Moving bounds from bgfx to bx.

include/bx/bounds.h

@@ -0,0 +1,460 @@
+/*
+ * Copyright 2011-2021 Branimir Karadzic. All rights reserved.
+ * License: https://github.com/bkaradzic/bgfx#license-bsd-2-clause
+ */
+
+#ifndef BX_BOUNDS_H_HEADER_GUARD
+#define BX_BOUNDS_H_HEADER_GUARD
+
+#include <bx/math.h>
+
+namespace bx
+{
+	///
+	struct Aabb
+	{
+		Vec3 min = init::None;
+		Vec3 max = init::None;
+	};
+
+	///
+	struct Capsule
+	{
+		Vec3 pos = init::None;
+		Vec3 end = init::None;
+		float    radius;
+	};
+
+	///
+	struct Cone
+	{
+		Vec3 pos = init::None;
+		Vec3 end = init::None;
+		float    radius;
+	};
+
+	///
+	struct Cylinder
+	{
+		Vec3 pos = init::None;
+		Vec3 end = init::None;
+		float    radius;
+	};
+
+	///
+	struct Disk
+	{
+		Vec3 center = init::None;
+		Vec3 normal = init::None;
+		float    radius;
+	};
+
+	///
+	struct Obb
+	{
+		float mtx[16];
+	};
+
+	///
+	struct Sphere
+	{
+		Vec3 center = init::None;
+		float    radius;
+	};
+
+	///
+	struct Triangle
+	{
+		Vec3 v0 = init::None;
+		Vec3 v1 = init::None;
+		Vec3 v2 = init::None;
+	};
+
+	///
+	struct Ray
+	{
+		Vec3 pos = init::None;
+		Vec3 dir = init::None;
+	};
+
+	///
+	struct Hit
+	{
+		Vec3  pos   = init::None;
+		Plane plane = init::None;
+	};
+
+	///
+	Vec3 getPointAt(const Ray& _ray, float _t);
+
+	///
+	Vec3 getCenter(const Aabb& _aabb);
+
+	///
+	Vec3 getExtents(const Aabb& _aabb);
+
+	///
+	Vec3 getCenter(const Triangle& _triangle);
+
+	///
+	void toAabb(Aabb& _outAabb, const Vec3& _extents);
+
+	///
+	void toAabb(Aabb& _outAabb, const Vec3& _center, const Vec3& _extents);
+
+	/// Convert cylinder to axis aligned bounding box.
+	void toAabb(Aabb& _outAabb, const Cylinder& _cylinder);
+
+	/// Convert disk to axis aligned bounding box.
+	void toAabb(Aabb& _outAabb, const Disk& _disk);
+
+	/// Convert oriented bounding box to axis aligned bounding box.
+	void toAabb(Aabb& _outAabb, const Obb& _obb);
+
+	/// Convert sphere to axis aligned bounding box.
+	void toAabb(Aabb& _outAabb, const Sphere& _sphere);
+
+	/// Convert triangle to axis aligned bounding box.
+	void toAabb(Aabb& _outAabb, const Triangle& _triangle);
+
+	/// Calculate axis aligned bounding box.
+	void toAabb(Aabb& _outAabb, const void* _vertices, uint32_t _numVertices, uint32_t _stride);
+
+	/// Transform vertices and calculate axis aligned bounding box.
+	void toAabb(Aabb& _outAabb, const float* _mtx, const void* _vertices, uint32_t _numVertices, uint32_t _stride);
+
+	/// Expand AABB.
+	void aabbExpand(Aabb& _outAabb, float _factor);
+
+	/// Expand AABB with xyz.
+	void aabbExpand(Aabb& _outAabb, const Vec3& _pos);
+
+	/// Calculate surface area of axis aligned bounding box.
+	float calcAreaAabb(const Aabb& _aabb);
+
+	/// Convert axis aligned bounding box to oriented bounding box.
+	void toObb(Obb& _outObb, const Aabb& _aabb);
+
+	/// Calculate oriented bounding box.
+	void calcObb(Obb& _outObb, const void* _vertices, uint32_t _numVertices, uint32_t _stride, uint32_t _steps = 17);
+
+	/// Calculate maximum bounding sphere.
+	void calcMaxBoundingSphere(Sphere& _outSphere, const void* _vertices, uint32_t _numVertices, uint32_t _stride);
+
+	/// Calculate minimum bounding sphere.
+	void calcMinBoundingSphere(Sphere& _outSphere, const void* _vertices, uint32_t _numVertices, uint32_t _stride, float _step = 0.01f);
+
+	/// Returns 6 (near, far, left, right, top, bottom) planes representing frustum planes.
