add b3QHull object

b3QHull allows users to create hull shapes from a list of points quickly. Example usage:

vec3* points = 0;
uint count = create_points(points);

b3QHull hull;
hull.Set(points, count);

include/bounce/bounce.h

@@ -36,6 +36,7 @@
 #include <bounce/collision/shapes/capsule.h>
 #include <bounce/collision/shapes/hull.h>
 #include <bounce/collision/shapes/box_hull.h>
+#include <bounce/collision/shapes/qhull.h>
 #include <bounce/collision/shapes/mesh.h>
 #include <bounce/collision/shapes/grid_mesh.h>
 

include/bounce/collision/shapes/hull.h

@@ -58,8 +58,6 @@ struct b3Hull
 	
 	u32 GetSize() const;
 
-	b3Vec3 GetCentroid() const;
-
 	void Validate() const;
 	void Validate(const b3Face* face) const;
 	void Validate(const b3HalfEdge* edge) const;

include/bounce/collision/shapes/qhull.h

@@ -0,0 +1,44 @@
+/*
+* Copyright (c) 2016-2016 Irlan Robson http://www.irlan.net
+*
+* 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.
+*/
+
+#ifndef B3_Q_HULL_H
+#define B3_Q_HULL_H
+
+#include <bounce/collision/shapes/hull.h>
+
+struct b3QHull : public b3Hull
+{
+	b3QHull();
+	~b3QHull();
+
+	// Create a convex hull from a point list.
+	// If the point list defines a degenerate polyhedron 
+	// the old hull is not cleared.
+	//
+	// Coincident points are removed.
+	// Coplanar faces are merged.
+	void Set(const b3Vec3* points, u32 count);
+
+	// Set this hull as a cylinder located at the origin.
+	void SetAsCylinder(float32 radius = 1.0f, float32 height = 1.0f);
+
+	// Set this hull as a cone located at the origin.
+	void SetAsCone(float32 radius = 1.0f, float32 height = 1.0f);
+};
+
+#endif

