text: /*
   * Copyright (c) 2007-2009 Erin Catto http://www.box2d.org
   *
   * 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 <Box2DRef/Collision/b2Collision.h>
  #include <Box2DRef/Collision/Shapes/b2CircleShape.h>
  #include <Box2DRef/Collision/Shapes/b2EdgeShape.h>
  #include <Box2DRef/Collision/Shapes/b2PolygonShape.h>
  
  
  namespace box2dref
  {
  // Compute contact points for edge versus circle.
  // This accounts for edge connectivity.
  void b2CollideEdgeAndCircle(b2Manifold* manifold,
  							const b2EdgeShape* edgeA, const b2Transform& xfA,
  							const b2CircleShape* circleB, const b2Transform& xfB)
  {
  	manifold->pointCount = 0;
  	
  	// Compute circle in frame of edge
  	b2Vec2 Q = b2MulT(xfA, b2Mul(xfB, circleB->m_p));
  	
  	b2Vec2 A = edgeA->m_vertex1, B = edgeA->m_vertex2;
  	b2Vec2 e = B - A;
  	
  	// Barycentric coordinates
  	float32 u = b2Dot(e, B - Q);
  	float32 v = b2Dot(e, Q - A);
  	
  	float32 radius = edgeA->m_radius + circleB->m_radius;
  	
  	b2ContactFeature cf;
  	cf.indexB = 0;
  	cf.typeB = b2ContactFeature::e_vertex;
  	
  	// Region A
  	if (v <= 0.0f)
  	{
  		b2Vec2 P = A;
  		b2Vec2 d = Q - P;
  		float32 dd = b2Dot(d, d);
  		if (dd > radius * radius)
  		{
  			return;
  		}
  		
  		// Is there an edge connected to A?
  		if (edgeA->m_hasVertex0)
  		{
  			b2Vec2 A1 = edgeA->m_vertex0;
  			b2Vec2 B1 = A;
  			b2Vec2 e1 = B1 - A1;
  			float32 u1 = b2Dot(e1, B1 - Q);
  			
  			// Is the circle in Region AB of the previous edge?
  			if (u1 > 0.0f)
  			{
  				return;
  			}
  		}
  		
  		cf.indexA = 0;
  		cf.typeA = b2ContactFeature::e_vertex;
  		manifold->pointCount = 1;
  		manifold->type = b2Manifold::e_circles;
  		manifold->localNormal.SetZero();
  		manifold->localPoint = P;
  		manifold->points[0].id.key = 0;
  		manifold->points[0].id.cf = cf;
  		manifold->points[0].localPoint = circleB->m_p;
  		return;
  	}
  	
  	// Region B
  	if (u <= 0.0f)
  	{
  		b2Vec2 P = B;
  		b2Vec2 d = Q - P;
  		float32 dd = b2Dot(d, d);
  		if (dd > radius * radius)
  		{
  			return;
  		}
  		
  		// Is there an edge connected to B?
  		if (edgeA->m_hasVertex3)
  		{
  			b2Vec2 B2 = edgeA->m_vertex3;
  			b2Vec2 A2 = B;
  			b2Vec2 e2 = B2 - A2;
  			float32 v2 = b2Dot(e2, Q - A2);
  			
  			// Is the circle in Region AB of the next edge?
  			if (v2 > 0.0f)
  			{
  				return;
  			}
  		}
  		
  		cf.indexA = 1;
  		cf.typeA = b2ContactFeature::e_vertex;
  		manifold->pointCount = 1;
  		manifold->type = b2Manifold::e_circles;
  		manifold->localNormal.SetZero();
  		manifold->localPoint = P;
  		manifold->points[0].id.key = 0;
  		manifold->points[0].id.cf = cf;
  		manifold->points[0].localPoint = circleB->m_p;
  		return;
  	}
  	