+	void buildFrustumPlanes(Plane* _outPlanes, const float* _viewProj);
+
+	/// Returns point from 3 intersecting planes.
+	Vec3 intersectPlanes(const Plane& _pa, const Plane& _pb, const Plane& _pc);
+
+	/// Make screen space ray from x, y coordinate and inverse view-projection matrix.
+	Ray makeRay(float _x, float _y, const float* _invVp);
+
+	/// Intersect ray / AABB.
+	bool intersect(const Ray& _ray, const Aabb& _aabb, Hit* _hit = NULL);
+
+	/// Intersect ray / OBB.
+	bool intersect(const Ray& _ray, const Obb& _obb, Hit* _hit = NULL);
+
+	/// Intersect ray / cylinder.
+	bool intersect(const Ray& _ray, const Cylinder& _cylinder, Hit* _hit = NULL);
+
+	/// Intersect ray / capsule.
+	bool intersect(const Ray& _ray, const Capsule& _capsule, Hit* _hit = NULL);
+
+	/// Intersect ray / cone.
+	bool intersect(const Ray& _ray, const Cone& _cone, Hit* _hit = NULL);
+
+	/// Intersect ray / disk.
+	bool intersect(const Ray& _ray, const Disk& _disk, Hit* _hit = NULL);
+
+	/// Intersect ray / plane.
+	bool intersect(const Ray& _ray, const Plane& _plane, Hit* _hit = NULL);
+
+	/// Intersect ray / plane.
+	bool intersect(const Ray& _ray, const Plane& _plane, bool _doublesided, Hit* _hit = NULL);
+
+	/// Intersect ray / sphere.
+	bool intersect(const Ray& _ray, const Sphere& _sphere, Hit* _hit = NULL);
+
+	/// Intersect ray / triangle.
+	bool intersect(const Ray& _ray, const Triangle& _triangle, Hit* _hit = NULL);
+
+	///
+	bool overlap(const Aabb& _aabb, const Vec3& _pos);
+
+	///
+	bool overlap(const Aabb& _aabb, const Sphere& _sphere);
+
+	///
+	bool overlap(const Aabb& _aabbA, const Aabb& _aabbB);
+
+	///
+	bool overlap(const Aabb& _aabb, const Plane& _plane);
+
+	///
+	bool overlap(const Aabb& _aabb, const Triangle& _triangle);
+
+	///
+	bool overlap(const Aabb& _aabb, const Cylinder& _cylinder);
+
+	///
+	bool overlap(const Aabb& _aabb, const Capsule& _capsule);
+
+	///
+	bool overlap(const Aabb& _aabb, const Cone& _cone);
+
+	///
+	bool overlap(const Aabb& _aabb, const Disk& _disk);
+
+	///
+	bool overlap(const Aabb& _aabb, const Obb& _obb);
+
+	///
+	bool overlap(const Capsule& _capsule, const Vec3& _pos);
+
+	///
+	bool overlap(const Capsule& _capsule, const Sphere& _sphere);
+
+	///
+	bool overlap(const Capsule& _capsule, const Aabb& _aabb);
+
+	///
+	bool overlap(const Capsule& _capsule, const Plane& _plane);
+
+	///
+	bool overlap(const Capsule& _capsule, const Triangle& _triangle);
+
+	///
+	bool overlap(const Capsule& _capsule, const Cylinder& _cylinder);
+
+	///
+	bool overlap(const Capsule& _capsuleA, const Capsule& _capsuleB);
+
+	///
+	bool overlap(const Capsule& _capsule, const Cone& _cone);
+
+	///
+	bool overlap(const Capsule& _capsule, const Disk& _disk);
+
+	///
+	bool overlap(const Capsule& _capsule, const Obb& _obb);
+
+	///
+	bool overlap(const Cone& _cone, const Vec3& _pos);
+
+	///
+	bool overlap(const Cone& _cone, const Sphere& _sphere);
+
+	///
+	bool overlap(const Cone& _cone, const Aabb& _aabb);
+
+	///
+	bool overlap(const Cone& _cone, const Plane& _plane);
+
+	///
+	bool overlap(const Cone& _cone, const Triangle& _triangle);
+
+	///
+	bool overlap(const Cone& _cone, const Cylinder& _cylinder);
+
+	///
+	bool overlap(const Cone& _cone, const Capsule& _capsule);
+
+	///
+	bool overlap(const Cone& _coneA, const Cone& _coneB);
+
+	///
+	bool overlap(const Cone& _cone, const Disk& _disk);
+
+	///
+	bool overlap(const Cone& _cone, const Obb& _obb);
+
+	///
+	bool overlap(const Cylinder& _cylinder, const Vec3& _pos);
+
+	///
+	bool overlap(const Cylinder& _cylinder, const Sphere& _sphere);
+
+	///
+	bool overlap(const Cylinder& _cylinder, const Aabb& _aabb);
+
+	///
+	bool overlap(const Cylinder& _cylinder, const Plane& _plane);
+
+	///
+	bool overlap(const Cylinder& _cylinder, const Triangle& _triangle);
+
+	///
+	bool overlap(const Cylinder& _cylinderA, const Cylinder& _cylinderB);