src/bounce/collision/shapes/qhull.cpp

@@ -0,0 +1,439 @@
+/*
+* Copyright (c) 2016-2016 Irlan Robson http://www.irlan.net
+*
+* 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.
+*/
+
+#include <bounce/collision/shapes/qhull.h>
+#include <bounce/quickhull/qh_hull.h>
+
+// Euler's formula
+// V - E + F = 2
+//#define B3_MAX_HULL_VERTICES 87
+//#define B3_MAX_HULL_EDGES (3 * B3_MAX_HULL_VERTICES - 6)
+//#define B3_MAX_HULL_FACES (2 * B3_MAX_HULL_VERTICES - 4)
+
+#define B3_MAX_HULL_FEATURES 256
+
+#define B3_NULL_HULL_FEATURE 0xFF
+
+//
+struct b3PointerIndex
+{
+	void* key;
+	u8 value;
+};
+
+// 
+template<u32 N>
+struct b3PointerMap
+{
+	void Add(const b3PointerIndex& entry)
+	{
+		m_entries.PushBack(entry);
+	}
+
+	b3PointerIndex* Find(void* key)
+	{
+		for (u32 i = 0; i < m_entries.Count(); ++i)
+		{
+			b3PointerIndex* index = m_entries.Get(i);
+			if (index->key == key)
+			{
+				return index;
+			}
+		}
+		return NULL;
+	}
+	
+	b3StackArray<b3PointerIndex, N> m_entries;
+};
+
+b3QHull::b3QHull()
+{
+	centroid.SetZero();
+	vertexCount = 0;
+	vertices = NULL;
+	edgeCount = 0;
+	edges = NULL;
+	faceCount = 0;
+	faces = NULL;
+	planes = NULL;
+}
+
+b3QHull::~b3QHull()
+{
+	b3Free(vertices);
+	b3Free(edges);
+	b3Free(faces);
+	b3Free(planes);
+}
+
+//
+static b3Vec3 b3ComputeCentroid(b3QHull* hull)
+{
+	// centroid.x = (1 / volume) * int(x * dV)
+	// centroid.y = (1 / volume) * int(y * dV)
+	// centroid.z = (1 / volume) * int(z * dV)
+	b3Vec3 centroid;
+	centroid.SetZero();
+
+	float32 volume = 0.0f;
+
+	const float32 inv6 = 1.0f / 6.0f;
+	const float32 inv12 = 1.0f / 12.0f;
+
+	for (u32 i = 0; i < hull->faceCount; ++i)
+	{
+		const b3Face* face = hull->GetFace(i);
+		const b3HalfEdge* begin = hull->GetEdge(face->edge);
+
+		const b3HalfEdge* edge = hull->GetEdge(begin->next);
+		do
+		{
+			const b3HalfEdge* next = hull->GetEdge(edge->next);
+
+			u32 i1 = begin->origin;
+			u32 i2 = edge->origin;
+			u32 i3 = next->origin;
+
+			b3Vec3 e1 = hull->GetVertex(i1);
+			b3Vec3 e2 = hull->GetVertex(i2);
+			b3Vec3 e3 = hull->GetVertex(i3);
+
+			float32 ex1 = e1.x, ey1 = e1.y, ez1 = e1.z;
+			float32 ex2 = e2.x, ey2 = e2.y, ez2 = e2.z;
+			float32 ex3 = e3.x, ey3 = e3.y, ez3 = e3.z;
+
+			// D = cross(e2 - e1, e3 - e1);
+			float32 a1 = ex2 - ex1, a2 = ey2 - ey1, a3 = ez2 - ez1;
+			float32 b1 = ex3 - ex1, b2 = ey3 - ey1, b3 = ez3 - ez1;
+
+			float32 D1 = a2 * b3 - a3 * b2;
+			float32 D2 = a3 * b1 - a1 * b3;
+			float32 D3 = a1 * b2 - a2 * b1;
+
+			//
+			float32 intx = ex1 + ex2 + ex3;
+			volume += (inv6 * D1) * intx;
+
+			//
+			float32 intx2 = ex1 * ex1 + ex1 * ex2 + ex1 * ex3 + ex2 * ex2 + ex2 * ex3 + ex3 * ex3;
+			float32 inty2 = ey1 * ey1 + ey1 * ey2 + ey1 * ey3 + ey2 * ey2 + ey2 * ey3 + ey3 * ey3;
+			float32 intz2 = ez1 * ez1 + ez1 * ez2 + ez1 * ez3 + ez2 * ez2 + ez2 * ez3 + ez3 * ez3;
+
+			centroid.x += (0.5f * inv12 * D1) * intx2;