  	// Region AB
  	float32 den = b2Dot(e, e);
  	b2Assert(den > 0.0f);
  	b2Vec2 P = (1.0f / den) * (u * A + v * B);
  	b2Vec2 d = Q - P;
  	float32 dd = b2Dot(d, d);
  	if (dd > radius * radius)
  	{
  		return;
  	}
  	
  	b2Vec2 n(-e.y, e.x);
  	if (b2Dot(n, Q - A) < 0.0f)
  	{
  		n.Set(-n.x, -n.y);
  	}
  	n.Normalize();
  	
  	cf.indexA = 0;
  	cf.typeA = b2ContactFeature::e_face;
  	manifold->pointCount = 1;
  	manifold->type = b2Manifold::e_faceA;
  	manifold->localNormal = n;
  	manifold->localPoint = A;
  	manifold->points[0].id.key = 0;
  	manifold->points[0].id.cf = cf;
  	manifold->points[0].localPoint = circleB->m_p;
  }
  
  // This structure is used to keep track of the best separating axis.
  struct b2EPAxis
  {
  	enum Type
  	{
  		e_unknown,
  		e_edgeA,
  		e_edgeB
  	};
  	
  	Type type;
  	int32 index;
  	float32 separation;
  };
  
  // This holds polygon B expressed in frame A.
  struct b2TempPolygon
  {
  	b2Vec2 vertices[b2_maxPolygonVertices];
  	b2Vec2 normals[b2_maxPolygonVertices];
  	int32 count;
  };
  
  // Reference face used for clipping
  struct b2ReferenceFace
  {
  	int32 i1, i2;
  	
  	b2Vec2 v1, v2;
  	
  	b2Vec2 normal;
  	
  	b2Vec2 sideNormal1;
  	float32 sideOffset1;
  	
  	b2Vec2 sideNormal2;
  	float32 sideOffset2;
  };
  
  // This class collides and edge and a polygon, taking into account edge adjacency.
  struct b2EPCollider
  {
  	void Collide(b2Manifold* manifold, const b2EdgeShape* edgeA, const b2Transform& xfA,
  				 const b2PolygonShape* polygonB, const b2Transform& xfB);
  	b2EPAxis ComputeEdgeSeparation();
  	b2EPAxis ComputePolygonSeparation();
  	
  	enum VertexType
  	{
  		e_isolated,
  		e_concave,
  		e_convex
  	};
  	
  	b2TempPolygon m_polygonB;
  	
  	b2Transform m_xf;
  	b2Vec2 m_centroidB;
  	b2Vec2 m_v0, m_v1, m_v2, m_v3;
  	b2Vec2 m_normal0, m_normal1, m_normal2;
  	b2Vec2 m_normal;
  	VertexType m_type1, m_type2;
  	b2Vec2 m_lowerLimit, m_upperLimit;
  	float32 m_radius;
  	bool m_front;
  };
  
  // Algorithm:
  // 1. Classify v1 and v2
  // 2. Classify polygon centroid as front or back
  // 3. Flip normal if necessary
  // 4. Initialize normal range to [-pi, pi] about face normal
  // 5. Adjust normal range according to adjacent edges
  // 6. Visit each separating axes, only accept axes within the range
  // 7. Return if _any_ axis indicates separation
  // 8. Clip
  void b2EPCollider::Collide(b2Manifold* manifold, const b2EdgeShape* edgeA, const b2Transform& xfA,
  						   const b2PolygonShape* polygonB, const b2Transform& xfB)
  {
  	m_xf = b2MulT(xfA, xfB);
  	
  	m_centroidB = b2Mul(m_xf, polygonB->m_centroid);
  	
  	m_v0 = edgeA->m_vertex0;
  	m_v1 = edgeA->m_vertex1;
  	m_v2 = edgeA->m_vertex2;
  	m_v3 = edgeA->m_vertex3;
  	
  	bool hasVertex0 = edgeA->m_hasVertex0;
  	bool hasVertex3 = edgeA->m_hasVertex3;
  	
  	b2Vec2 edge1 = m_v2 - m_v1;
  	edge1.Normalize();
  	m_normal1.Set(edge1.y, -edge1.x);
  	float32 offset1 = b2Dot(m_normal1, m_centroidB - m_v1);
  	float32 offset0 = 0.0f, offset2 = 0.0f;
  	bool convex1 = false, convex2 = false;
  	
