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+/*
+ * 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 "Box2D/Collision/b2Collision.h"
+#include "Box2D/Collision/Shapes/b2CircleShape.h"
+#include "Box2D/Collision/Shapes/b2EdgeShape.h"
+#include "Box2D/Collision/Shapes/b2PolygonShape.h"
+
+
+// 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 = polygonB->m_radius + edgeA->m_radius;
+
+ 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);
+}
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