+			centroid.y += (0.5f * inv12 * D2) * inty2;
+			centroid.z += (0.5f * inv12 * D3) * intz2;
+
+			edge = next;
+		} while (hull->GetEdge(edge->next) != begin);
+	}
+
+	// Centroid
+	B3_ASSERT(volume > B3_EPSILON);
+	centroid /= volume;
+	return centroid;
+}
+
+void b3QHull::Set(const b3Vec3* points, u32 count)
+{
+	// Copy points into local buffer, remove coincident points.
+	b3StackArray<b3Vec3, 256> ps;
+	for (u32 i = 0; i < count; ++i)
+	{
+		b3Vec3 p = points[i];
+
+		bool unique = true;
+
+		for (u32 j = 0; j < ps.Count(); ++j)
+		{
+			const float32 kTol = 0.5f * B3_LINEAR_SLOP;
+			if (b3DistanceSquared(p, ps[j]) < kTol * kTol)
+			{
+				unique = false;
+				break;
+			}
+		}
+
+		if (unique)
+		{
+			ps.PushBack(p);
+		}
+	}
+
+	if (ps.Count() < 3)
+	{
+		// Polyhedron is degenerate.
+		return;
+	}
+
+	// Create a convex hull.
+	u32 qh_size = qhGetMemorySize(ps.Count());
+	void* qh_memory = b3Alloc(qh_size);
+
+	qhHull hull;
+	hull.Construct(qh_memory, ps);
+
+	// Count vertices, edges, and faces in the convex hull.
+	u32 V = 0;
+	u32 E = 0;
+	u32 F = 0;
+
+	const qhList<qhFace>& faceList = hull.GetFaceList();
+
+	qhFace* face = faceList.head;
+	while (face)
+	{
+		qhHalfEdge* e = face->edge;
+		do
+		{
+			++E;
+			++V;
+			e = e->next;
+		} while (e != face->edge);
+
+		++F;
+		face = face->next;
+	}
+
+	if (V > B3_MAX_HULL_FEATURES) 
+	{
+		b3Free(qh_memory);
+		return; 
+	}
+	
+	if (E > B3_MAX_HULL_FEATURES) 
+	{ 
+		b3Free(qh_memory);
+		return;
+	}
+
+	if (F > B3_MAX_HULL_FEATURES) 
+	{ 
+		b3Free(qh_memory);
+		return;
+	}
+
+	b3Free(vertices);
+	b3Free(edges);
+	b3Free(faces);
+
+	vertexCount = 0;
+	vertices = (b3Vec3*)b3Alloc(V * sizeof(b3Vec3));
+	edgeCount = 0;
+	edges = (b3HalfEdge*)b3Alloc(E * sizeof(b3HalfEdge));
+	faceCount = 0;
+	faces = (b3Face*)b3Alloc(F * sizeof(b3Face));
+	planes = (b3Plane*)b3Alloc(F * sizeof(b3Plane));
+
+	b3PointerMap<B3_MAX_HULL_FEATURES> vertexMap;
+	b3PointerMap<B3_MAX_HULL_FEATURES> edgeMap;
+
+	face = faceList.head;
+	while (face)
+	{
+		B3_ASSERT(faceCount < F);
+		u8 iface = faceCount;
+		b3Face* f = faces + faceCount;
+		b3Plane* plane = planes + faceCount;
+		++faceCount;
+
+		*plane = face->plane;
+
+		b3StackArray<u8, 32> faceEdges;
+
+		qhHalfEdge* edge = face->edge;
+		do
+		{
+			qhHalfEdge* twin = edge->twin;
+			qhVertex* v1 = edge->tail;
+			qhVertex* v2 = twin->tail;
+
+			b3PointerIndex* mte = edgeMap.Find(edge);
+			b3PointerIndex* mv1 = vertexMap.Find(v1);
+			b3PointerIndex* mv2 = vertexMap.Find(v2);
+
+			u8 iv1;
+			if (mv1)
+			{
+				iv1 = mv1->value;
+			}
+			else
+			{
+				B3_ASSERT(vertexCount < V);
+				iv1 = vertexCount;
+				vertices[iv1] = v1->position;
+				vertexMap.Add({ v1, iv1 });
+				++vertexCount;
+			}
+
+			u8 iv2;
+			if (mv2)
+			{
+				iv2 = mv2->value;
+			}
+			else
+			{
+				B3_ASSERT(vertexCount < V);
+				iv2 = vertexCount;
