godot/servers/physics/gjk_epa.cpp

/*************************************************************************/
/*  gjk_epa.cpp                                                          */
/*************************************************************************/
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/*                           GODOT ENGINE                                */
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/* Copyright (c) 2007-2018 Juan Linietsky, Ariel Manzur.                 */
/* Copyright (c) 2014-2018 Godot Engine contributors (cf. AUTHORS.md)    */
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#include "gjk_epa.h"

/*************** Bullet's GJK-EPA2 IMPLEMENTATION *******************/

/*
Bullet Continuous Collision Detection and Physics Library
Copyright (c) 2003-2008 Erwin Coumans  http://continuousphysics.com/Bullet/

This software is provided 'as-is', without any express or implied warranty.
In no event will the authors be held liable for any damages arising from the
use of this software.
Permission is granted to anyone to use this software for any purpose,
including commercial applications, and to alter it and redistribute it
freely,
subject to the following restrictions:

1. The origin of this software must not be misrepresented; you must not
claim that you wrote the original software. If you use this software in a
product, an acknowledgment in the product documentation would be appreciated
but is not required.
2. Altered source versions must be plainly marked as such, and must not be
misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
*/

/*
GJK-EPA collision solver by Nathanael Presson, 2008
*/

// Config

/* GJK	*/
#define GJK_MAX_ITERATIONS 128
#define GJK_ACCURARY ((real_t)0.0001)
#define GJK_MIN_DISTANCE ((real_t)0.0001)
#define GJK_DUPLICATED_EPS ((real_t)0.0001)
#define GJK_SIMPLEX2_EPS ((real_t)0.0)
#define GJK_SIMPLEX3_EPS ((real_t)0.0)
#define GJK_SIMPLEX4_EPS ((real_t)0.0)

/* EPA	*/
#define EPA_MAX_VERTICES 64
#define EPA_MAX_FACES (EPA_MAX_VERTICES * 2)
#define EPA_MAX_ITERATIONS 255
#define EPA_ACCURACY ((real_t)0.0001)
#define EPA_FALLBACK (10 * EPA_ACCURACY)
#define EPA_PLANE_EPS ((real_t)0.00001)
#define EPA_INSIDE_EPS ((real_t)0.01)

namespace GjkEpa2 {

struct sResults {
	enum eStatus {
		Separated, /* Shapes doesnt penetrate */
		Penetrating, /* Shapes are penetrating */
		GJK_Failed, /* GJK phase fail, no big issue, shapes are probably just 'touching'	*/
		EPA_Failed /* EPA phase fail, bigger problem, need to save parameters, and debug	*/
	} status;

	Vector3 witnesses[2];
	Vector3 normal;
	real_t distance;
};

// Shorthands
typedef unsigned int U;
typedef unsigned char U1;

// MinkowskiDiff
struct MinkowskiDiff {

	const ShapeSW *m_shapes[2];

	Transform transform_A;
	Transform transform_B;

	// i wonder how this could be sped up... if it can
	_FORCE_INLINE_ Vector3 Support0(const Vector3 &d) const {
		return transform_A.xform(m_shapes[0]->get_support(transform_A.basis.xform_inv(d).normalized()));
	}

	_FORCE_INLINE_ Vector3 Support1(const Vector3 &d) const {
		return transform_B.xform(m_shapes[1]->get_support(transform_B.basis.xform_inv(d).normalized()));
	}

	_FORCE_INLINE_ Vector3 Support(const Vector3 &d) const {
		return (Support0(d) - Support1(-d));
	}

	_FORCE_INLINE_ Vector3 Support(const Vector3 &d, U index) const {
		if (index)
			return (Support1(d));
		else
			return (Support0(d));
	}
};

typedef MinkowskiDiff tShape;