+
+	///
+	bool overlap(const Cylinder& _cylinder, const Capsule& _capsule);
+
+	///
+	bool overlap(const Cylinder& _cylinder, const Cone& _cone);
+
+	///
+	bool overlap(const Cylinder& _cylinder, const Disk& _disk);
+
+	///
+	bool overlap(const Cylinder& _cylinder, const Obb& _obb);
+
+	///
+	bool overlap(const Disk& _disk, const Vec3& _pos);
+
+	///
+	bool overlap(const Disk& _disk, const Sphere& _sphere);
+
+	///
+	bool overlap(const Disk& _disk, const Aabb& _aabb);
+
+	///
+	bool overlap(const Disk& _disk, const Plane& _plane);
+
+	///
+	bool overlap(const Disk& _disk, const Triangle& _triangle);
+
+	///
+	bool overlap(const Disk& _disk, const Cylinder& _cylinder);
+
+	///
+	bool overlap(const Disk& _disk, const Capsule& _capsule);
+
+	///
+	bool overlap(const Disk& _disk, const Cone& _cone);
+
+	///
+	bool overlap(const Disk& _diskA, const Disk& _diskB);
+
+	///
+	bool overlap(const Disk& _disk, const Obb& _obb);
+
+	///
+	bool overlap(const Obb& _obb, const Vec3& _pos);
+
+	///
+	bool overlap(const Obb& _obb, const Sphere& _sphere);
+
+	///
+	bool overlap(const Obb& _obb, const Aabb& _aabb);
+
+	///
+	bool overlap(const Obb& _obb, const Plane& _plane);
+
+	///
+	bool overlap(const Obb& _obb, const Triangle& _triangle);
+
+	///
+	bool overlap(const Obb& _obb, const Cylinder& _cylinder);
+
+	///
+	bool overlap(const Obb& _obb, const Capsule& _capsule);
+
+	///
+	bool overlap(const Obb& _obb, const Cone& _cone);
+
+	///
+	bool overlap(const Obb& _obb, const Disk& _disk);
+
+	///
+	bool overlap(const Obb& _obbA, const Obb& _obbB);
+
+	///
+	bool overlap(const Plane& _plane, const Vec3& _pos);
+
+	///
+	bool overlap(const Plane& _plane, const Sphere& _sphere);
+
+	///
+	bool overlap(const Plane& _plane, const Aabb& _aabb);
+
+	///
+	bool overlap(const Plane& _planeA, const Plane& _planeB);
+
+	///
+	bool overlap(const Plane& _plane, const Triangle& _triangle);
+
+	///
+	bool overlap(const Plane& _plane, const Cylinder& _cylinder);
+
+	///
+	bool overlap(const Plane& _plane, const Capsule& _capsule);
+
+	///
+	bool overlap(const Plane& _plane, const Cone& _cone);
+
+	///
+	bool overlap(const Plane& _plane, const Disk& _disk);
+
+	///
+	bool overlap(const Plane& _plane, const Obb& _obb);
+
+	///
+	bool overlap(const Sphere& _sphere, const Vec3& _pos);
+
+	///
+	bool overlap(const Sphere& _sphereA, const Sphere& _sphereB);
+
+	///
+	bool overlap(const Sphere& _sphere, const Aabb& _aabb);
+
+	///
+	bool overlap(const Sphere& _sphere, const Plane& _plane);
+
+	///
+	bool overlap(const Sphere& _sphere, const Triangle& _triangle);
+
+	///
+	bool overlap(const Sphere& _sphere, const Cylinder& _cylinder);
+
+	///
+	bool overlap(const Sphere& _sphere, const Capsule& _capsule);
+
+	///
+	bool overlap(const Sphere& _sphere, const Cone& _cone);
+
+	///
+	bool overlap(const Sphere& _sphere, const Disk& _disk);
+
+	///
+	bool overlap(const Sphere& _sphere, const Obb& _obb);
+
+	///
+	bool overlap(const Triangle& _triangle, const Vec3& _pos);
+
+	///
+	bool overlap(const Triangle& _triangle, const Sphere& _sphere);
+
+	///
+	bool overlap(const Triangle& _triangle, const Aabb& _aabb);
+
+	///
+	bool overlap(const Triangle& _triangle, const Plane& _plane);
+
+	///
+	bool overlap(const Triangle& _triangleA, const Triangle& _triangleB);
+
+	///
+	bool overlap(const Triangle& _triangle, const Cylinder& _cylinder);
+
+	///
+	bool overlap(const Triangle& _triangle, const Capsule& _capsule);
+
+	///
+	bool overlap(const Triangle& _triangle, const Cone& _cone);
+
+	///
+	bool overlap(const Triangle& _triangle, const Disk& _disk);
+
+	///
+	bool overlap(const Triangle& _triangle, const Obb& _obb);
+
+} // namespace bx
+
+#include "inline/bounds.inl"
+
+#endif // BX_BOUNDS_H_HEADER_GUARD

include/bx/inline/bounds.inl

@@ -0,0 +1,202 @@
+/*
+ * Copyright 2011-2021 Branimir Karadzic. All rights reserved.