  	// Is there a preceding edge?
  	if (hasVertex0)
  	{
  		b2Vec2 edge0 = m_v1 - m_v0;
  		edge0.Normalize();
  		m_normal0.Set(edge0.y, -edge0.x);
  		convex1 = b2Cross(edge0, edge1) >= 0.0f;
  		offset0 = b2Dot(m_normal0, m_centroidB - m_v0);
  	}
  	
  	// Is there a following edge?
  	if (hasVertex3)
  	{
  		b2Vec2 edge2 = m_v3 - m_v2;
  		edge2.Normalize();
  		m_normal2.Set(edge2.y, -edge2.x);
  		convex2 = b2Cross(edge1, edge2) > 0.0f;
  		offset2 = b2Dot(m_normal2, m_centroidB - m_v2);
  	}
  	
  	// Determine front or back collision. Determine collision normal limits.
  	if (hasVertex0 && hasVertex3)
  	{
  		if (convex1 && convex2)
  		{
  			m_front = offset0 >= 0.0f || offset1 >= 0.0f || offset2 >= 0.0f;
  			if (m_front)
  			{
  				m_normal = m_normal1;
  				m_lowerLimit = m_normal0;
  				m_upperLimit = m_normal2;
  			}
  			else
  			{
  				m_normal = -m_normal1;
  				m_lowerLimit = -m_normal1;
  				m_upperLimit = -m_normal1;
  			}
  		}
  		else if (convex1)
  		{
  			m_front = offset0 >= 0.0f || (offset1 >= 0.0f && offset2 >= 0.0f);
  			if (m_front)
  			{
  				m_normal = m_normal1;
  				m_lowerLimit = m_normal0;
  				m_upperLimit = m_normal1;
  			}
  			else
  			{
  				m_normal = -m_normal1;
  				m_lowerLimit = -m_normal2;
  				m_upperLimit = -m_normal1;
  			}
  		}
  		else if (convex2)
  		{
  			m_front = offset2 >= 0.0f || (offset0 >= 0.0f && offset1 >= 0.0f);
  			if (m_front)
  			{
  				m_normal = m_normal1;
  				m_lowerLimit = m_normal1;
  				m_upperLimit = m_normal2;
  			}
  			else
  			{
  				m_normal = -m_normal1;
  				m_lowerLimit = -m_normal1;
  				m_upperLimit = -m_normal0;
  			}
  		}
  		else
  		{
  			m_front = offset0 >= 0.0f && offset1 >= 0.0f && offset2 >= 0.0f;
  			if (m_front)
  			{
  				m_normal = m_normal1;
  				m_lowerLimit = m_normal1;
  				m_upperLimit = m_normal1;
  			}
  			else
  			{
  				m_normal = -m_normal1;
  				m_lowerLimit = -m_normal2;
  				m_upperLimit = -m_normal0;
  			}
  		}
  	}
  	else if (hasVertex0)
  	{
  		if (convex1)
  		{
  			m_front = offset0 >= 0.0f || offset1 >= 0.0f;
  			if (m_front)
  			{
  				m_normal = m_normal1;
  				m_lowerLimit = m_normal0;
  				m_upperLimit = -m_normal1;
  			}
  			else
  			{
  				m_normal = -m_normal1;
  				m_lowerLimit = m_normal1;
  				m_upperLimit = -m_normal1;
  			}
  		}
  		else
  		{
  			m_front = offset0 >= 0.0f && offset1 >= 0.0f;
  			if (m_front)
  			{
  				m_normal = m_normal1;
  				m_lowerLimit = m_normal1;
  				m_upperLimit = -m_normal1;
  			}
  			else
  			{
  				m_normal = -m_normal1;
  				m_lowerLimit = m_normal1;
  				m_upperLimit = -m_normal0;
  			}
  		}
  	}
  	else if (hasVertex3)
  	{
  		if (convex2)
  		{
  			m_front = offset1 >= 0.0f || offset2 >= 0.0f;
  			if (m_front)
  			{
  				m_normal = m_normal1;
  				m_lowerLimit = -m_normal1;
  				m_upperLimit = m_normal2;
  			}
  			else
  			{
  				m_normal = -m_normal1;
  				m_lowerLimit = -m_normal1;
  				m_upperLimit = m_normal1;
  			}
  		}
  		else
  		{
  			m_front = offset1 >= 0.0f && offset2 >= 0.0f;
  			if (m_front)
  			{
  				m_normal = m_normal1;
  				m_lowerLimit = -m_normal1;
  				m_upperLimit = m_normal1;
  			}
  			else
  			{
  				m_normal = -m_normal1;
  				m_lowerLimit = -m_normal2;
  				m_upperLimit = m_normal1;
  			}
  		}		
  	}
  	else
  	{
  		m_front = offset1 >= 0.0f;
  		if (m_front)
  		{
  			m_normal = m_normal1;
  			m_lowerLimit = -m_normal1;
  			m_upperLimit = -m_normal1;
  		}
  		else
  		{
  			m_normal = -m_normal1;
  			m_lowerLimit = m_normal1;
  			m_upperLimit = m_normal1;
  		}
  	}
  	