// GJK
struct GJK {
	/* Types		*/
	struct sSV {
		Vector3 d, w;
	};
	struct sSimplex {
		sSV *c[4];
		real_t p[4];
		U rank;
	};
	struct eStatus {
		enum _ {
			Valid,
			Inside,
			Failed
		};
	};
	/* Fields		*/
	tShape m_shape;
	Vector3 m_ray;
	real_t m_distance;
	sSimplex m_simplices[2];
	sSV m_store[4];
	sSV *m_free[4];
	U m_nfree;
	U m_current;
	sSimplex *m_simplex;
	eStatus::_ m_status;
	/* Methods		*/
	GJK() {
		Initialize();
	}
	void Initialize() {
		m_ray = Vector3(0, 0, 0);
		m_nfree = 0;
		m_status = eStatus::Failed;
		m_current = 0;
		m_distance = 0;
	}
	eStatus::_ Evaluate(const tShape &shapearg, const Vector3 &guess) {
		U iterations = 0;
		real_t sqdist = 0;
		real_t alpha = 0;
		Vector3 lastw[4];
		U clastw = 0;
		/* Initialize solver		*/
		m_free[0] = &m_store[0];
		m_free[1] = &m_store[1];
		m_free[2] = &m_store[2];
		m_free[3] = &m_store[3];
		m_nfree = 4;
		m_current = 0;
		m_status = eStatus::Valid;
		m_shape = shapearg;
		m_distance = 0;
		/* Initialize simplex		*/
		m_simplices[0].rank = 0;
		m_ray = guess;
		const real_t sqrl = m_ray.length_squared();
		appendvertice(m_simplices[0], sqrl > 0 ? -m_ray : Vector3(1, 0, 0));
		m_simplices[0].p[0] = 1;
		m_ray = m_simplices[0].c[0]->w;
		sqdist = sqrl;
		lastw[0] =
				lastw[1] =
						lastw[2] =
								lastw[3] = m_ray;
		/* Loop						*/
		do {
			const U next = 1 - m_current;
			sSimplex &cs = m_simplices[m_current];
			sSimplex &ns = m_simplices[next];
			/* Check zero							*/
			const real_t rl = m_ray.length();
			if (rl < GJK_MIN_DISTANCE) { /* Touching or inside				*/
				m_status = eStatus::Inside;
				break;
			}
			/* Append new vertice in -'v' direction	*/
			appendvertice(cs, -m_ray);
			const Vector3 &w = cs.c[cs.rank - 1]->w;
			bool found = false;
			for (U i = 0; i < 4; ++i) {
				if ((w - lastw[i]).length_squared() < GJK_DUPLICATED_EPS) {
					found = true;
					break;
				}
			}
			if (found) { /* Return old simplex				*/
				removevertice(m_simplices[m_current]);
				break;
			} else { /* Update lastw					*/
				lastw[clastw = (clastw + 1) & 3] = w;
			}
			/* Check for termination				*/
			const real_t omega = vec3_dot(m_ray, w) / rl;
			alpha = MAX(omega, alpha);
			if (((rl - alpha) - (GJK_ACCURARY * rl)) <= 0) { /* Return old simplex				*/
				removevertice(m_simplices[m_current]);
				break;
			}
			/* Reduce simplex						*/
			real_t weights[4];
			U mask = 0;
			switch (cs.rank) {
				case 2:
					sqdist = projectorigin(cs.c[0]->w,
							cs.c[1]->w,
							weights, mask);
					break;
				case 3:
					sqdist = projectorigin(cs.c[0]->w,
							cs.c[1]->w,
							cs.c[2]->w,
							weights, mask);
					break;
				case 4:
					sqdist = projectorigin(cs.c[0]->w,
							cs.c[1]->w,
							cs.c[2]->w,
							cs.c[3]->w,
							weights, mask);
					break;
			}
			if (sqdist >= 0) { /* Valid	*/
				ns.rank = 0;
				m_ray = Vector3(0, 0, 0);
				m_current = next;
