment line = + { + _cone.pos, + _cone.end, + }; + + float ta0 = 0.0f, tb0 = 0.0f; + const bool i0 = intersect(ta0, tb0, ab, line); + + float ta1, tb1; + const bool i1 = intersect(ta1, tb1, bc, line); + + float ta2, tb2; + const bool i2 = intersect(ta2, tb2, ca, line); + + if (!i0 + || !i1 + || !i2) + { + return false; + } + + ta0 = clamp(ta0, 0.0f, 1.0f); + ta1 = clamp(ta1, 0.0f, 1.0f); + ta2 = clamp(ta2, 0.0f, 1.0f); + tb0 = clamp(tb0, 0.0f, 1.0f); + tb1 = clamp(tb1, 0.0f, 1.0f); + tb2 = clamp(tb2, 0.0f, 1.0f); + + const Vec3 pa0 = getPointAt(ab, ta0); + const Vec3 pa1 = getPointAt(bc, ta1); + const Vec3 pa2 = getPointAt(ca, ta2); + + const Vec3 pb0 = getPointAt(line, tb0); + const Vec3 pb1 = getPointAt(line, tb1); + const Vec3 pb2 = getPointAt(line, tb2); + + const float d0 = distanceSq(pa0, pb0); + const float d1 = distanceSq(pa1, pb1); + const float d2 = distanceSq(pa2, pb2); + + if (d0 <= d1 + && d0 <= d2) + { + return overlap(_cone, pa0); + } + else if (d1 <= d2) + { + return overlap(_cone, pa1); + } + + return overlap(_cone, pa2); +} + +bool overlap(const Triangle& _triangle, const Disk& _disk) +{ + if (!overlap(_triangle, Sphere{_disk.center, _disk.radius}) ) + { + return false; + } + + Plane plane(init::None); + calcPlane(plane, _disk.normal, _disk.center); + + return overlap(_triangle, plane); +} + +bool overlap(const Triangle& _triangle, const Obb& _obb) +{ + const Srt srt = toSrt(_obb.mtx); + + Aabb aabb; + toAabb(aabb, srt.scale); + + const Quaternion invRotation = invert(srt.rotation); + + const Triangle triangle = + { + mul(sub(_triangle.v0, srt.translation), invRotation), + mul(sub(_triangle.v1, srt.translation), invRotation), + mul(sub(_triangle.v2, srt.translation), invRotation), + }; + + return overlap(triangle, aabb); +} |