+ * License: https://github.com/bkaradzic/bgfx#license-bsd-2-clause
+ */
+
+#ifndef BX_BOUNDS_H_HEADER_GUARD
+#	error "Must be included from bounds.h!"
+#endif // BX_BOUNDS_H_HEADER_GUARD
+
+namespace bx
+{
+	inline Vec3 getPointAt(const Ray& _ray, float _t)
+	{
+		return mad(_ray.dir, _t, _ray.pos);
+	}
+
+	inline bool intersect(const Ray& _ray, const Plane& _plane, Hit* _hit)
+	{
+		return intersect(_ray, _plane, false, _hit);
+	}
+
+	inline bool overlap(const Aabb& _aabb, const Sphere& _sphere)
+	{
+		return overlap(_sphere, _aabb);
+	}
+
+	inline bool overlap(const Aabb& _aabb, const Cylinder& _cylinder)
+	{
+		return overlap(_cylinder, _aabb);
+	}
+
+	inline bool overlap(const Capsule& _capsule, const Sphere& _sphere)
+	{
+		return overlap(_sphere, _capsule);
+	}
+
+	inline bool overlap(const Capsule& _capsule, const Aabb& _aabb)
+	{
+		return overlap(_aabb, _capsule);
+	}
+
+	inline bool overlap(const Capsule& _capsule, const Triangle& _triangle)
+	{
+		return overlap(_triangle, _capsule);
+	}
+
+	inline bool overlap(const Capsule& _capsule, const Cone& _cone)
+	{
+		return overlap(_cone, _capsule);
+	}
+
+	inline bool overlap(const Capsule& _capsule, const Cylinder& _cylinder)
+	{
+		return overlap(_cylinder, _capsule);
+	}
+
+	inline bool overlap(const Capsule& _capsule, const Disk& _disk)
+	{
+		return overlap(_disk, _capsule);
+	}
+
+	inline bool overlap(const Capsule& _capsule, const Obb& _obb)
+	{
+		return overlap(_obb, _capsule);
+	}
+
+	inline bool overlap(const Cone& _cone, const Sphere& _sphere)
+	{
+		return overlap(_sphere, _cone);
+	}
+
+	inline bool overlap(const Cone& _cone, const Aabb& _aabb)
+	{
+		return overlap(_aabb, _cone);
+	}
+
+	inline bool overlap(const Cone& _cone, const Plane& _plane)
+	{
+		return overlap(_plane, _cone);
+	}
+
+	inline bool overlap(const Cone& _cone, const Triangle& _triangle)
+	{
+		return overlap(_triangle, _cone);
+	}
+
+	inline bool overlap(const Cylinder& _cylinder, const Triangle& _triangle)
+	{
+		return overlap(_triangle, _cylinder);
+	}
+
+	inline bool overlap(const Cylinder& _cylinder, const Cone& _cone)
+	{
+		return overlap(_cone, _cylinder);
+	}
+
+	inline bool overlap(const Disk& _disk, const Sphere& _sphere)
+	{
+		return overlap(_sphere, _disk);
+	}
+
+	inline bool overlap(const Disk& _disk, const Aabb& _aabb)
+	{
+		return overlap(_aabb, _disk);
+	}
+
+	inline bool overlap(const Disk& _disk, const Triangle& _triangle)
+	{
+		return overlap(_triangle, _disk);
+	}
+
+	inline bool overlap(const Disk& _disk, const Cylinder& _cylinder)
+	{
+		return overlap(_cylinder, _disk);
+	}
+
+	inline bool overlap(const Disk& _disk, const Cone& _cone)
+	{
+		return overlap(_cone, _disk);
+	}
+
+	inline bool overlap(const Obb& _obb, const Sphere& _sphere)
+	{
+		return overlap(_sphere, _obb);
+	}
+
+	inline bool overlap(const Obb& _obb, const Aabb& _aabb)
+	{
+		return overlap(_aabb, _obb);
+	}
+
+	inline bool overlap(const Obb& _obb, const Triangle& _triangle)
+	{
+		return overlap(_triangle, _obb);
+	}
+
+	inline bool overlap(const Obb& _obb, const Cylinder& _cylinder)
+	{
+		return overlap(_cylinder, _obb);
+	}
+
+	inline bool overlap(const Obb& _obb, const Cone& _cone)
+	{
+		return overlap(_cone, _obb);
+	}
+
+	inline bool overlap(const Obb& _obb, const Disk& _disk)
+	{
+		return overlap(_disk, _obb);
+	}
+
+	inline bool overlap(const Plane& _plane, const Sphere& _sphere)
+	{
+		return overlap(_sphere, _plane);
+	}
+
+	inline bool overlap(const Plane& _plane, const Aabb& _aabb)
+	{
+		return overlap(_aabb, _plane);
+	}
+
+	inline bool overlap(const Plane& _plane, const Triangle& _triangle)