				for (U i = 0, ni = cs.rank; i < ni; ++i) {
					if (mask & (1 << i)) {
						ns.c[ns.rank] = cs.c[i];
						ns.p[ns.rank++] = weights[i];
						m_ray += cs.c[i]->w * weights[i];
					} else {
						m_free[m_nfree++] = cs.c[i];
					}
				}
				if (mask == 15) m_status = eStatus::Inside;
			} else { /* Return old simplex				*/
				removevertice(m_simplices[m_current]);
				break;
			}
			m_status = ((++iterations) < GJK_MAX_ITERATIONS) ? m_status : eStatus::Failed;
		} while (m_status == eStatus::Valid);
		m_simplex = &m_simplices[m_current];
		switch (m_status) {
			case eStatus::Valid: m_distance = m_ray.length(); break;
			case eStatus::Inside: m_distance = 0; break;
			default: {}
		}
		return (m_status);
	}
	bool EncloseOrigin() {
		switch (m_simplex->rank) {
			case 1: {
				for (U i = 0; i < 3; ++i) {
					Vector3 axis = Vector3(0, 0, 0);
					axis[i] = 1;
					appendvertice(*m_simplex, axis);
					if (EncloseOrigin()) return (true);
					removevertice(*m_simplex);
					appendvertice(*m_simplex, -axis);
					if (EncloseOrigin()) return (true);
					removevertice(*m_simplex);
				}
			} break;
			case 2: {
				const Vector3 d = m_simplex->c[1]->w - m_simplex->c[0]->w;
				for (U i = 0; i < 3; ++i) {
					Vector3 axis = Vector3(0, 0, 0);
					axis[i] = 1;
					const Vector3 p = vec3_cross(d, axis);
					if (p.length_squared() > 0) {
						appendvertice(*m_simplex, p);
						if (EncloseOrigin()) return (true);
						removevertice(*m_simplex);
						appendvertice(*m_simplex, -p);
						if (EncloseOrigin()) return (true);
						removevertice(*m_simplex);
					}
				}
			} break;
			case 3: {
				const Vector3 n = vec3_cross(m_simplex->c[1]->w - m_simplex->c[0]->w,
						m_simplex->c[2]->w - m_simplex->c[0]->w);
				if (n.length_squared() > 0) {
					appendvertice(*m_simplex, n);
					if (EncloseOrigin()) return (true);
					removevertice(*m_simplex);
					appendvertice(*m_simplex, -n);
					if (EncloseOrigin()) return (true);
					removevertice(*m_simplex);
				}
			} break;
			case 4: {
				if (Math::abs(det(m_simplex->c[0]->w - m_simplex->c[3]->w,
							m_simplex->c[1]->w - m_simplex->c[3]->w,
							m_simplex->c[2]->w - m_simplex->c[3]->w)) > 0)
					return (true);
			} break;
		}
		return (false);
	}
	/* Internals	*/
	void getsupport(const Vector3 &d, sSV &sv) const {
		sv.d = d / d.length();
		sv.w = m_shape.Support(sv.d);
	}
	void removevertice(sSimplex &simplex) {
		m_free[m_nfree++] = simplex.c[--simplex.rank];
	}
	void appendvertice(sSimplex &simplex, const Vector3 &v) {
		simplex.p[simplex.rank] = 0;
		simplex.c[simplex.rank] = m_free[--m_nfree];
		getsupport(v, *simplex.c[simplex.rank++]);
	}
	static real_t det(const Vector3 &a, const Vector3 &b, const Vector3 &c) {
		return (a.y * b.z * c.x + a.z * b.x * c.y -
				a.x * b.z * c.y - a.y * b.x * c.z +
				a.x * b.y * c.z - a.z * b.y * c.x);
	}
	static real_t projectorigin(const Vector3 &a,
