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author R. Belmont <rb6502@users.noreply.github.com>2023-01-04 23:29:18 -0500
committer GitHub <noreply@github.com>2023-01-04 23:29:18 -0500
commit94b1e168b2b97b48b81f7a8f64406b0a6f64184e (patch)
treef57362a0fa01bfe8f0ad75a447c4c9e10bc15756 /3rdparty/bgfx/examples/common/bounds.cpp
parent5581eaa50a42256242f32569f59ce10d70ddd8c2 (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.cpp2104
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);
+}