+	{
+		return overlap(_triangle, _plane);
+	}
+
+	inline bool overlap(const Plane& _plane, const Cylinder& _cylinder)
+	{
+		return overlap(_cylinder, _plane);
+	}
+
+	inline bool overlap(const Plane& _plane, const Capsule& _capsule)
+	{
+		return overlap(_capsule, _plane);
+	}
+
+	inline bool overlap(const Plane& _plane, const Disk& _disk)
+	{
+		return overlap(_disk, _plane);
+	}
+
+	inline bool overlap(const Plane& _plane, const Obb& _obb)
+	{
+		return overlap(_obb, _plane);
+	}
+
+	inline bool overlap(const Sphere& _sphere, const Cylinder& _cylinder)
+	{
+		return overlap(_cylinder, _sphere);
+	}
+
+	inline bool overlap(const Triangle& _triangle, const Sphere& _sphere)
+	{
+		return overlap(_sphere, _triangle);
+	}
+
+	inline bool overlap(const Triangle& _triangle, const Aabb& _aabb)
+	{
+		return overlap(_aabb, _triangle);
+	}
+
+} // namespace bx

src/bounds.cpp

@@ -0,0 +1,2099 @@
+/*
+ * Copyright 2011-2021 Branimir Karadzic. All rights reserved.
+ * License: https://github.com/bkaradzic/bgfx#license-bsd-2-clause
+ */
+
+#include "bx_p.h"
+#include <bx/rng.h>
+#include <bx/math.h>
+#include <bx/bounds.h>
+
+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 * sqrt( (nsq.x + nsq.y * nsq.z) * inv),
+			_cylinder.radius * tmp.y * sqrt( (nsq.y + nsq.z * nsq.x) * inv),
+			_cylinder.radius * tmp.z * 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 * sqrt( (nsq.x + nsq.y * nsq.z) * inv),
+			_disk.radius * tmp.y * sqrt( (nsq.y + nsq.z * nsq.x) * inv),
+			_disk.radius * tmp.z * 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 = 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 = 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;
+	}
+
+	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   = 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 - abs(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    = 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 = 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, bool _doublesided, Hit* _hit)
+	{
+		const float dist  = distance(_plane, _ray.pos);
+		const float ndotd = dot(_ray.dir, _plane.normal);
+
+		if (!_doublesided
+		&& (0.0f > dist || 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 = 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 = 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 =
+		{
+			sqrt(xx*xx + xy*xy + xz*xz),
+			sqrt(yx*yx + yy*yy + yz*yz),
+			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 * 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 * 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 * 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)
+	{
+		mtxFromQuaternion(_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 isEqual(_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), abs(pd), 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 = 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  = abs(_plane.normal);
+		const float radius = dot(extents, normal);
+
+		return 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(
+		Vec3* _outVertices
+		, const Vec3& _axisX
+		, const Vec3& _axisY
+		, const Vec3& _axisZ
+		, const Vec3& _pos
+		, const 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 sqrt(square(_diskA.radius) - square(lenA) )
+			+  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   = abs(distance(_plane, srt.translation) );
+		const float radius = dot(srt.scale, 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 = 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 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);
+	}
+
+} // namespace bx