			const Vector3 &b,
			real_t *w, U &m) {
		const Vector3 d = b - a;
		const real_t l = d.length_squared();
		if (l > GJK_SIMPLEX2_EPS) {
			const real_t t(l > 0 ? -vec3_dot(a, d) / l : 0);
			if (t >= 1) {
				w[0] = 0;
				w[1] = 1;
				m = 2;
				return (b.length_squared());
			} else if (t <= 0) {
				w[0] = 1;
				w[1] = 0;
				m = 1;
				return (a.length_squared());
			} else {
				w[0] = 1 - (w[1] = t);
				m = 3;
				return ((a + d * t).length_squared());
			}
		}
		return (-1);
	}
	static real_t projectorigin(const Vector3 &a,
			const Vector3 &b,
			const Vector3 &c,
			real_t *w, U &m) {
		static const U imd3[] = { 1, 2, 0 };
		const Vector3 *vt[] = { &a, &b, &c };
		const Vector3 dl[] = { a - b, b - c, c - a };
		const Vector3 n = vec3_cross(dl[0], dl[1]);
		const real_t l = n.length_squared();
		if (l > GJK_SIMPLEX3_EPS) {
			real_t mindist = -1;
			real_t subw[2];
			U subm;
			for (U i = 0; i < 3; ++i) {
				if (vec3_dot(*vt[i], vec3_cross(dl[i], n)) > 0) {
					const U j = imd3[i];
					const real_t subd(projectorigin(*vt[i], *vt[j], subw, subm));
					if ((mindist < 0) || (subd < mindist)) {
						mindist = subd;
						m = static_cast<U>(((subm & 1) ? 1 << i : 0) + ((subm & 2) ? 1 << j : 0));
						w[i] = subw[0];
						w[j] = subw[1];
						w[imd3[j]] = 0;
					}
				}
			}
			if (mindist < 0) {
				const real_t d = vec3_dot(a, n);
				const real_t s = Math::sqrt(l);
				const Vector3 p = n * (d / l);
				mindist = p.length_squared();
				m = 7;
				w[0] = (vec3_cross(dl[1], b - p)).length() / s;
				w[1] = (vec3_cross(dl[2], c - p)).length() / s;
				w[2] = 1 - (w[0] + w[1]);
			}
			return (mindist);
		}
		return (-1);
	}
	static real_t projectorigin(const Vector3 &a,
			const Vector3 &b,
			const Vector3 &c,
			const Vector3 &d,
			real_t *w, U &m) {
		static const U imd3[] = { 1, 2, 0 };
		const Vector3 *vt[] = { &a, &b, &c, &d };
		const Vector3 dl[] = { a - d, b - d, c - d };
		const real_t vl = det(dl[0], dl[1], dl[2]);
		const bool ng = (vl * vec3_dot(a, vec3_cross(b - c, a - b))) <= 0;
		if (ng && (Math::abs(vl) > GJK_SIMPLEX4_EPS)) {
			real_t mindist = -1;
			real_t subw[3];
			U subm;
			for (U i = 0; i < 3; ++i) {
				const U j = imd3[i];
				const real_t s = vl * vec3_dot(d, vec3_cross(dl[i], dl[j]));
				if (s > 0) {
					const real_t subd = projectorigin(*vt[i], *vt[j], d, subw, subm);
					if ((mindist < 0) || (subd < mindist)) {
						mindist = subd;
						m = static_cast<U>((subm & 1 ? 1 << i : 0) +
										   (subm & 2 ? 1 << j : 0) +
										   (subm & 4 ? 8 : 0));
						w[i] = subw[0];
						w[j] = subw[1];
						w[imd3[j]] = 0;
						w[3] = subw[2];
					}
				}
			}
			if (mindist < 0) {
				mindist = 0;
				m = 15;
				w[0] = det(c, b, d) / vl;
				w[1] = det(a, c, d) / vl;
				w[2] = det(b, a, d) / vl;
				w[3] = 1 - (w[0] + w[1] + w[2]);
			}
			return (mindist);
		}
		return (-1);
	}
};