+				vertices[iv2] = v2->position;
+				vertexMap.Add({ v2, iv2 });
+				++vertexCount;
+			}
+
+			if (mte)
+			{
+				u8 ie2 = mte->value;
+				b3HalfEdge* e2 = edges + ie2;
+				B3_ASSERT(e2->face == B3_NULL_HULL_FEATURE);
+				e2->face = iface;
+				faceEdges.PushBack(ie2);
+			}
+			else
+			{
+				B3_ASSERT(edgeCount < E);
+				u8 ie1 = edgeCount;
+				b3HalfEdge* e1 = edges + edgeCount;
+				++edgeCount;
+
+				B3_ASSERT(edgeCount < E);
+				u8 ie2 = edgeCount;
+				b3HalfEdge* e2 = edges + edgeCount;
+				++edgeCount;
+
+				e1->face = iface;
+				e1->origin = iv1;
+				e1->twin = ie2;
+
+				e2->face = B3_NULL_HULL_FEATURE;
+				e2->origin = iv2;
+				e2->twin = ie1;
+
+				faceEdges.PushBack(ie1);
+
+				edgeMap.Add({ edge, ie1 });
+				edgeMap.Add({ twin, ie2 });
+			}
+
+			edge = edge->next;
+		} while (edge != face->edge);
+
+		f->edge = faceEdges[0];
+		for (u32 i = 0; i < faceEdges.Count(); ++i)
+		{
+			u32 j = i < faceEdges.Count() - 1 ? i + 1 : 0;
+			edges[faceEdges[i]].next = faceEdges[j];
+		}
+
+		face = face->next;
+	}
+
+	// 
+	b3Free(qh_memory);
+
+	// Validate
+	Validate();
+
+	// Compute the centroid.
+	centroid = b3ComputeCentroid(this);
+}
+
+void b3QHull::SetAsCylinder(float32 radius, float32 height)
+{
+	B3_ASSERT(radius > 0.0f);
+	B3_ASSERT(height > 0.0f);
+
+	const u32 kEdgeCount = 20;
+	const u32 kVertexCount = 4 * kEdgeCount;
+	b3Vec3 vs[kVertexCount];
+
+	u32 count = 0;
+
+	float32 kAngleInc = 2.0f * B3_PI / float32(kEdgeCount);
+	b3Quat q = b3QuatRotationY(kAngleInc);
+
+	{
+		b3Vec3 center(0.0f, 0.0f, 0.0f);
+		b3Vec3 n1(1.0f, 0.0f, 0.0f);
+		b3Vec3 v1 = center + radius * n1;
+		for (u32 i = 0; i < kEdgeCount; ++i)
+		{
+			b3Vec3 n2 = b3Mul(q, n1);
+			b3Vec3 v2 = center + radius * n2;
+
+			vs[count++] = v1;
+			vs[count++] = v2;
+
+			n1 = n2;
+			v1 = v2;
+		}
+	}
+
+	{
+		b3Vec3 center(0.0f, height, 0.0f);
+		b3Vec3 n1(1.0f, 0.0f, 0.0f);
+		b3Vec3 v1 = center + radius * n1;
+		for (u32 i = 0; i < kEdgeCount; ++i)
+		{
+			b3Vec3 n2 = b3Mul(q, n1);
+			b3Vec3 v2 = center + radius * n2;
+
+			vs[count++] = v1;
+			vs[count++] = v2;
+
+			n1 = n2;
+			v1 = v2;
+		}
+	}
+
+	// Set
+	Set(vs, count);
+}
+
+void b3QHull::SetAsCone(float32 radius, float32 height)
+{
+	B3_ASSERT(radius > 0.0f);
+	B3_ASSERT(height > 0.0f);
+	
+	const u32 kEdgeCount = 20;
+	const u32 kVertexCount = 2 * kEdgeCount + 1;
+	b3Vec3 vs[kVertexCount];
+
+	u32 count = 0;
+
+	float32 kAngleInc = 2.0f * B3_PI / float32(kEdgeCount);
+	b3Quat q = b3QuatRotationY(kAngleInc);
+
+	b3Vec3 center(0.0f, 0.0f, 0.0f);
+	b3Vec3 n1(1.0f, 0.0f, 0.0f);
+	b3Vec3 v1 = center + radius * n1;
+	for (u32 i = 0; i < kEdgeCount; ++i)
+	{
+		b3Vec3 n2 = b3Mul(q, n1);
+		b3Vec3 v2 = center + radius * n2;
+
+		vs[count++] = v1;
+		vs[count++] = v2;
+
+		n1 = n2;
+		v1 = v2;
+	}
+
+	vs[count++].Set(0.0f, height, 0.0f);
+
+	// Set
+	Set(vs, count);
+}