  	// Get polygonB in frameA
  	m_polygonB.count = polygonB->m_count;
  	for (int32 i = 0; i < polygonB->m_count; ++i)
  	{
  		m_polygonB.vertices[i] = b2Mul(m_xf, polygonB->m_vertices[i]);
  		m_polygonB.normals[i] = b2Mul(m_xf.q, polygonB->m_normals[i]);
  	}
  	
  	m_radius = 2.0f * b2_polygonRadius;
  	
  	manifold->pointCount = 0;
  	
  	b2EPAxis edgeAxis = ComputeEdgeSeparation();
  	
  	// If no valid normal can be found than this edge should not collide.
  	if (edgeAxis.type == b2EPAxis::e_unknown)
  	{
  		return;
  	}
  	
  	if (edgeAxis.separation > m_radius)
  	{
  		return;
  	}
  	
  	b2EPAxis polygonAxis = ComputePolygonSeparation();
  	if (polygonAxis.type != b2EPAxis::e_unknown && polygonAxis.separation > m_radius)
  	{
  		return;
  	}
  	
  	// Use hysteresis for jitter reduction.
  	const float32 k_relativeTol = 0.98f;
  	const float32 k_absoluteTol = 0.001f;
  	
  	b2EPAxis primaryAxis;
  	if (polygonAxis.type == b2EPAxis::e_unknown)
  	{
  		primaryAxis = edgeAxis;
  	}
  	else if (polygonAxis.separation > k_relativeTol * edgeAxis.separation + k_absoluteTol)
  	{
  		primaryAxis = polygonAxis;
  	}
  	else
  	{
  		primaryAxis = edgeAxis;
  	}
  	
  	b2ClipVertex ie[2];
  	b2ReferenceFace rf;
  	if (primaryAxis.type == b2EPAxis::e_edgeA)
  	{
  		manifold->type = b2Manifold::e_faceA;
  		