// EPA
struct EPA {
	/* Types		*/
	typedef GJK::sSV sSV;
	struct sFace {
		Vector3 n;
		real_t d;
		real_t p;
		sSV *c[3];
		sFace *f[3];
		sFace *l[2];
		U1 e[3];
		U1 pass;
	};
	struct sList {
		sFace *root;
		U count;
		sList() :
				root(0),
				count(0) {}
	};
	struct sHorizon {
		sFace *cf;
		sFace *ff;
		U nf;
		sHorizon() :
				cf(0),
				ff(0),
				nf(0) {}
	};
	struct eStatus {
		enum _ {
			Valid,
			Touching,
			Degenerated,
			NonConvex,
			InvalidHull,
			OutOfFaces,
			OutOfVertices,
			AccuraryReached,
			FallBack,
			Failed
		};
	};
	/* Fields		*/
	eStatus::_ m_status;
	GJK::sSimplex m_result;
	Vector3 m_normal;
	real_t m_depth;
	sSV m_sv_store[EPA_MAX_VERTICES];
	sFace m_fc_store[EPA_MAX_FACES];
	U m_nextsv;
	sList m_hull;
	sList m_stock;
	/* Methods		*/
	EPA() {
		Initialize();
	}

	static inline void bind(sFace *fa, U ea, sFace *fb, U eb) {
		fa->e[ea] = (U1)eb;
		fa->f[ea] = fb;
		fb->e[eb] = (U1)ea;
		fb->f[eb] = fa;
	}
	static inline void append(sList &list, sFace *face) {
		face->l[0] = 0;
		face->l[1] = list.root;
		if (list.root) list.root->l[0] = face;
		list.root = face;
		++list.count;
	}
	static inline void remove(sList &list, sFace *face) {
		if (face->l[1]) face->l[1]->l[0] = face->l[0];
		if (face->l[0]) face->l[0]->l[1] = face->l[1];
		if (face == list.root) list.root = face->l[1];
		--list.count;
	}

