godot/servers/physics/gjk_epa.cpp

/*************************************************************************/
/*  gjk_epa.cpp                                                          */
/*************************************************************************/
/*                       This file is part of:                           */
/*                           GODOT ENGINE                                */
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/* Copyright (c) 2007-2017 Juan Linietsky, Ariel Manzur.                 */
/* Copyright (c) 2014-2017 Godot Engine contributors (cf. AUTHORS.md)    */
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#include "gjk_epa.h"

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

// 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

} // end of namespace

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;
}