  		// Search for the polygon normal that is most anti-parallel to the edge normal.
  		int32 bestIndex = 0;
  		float32 bestValue = b2Dot(m_normal, m_polygonB.normals[0]);
  		for (int32 i = 1; i < m_polygonB.count; ++i)
  		{
  			float32 value = b2Dot(m_normal, m_polygonB.normals[i]);
  			if (value < bestValue)
  			{
  				bestValue = value;
  				bestIndex = i;
  			}
  		}
  		
  		int32 i1 = bestIndex;
  		int32 i2 = i1 + 1 < m_polygonB.count ? i1 + 1 : 0;
  		
  		ie[0].v = m_polygonB.vertices[i1];
  		ie[0].id.cf.indexA = 0;
  		ie[0].id.cf.indexB = static_cast<uint8>(i1);
  		ie[0].id.cf.typeA = b2ContactFeature::e_face;
  		ie[0].id.cf.typeB = b2ContactFeature::e_vertex;
  		
  		ie[1].v = m_polygonB.vertices[i2];
  		ie[1].id.cf.indexA = 0;
  		ie[1].id.cf.indexB = static_cast<uint8>(i2);
  		ie[1].id.cf.typeA = b2ContactFeature::e_face;
  		ie[1].id.cf.typeB = b2ContactFeature::e_vertex;
  		
  		if (m_front)
  		{
  			rf.i1 = 0;
  			rf.i2 = 1;
  			rf.v1 = m_v1;
  			rf.v2 = m_v2;
  			rf.normal = m_normal1;
  		}
  		else
  		{
  			rf.i1 = 1;
  			rf.i2 = 0;
  			rf.v1 = m_v2;
  			rf.v2 = m_v1;
  			rf.normal = -m_normal1;
  		}		
  	}
  	else
  	{
  		manifold->type = b2Manifold::e_faceB;
  		
  		ie[0].v = m_v1;
  		ie[0].id.cf.indexA = 0;
  		ie[0].id.cf.indexB = static_cast<uint8>(primaryAxis.index);
  		ie[0].id.cf.typeA = b2ContactFeature::e_vertex;
  		ie[0].id.cf.typeB = b2ContactFeature::e_face;
  		
  		ie[1].v = m_v2;
  		ie[1].id.cf.indexA = 0;
  		ie[1].id.cf.indexB = static_cast<uint8>(primaryAxis.index);		
  		ie[1].id.cf.typeA = b2ContactFeature::e_vertex;
  		ie[1].id.cf.typeB = b2ContactFeature::e_face;
  		
  		rf.i1 = primaryAxis.index;
  		rf.i2 = rf.i1 + 1 < m_polygonB.count ? rf.i1 + 1 : 0;
  		rf.v1 = m_polygonB.vertices[rf.i1];
  		rf.v2 = m_polygonB.vertices[rf.i2];
  		rf.normal = m_polygonB.normals[rf.i1];
  	}
  	
  	rf.sideNormal1.Set(rf.normal.y, -rf.normal.x);
  	rf.sideNormal2 = -rf.sideNormal1;
  	rf.sideOffset1 = b2Dot(rf.sideNormal1, rf.v1);
  	rf.sideOffset2 = b2Dot(rf.sideNormal2, rf.v2);
  	
  	// Clip incident edge against extruded edge1 side edges.
  	b2ClipVertex clipPoints1[2];
  	b2ClipVertex clipPoints2[2];
  	int32 np;
  	
  	// Clip to box side 1
  	np = b2ClipSegmentToLine(clipPoints1, ie, rf.sideNormal1, rf.sideOffset1, rf.i1);
  	
  	if (np < b2_maxManifoldPoints)
  	{
  		return;
  	}
  	
  	// Clip to negative box side 1
  	np = b2ClipSegmentToLine(clipPoints2, clipPoints1, rf.sideNormal2, rf.sideOffset2, rf.i2);
  	