	void Initialize() {
		m_status = eStatus::Failed;
		m_normal = Vector3(0, 0, 0);
		m_depth = 0;
		m_nextsv = 0;
		for (U i = 0; i < EPA_MAX_FACES; ++i) {
			append(m_stock, &m_fc_store[EPA_MAX_FACES - i - 1]);
		}
	}
	eStatus::_ Evaluate(GJK &gjk, const Vector3 &guess) {
		GJK::sSimplex &simplex = *gjk.m_simplex;
		if ((simplex.rank > 1) && gjk.EncloseOrigin()) {

			/* Clean up				*/
			while (m_hull.root) {
				sFace *f = m_hull.root;
				remove(m_hull, f);
				append(m_stock, f);
			}
			m_status = eStatus::Valid;
			m_nextsv = 0;
			/* Orient simplex		*/
			if (gjk.det(simplex.c[0]->w - simplex.c[3]->w,
						simplex.c[1]->w - simplex.c[3]->w,
						simplex.c[2]->w - simplex.c[3]->w) < 0) {
				SWAP(simplex.c[0], simplex.c[1]);
				SWAP(simplex.p[0], simplex.p[1]);
			}
			/* Build initial hull	*/
			sFace *tetra[] = { newface(simplex.c[0], simplex.c[1], simplex.c[2], true),
				newface(simplex.c[1], simplex.c[0], simplex.c[3], true),
				newface(simplex.c[2], simplex.c[1], simplex.c[3], true),
				newface(simplex.c[0], simplex.c[2], simplex.c[3], true) };
			if (m_hull.count == 4) {
				sFace *best = findbest();
				sFace outer = *best;
				U pass = 0;
				U iterations = 0;
				bind(tetra[0], 0, tetra[1], 0);
				bind(tetra[0], 1, tetra[2], 0);
				bind(tetra[0], 2, tetra[3], 0);
				bind(tetra[1], 1, tetra[3], 2);
				bind(tetra[1], 2, tetra[2], 1);
				bind(tetra[2], 2, tetra[3], 1);
				m_status = eStatus::Valid;
				for (; iterations < EPA_MAX_ITERATIONS; ++iterations) {
					if (m_nextsv < EPA_MAX_VERTICES) {
						sHorizon horizon;
						sSV *w = &m_sv_store[m_nextsv++];
						bool valid = true;
						best->pass = (U1)(++pass);
						gjk.getsupport(best->n, *w);
						const real_t wdist = vec3_dot(best->n, w->w) - best->d;
						if (wdist > EPA_ACCURACY) {
							for (U j = 0; (j < 3) && valid; ++j) {
								valid &= expand(pass, w,
										best->f[j], best->e[j],
										horizon);
							}
							if (valid && (horizon.nf >= 3)) {
								bind(horizon.cf, 1, horizon.ff, 2);
								remove(m_hull, best);
								append(m_stock, best);
								best = findbest();
								if (best->p >= outer.p) outer = *best;
							} else {
								m_status = eStatus::InvalidHull;
								break;
							}
						} else {
							m_status = eStatus::AccuraryReached;
							break;
						}
					} else {
						m_status = eStatus::OutOfVertices;
						break;
					}
				}
				const Vector3 projection = outer.n * outer.d;
				m_normal = outer.n;
				m_depth = outer.d;
				m_result.rank = 3;
				m_result.c[0] = outer.c[0];
				m_result.c[1] = outer.c[1];
				m_result.c[2] = outer.c[2];
				m_result.p[0] = vec3_cross(outer.c[1]->w - projection,
						outer.c[2]->w - projection)
										.length();
				m_result.p[1] = vec3_cross(outer.c[2]->w - projection,
						outer.c[0]->w - projection)
										.length();
				m_result.p[2] = vec3_cross(outer.c[0]->w - projection,
						outer.c[1]->w - projection)
										.length();
				const real_t sum = m_result.p[0] + m_result.p[1] + m_result.p[2];
				m_result.p[0] /= sum;
				m_result.p[1] /= sum;
				m_result.p[2] /= sum;
				return (m_status);
			}
		}
		/* Fallback		*/
		m_status = eStatus::FallBack;
		m_normal = -guess;
		const real_t nl = m_normal.length();
		if (nl > 0)
			m_normal = m_normal / nl;
		else
			m_normal = Vector3(1, 0, 0);
		m_depth = 0;
		m_result.rank = 1;
		m_result.c[0] = simplex.c[0];
		m_result.p[0] = 1;
		return (m_status);
	}
	sFace *newface(sSV *a, sSV *b, sSV *c, bool forced) {
		if (m_stock.root) {
			sFace *face = m_stock.root;
			remove(m_stock, face);
			append(m_hull, face);
			face->pass = 0;
			face->c[0] = a;
			face->c[1] = b;
			face->c[2] = c;
			face->n = vec3_cross(b->w - a->w, c->w - a->w);
			const real_t l = face->n.length();
			const bool v = l > EPA_ACCURACY;
			face->p = MIN(MIN(
								  vec3_dot(a->w, vec3_cross(face->n, a->w - b->w)),
								  vec3_dot(b->w, vec3_cross(face->n, b->w - c->w))),
							  vec3_dot(c->w, vec3_cross(face->n, c->w - a->w))) /
					  (v ? l : 1);
			face->p = face->p >= -EPA_INSIDE_EPS ? 0 : face->p;
			if (v) {
				face->d = vec3_dot(a->w, face->n) / l;
				face->n /= l;
				if (forced || (face->d >= -EPA_PLANE_EPS)) {
					return (face);
				} else
					m_status = eStatus::NonConvex;
			} else
				m_status = eStatus::Degenerated;
			remove(m_hull, face);
			append(m_stock, face);
			return (0);
		}
		m_status = m_stock.root ? eStatus::OutOfVertices : eStatus::OutOfFaces;
		return (0);
	}
	sFace *findbest() {
		sFace *minf = m_hull.root;
		real_t mind = minf->d * minf->d;
		real_t maxp = minf->p;
		for (sFace *f = minf->l[1]; f; f = f->l[1]) {
			const real_t sqd = f->d * f->d;
			if ((f->p >= maxp) && (sqd < mind)) {
				minf = f;
				mind = sqd;
				maxp = f->p;
			}
		}
		return (minf);
	}
	bool expand(U pass, sSV *w, sFace *f, U e, sHorizon &horizon) {
		static const U i1m3[] = { 1, 2, 0 };
		static const U i2m3[] = { 2, 0, 1 };
		if (f->pass != pass) {
			const U e1 = i1m3[e];
			if ((vec3_dot(f->n, w->w) - f->d) < -EPA_PLANE_EPS) {
				sFace *nf = newface(f->c[e1], f->c[e], w, false);
				if (nf) {
					bind(nf, 0, f, e);
					if (horizon.cf)
						bind(horizon.cf, 1, nf, 2);
					else
						horizon.ff = nf;
					horizon.cf = nf;
					++horizon.nf;
					return (true);
				}
			} else {
				const U e2 = i2m3[e];
				f->pass = (U1)pass;
				if (expand(pass, w, f->f[e1], f->e[e1], horizon) &&
						expand(pass, w, f->f[e2], f->e[e2], horizon)) {
					remove(m_hull, f);
					append(m_stock, f);
					return (true);
				}
			}
		}
		return (false);
	}
};