  	if (np < b2_maxManifoldPoints)
  	{
  		return;
  	}
  	
  	// Now clipPoints2 contains the clipped points.
  	if (primaryAxis.type == b2EPAxis::e_edgeA)
  	{
  		manifold->localNormal = rf.normal;
  		manifold->localPoint = rf.v1;
  	}
  	else
  	{
  		manifold->localNormal = polygonB->m_normals[rf.i1];
  		manifold->localPoint = polygonB->m_vertices[rf.i1];
  	}
  	
  	int32 pointCount = 0;
  	for (int32 i = 0; i < b2_maxManifoldPoints; ++i)
  	{
  		float32 separation;
  		
  		separation = b2Dot(rf.normal, clipPoints2[i].v - rf.v1);
  		
  		if (separation <= m_radius)
  		{
  			b2ManifoldPoint* cp = manifold->points + pointCount;
  			
  			if (primaryAxis.type == b2EPAxis::e_edgeA)
  			{
  				cp->localPoint = b2MulT(m_xf, clipPoints2[i].v);
  				cp->id = clipPoints2[i].id;
  			}
  			else
  			{
  				cp->localPoint = clipPoints2[i].v;
  				cp->id.cf.typeA = clipPoints2[i].id.cf.typeB;
  				cp->id.cf.typeB = clipPoints2[i].id.cf.typeA;
  				cp->id.cf.indexA = clipPoints2[i].id.cf.indexB;
  				cp->id.cf.indexB = clipPoints2[i].id.cf.indexA;
  			}
  			
  			++pointCount;
  		}
  	}
  	
  	manifold->pointCount = pointCount;
  }
  
  b2EPAxis b2EPCollider::ComputeEdgeSeparation()
  {
  	b2EPAxis axis;
  	axis.type = b2EPAxis::e_edgeA;
  	axis.index = m_front ? 0 : 1;
  	axis.separation = FLT_MAX;
  	
  	for (int32 i = 0; i < m_polygonB.count; ++i)
  	{
  		float32 s = b2Dot(m_normal, m_polygonB.vertices[i] - m_v1);
  		if (s < axis.separation)
  		{
  			axis.separation = s;
  		}
  	}
  	
  	return axis;
  }
  
  b2EPAxis b2EPCollider::ComputePolygonSeparation()
  {
  	b2EPAxis axis;
  	axis.type = b2EPAxis::e_unknown;
  	axis.index = -1;
  	axis.separation = -FLT_MAX;
  
  	b2Vec2 perp(-m_normal.y, m_normal.x);
  
  	for (int32 i = 0; i < m_polygonB.count; ++i)
  	{
  		b2Vec2 n = -m_polygonB.normals[i];
  		
  		float32 s1 = b2Dot(n, m_polygonB.vertices[i] - m_v1);
  		float32 s2 = b2Dot(n, m_polygonB.vertices[i] - m_v2);
  		float32 s = b2Min(s1, s2);
  		
  		if (s > m_radius)
  		{
  			// No collision
  			axis.type = b2EPAxis::e_edgeB;
  			axis.index = i;
  			axis.separation = s;
  			return axis;
  		}
  		
  		// Adjacency
  		if (b2Dot(n, perp) >= 0.0f)
  		{
  			if (b2Dot(n - m_upperLimit, m_normal) < -b2_angularSlop)
  			{
  				continue;
  			}
  		}
  		else
  		{
  			if (b2Dot(n - m_lowerLimit, m_normal) < -b2_angularSlop)
  			{
  				continue;
  			}
  		}
  		
  		if (s > axis.separation)
  		{
  			axis.type = b2EPAxis::e_edgeB;
  			axis.index = i;
  			axis.separation = s;
  		}
  	}
  	
  	return axis;
  }
  
  void b2CollideEdgeAndPolygon(	b2Manifold* manifold,
  							 const b2EdgeShape* edgeA, const b2Transform& xfA,
  							 const b2PolygonShape* polygonB, const b2Transform& xfB)
  {
  	b2EPCollider collider;
  	collider.Collide(manifold, edgeA, xfA, polygonB, xfB);
  }
  }