//
static void Initialize(const ShapeSW *shape0, const Transform &wtrs0,
		const ShapeSW *shape1, const Transform &wtrs1,
		sResults &results,
		tShape &shape,
		bool withmargins) {
	/* Results		*/
	results.witnesses[0] =
			results.witnesses[1] = Vector3(0, 0, 0);
	results.status = sResults::Separated;
	/* Shape		*/
	shape.m_shapes[0] = shape0;
	shape.m_shapes[1] = shape1;
	shape.transform_A = wtrs0;
	shape.transform_B = wtrs1;
}

//
// Api
//

//

//
bool Distance(const ShapeSW *shape0,
		const Transform &wtrs0,
		const ShapeSW *shape1,
		const Transform &wtrs1,
		const Vector3 &guess,
		sResults &results) {
	tShape shape;
	Initialize(shape0, wtrs0, shape1, wtrs1, results, shape, false);
	GJK gjk;
	GJK::eStatus::_ gjk_status = gjk.Evaluate(shape, guess);
	if (gjk_status == GJK::eStatus::Valid) {
		Vector3 w0 = Vector3(0, 0, 0);
		Vector3 w1 = Vector3(0, 0, 0);
		for (U i = 0; i < gjk.m_simplex->rank; ++i) {
			const real_t p = gjk.m_simplex->p[i];
			w0 += shape.Support(gjk.m_simplex->c[i]->d, 0) * p;
			w1 += shape.Support(-gjk.m_simplex->c[i]->d, 1) * p;
		}
		results.witnesses[0] = w0;
		results.witnesses[1] = w1;
		results.normal = w0 - w1;
		results.distance = results.normal.length();
		results.normal /= results.distance > GJK_MIN_DISTANCE ? results.distance : 1;
		return (true);
	} else {
		results.status = gjk_status == GJK::eStatus::Inside ?
								 sResults::Penetrating :
								 sResults::GJK_Failed;
		return (false);
	}
}

//
bool Penetration(const ShapeSW *shape0,
		const Transform &wtrs0,
		const ShapeSW *shape1,
		const Transform &wtrs1,
		const Vector3 &guess,
		sResults &results) {
	tShape shape;
	Initialize(shape0, wtrs0, shape1, wtrs1, results, shape, false);
	GJK gjk;
	GJK::eStatus::_ gjk_status = gjk.Evaluate(shape, -guess);
	switch (gjk_status) {
		case GJK::eStatus::Inside: {
			EPA epa;
			EPA::eStatus::_ epa_status = epa.Evaluate(gjk, -guess);
			if (epa_status != EPA::eStatus::Failed) {
				Vector3 w0 = Vector3(0, 0, 0);
				for (U i = 0; i < epa.m_result.rank; ++i) {
					w0 += shape.Support(epa.m_result.c[i]->d, 0) * epa.m_result.p[i];
				}
				results.status = sResults::Penetrating;
				results.witnesses[0] = w0;
				results.witnesses[1] = w0 - epa.m_normal * epa.m_depth;
				results.normal = -epa.m_normal;
				results.distance = -epa.m_depth;
				return (true);
			} else
				results.status = sResults::EPA_Failed;
		} break;
		case GJK::eStatus::Failed:
			results.status = sResults::GJK_Failed;
			break;
		default: {}
	}
	return (false);
}

	/* Symbols cleanup		*/

#undef GJK_MAX_ITERATIONS
#undef GJK_ACCURARY
#undef GJK_MIN_DISTANCE
#undef GJK_DUPLICATED_EPS
#undef GJK_SIMPLEX2_EPS
#undef GJK_SIMPLEX3_EPS
#undef GJK_SIMPLEX4_EPS

#undef EPA_MAX_VERTICES
#undef EPA_MAX_FACES
#undef EPA_MAX_ITERATIONS
#undef EPA_ACCURACY
#undef EPA_FALLBACK
#undef EPA_PLANE_EPS
#undef EPA_INSIDE_EPS

} // namespace GjkEpa2

bool gjk_epa_calculate_distance(const ShapeSW *p_shape_A, const Transform &p_transform_A, const ShapeSW *p_shape_B, const Transform &p_transform_B, Vector3 &r_result_A, Vector3 &r_result_B) {

	GjkEpa2::sResults res;

	if (GjkEpa2::Distance(p_shape_A, p_transform_A, p_shape_B, p_transform_B, p_transform_B.origin - p_transform_A.origin, res)) {

		r_result_A = res.witnesses[0];
		r_result_B = res.witnesses[1];
		return true;
	}

	return false;
}

bool gjk_epa_calculate_penetration(const ShapeSW *p_shape_A, const Transform &p_transform_A, const ShapeSW *p_shape_B, const Transform &p_transform_B, CollisionSolverSW::CallbackResult p_result_callback, void *p_userdata, bool p_swap) {

	GjkEpa2::sResults res;

	if (GjkEpa2::Penetration(p_shape_A, p_transform_A, p_shape_B, p_transform_B, p_transform_B.origin - p_transform_A.origin, res)) {
		if (p_result_callback) {
			if (p_swap)
				p_result_callback(res.witnesses[1], res.witnesses[0], p_userdata);
			else
				p_result_callback(res.witnesses[0], res.witnesses[1], p_userdata);
		}
		return true;
	}

	return false;
}