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+// MIT License
+
+// Copyright (c) 2019 Erin Catto
+
+// Permission is hereby granted, free of charge, to any person obtaining a copy
+// of this software and associated documentation files (the "Software"), to deal
+// in the Software without restriction, including without limitation the rights
+// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+// copies of the Software, and to permit persons to whom the Software is
+// furnished to do so, subject to the following conditions:
+
+// The above copyright notice and this permission notice shall be included in all
+// copies or substantial portions of the Software.
+
+// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+// SOFTWARE.
+
+#include "box2d/b2_collision.h"
+#include "box2d/b2_polygon_shape.h"
+
+// Find the max separation between poly1 and poly2 using edge normals from poly1.
+static float b2FindMaxSeparation(int32* edgeIndex,
+ const b2PolygonShape* poly1, const b2Transform& xf1,
+ const b2PolygonShape* poly2, const b2Transform& xf2)
+{
+ int32 count1 = poly1->m_count;
+ int32 count2 = poly2->m_count;
+ const b2Vec2* n1s = poly1->m_normals;
+ const b2Vec2* v1s = poly1->m_vertices;
+ const b2Vec2* v2s = poly2->m_vertices;
+ b2Transform xf = b2MulT(xf2, xf1);
+
+ int32 bestIndex = 0;
+ float maxSeparation = -b2_maxFloat;
+ for (int32 i = 0; i < count1; ++i)
+ {
+ // Get poly1 normal in frame2.
+ b2Vec2 n = b2Mul(xf.q, n1s[i]);
+ b2Vec2 v1 = b2Mul(xf, v1s[i]);
+
+ // Find deepest point for normal i.
+ float si = b2_maxFloat;
+ for (int32 j = 0; j < count2; ++j)
+ {
+ float sij = b2Dot(n, v2s[j] - v1);
+ if (sij < si)
+ {
+ si = sij;
+ }
+ }
+
+ if (si > maxSeparation)
+ {
+ maxSeparation = si;
+ bestIndex = i;
+ }
+ }
+
+ *edgeIndex = bestIndex;
+ return maxSeparation;
+}
+
+static void b2FindIncidentEdge(b2ClipVertex c[2],
+ const b2PolygonShape* poly1, const b2Transform& xf1, int32 edge1,
+ const b2PolygonShape* poly2, const b2Transform& xf2)
+{
+ const b2Vec2* normals1 = poly1->m_normals;
+
+ int32 count2 = poly2->m_count;
+ const b2Vec2* vertices2 = poly2->m_vertices;
+ const b2Vec2* normals2 = poly2->m_normals;
+
+ b2Assert(0 <= edge1 && edge1 < poly1->m_count);
+
+ // Get the normal of the reference edge in poly2's frame.
+ b2Vec2 normal1 = b2MulT(xf2.q, b2Mul(xf1.q, normals1[edge1]));
+
+ // Find the incident edge on poly2.
+ int32 index = 0;
+ float minDot = b2_maxFloat;
+ for (int32 i = 0; i < count2; ++i)
+ {
+ float dot = b2Dot(normal1, normals2[i]);
+ if (dot < minDot)
+ {
+ minDot = dot;
+ index = i;
+ }
+ }
+
+ // Build the clip vertices for the incident edge.
+ int32 i1 = index;
+ int32 i2 = i1 + 1 < count2 ? i1 + 1 : 0;
+
+ c[0].v = b2Mul(xf2, vertices2[i1]);
+ c[0].id.cf.indexA = (uint8)edge1;
+ c[0].id.cf.indexB = (uint8)i1;
+ c[0].id.cf.typeA = b2ContactFeature::e_face;
+ c[0].id.cf.typeB = b2ContactFeature::e_vertex;
+
+ c[1].v = b2Mul(xf2, vertices2[i2]);
+ c[1].id.cf.indexA = (uint8)edge1;
+ c[1].id.cf.indexB = (uint8)i2;
+ c[1].id.cf.typeA = b2ContactFeature::e_face;
+ c[1].id.cf.typeB = b2ContactFeature::e_vertex;
+}
+
+// Find edge normal of max separation on A - return if separating axis is found
+// Find edge normal of max separation on B - return if separation axis is found
+// Choose reference edge as min(minA, minB)
+// Find incident edge
+// Clip
+
+// The normal points from 1 to 2
+void b2CollidePolygons(b2Manifold* manifold,
+ const b2PolygonShape* polyA, const b2Transform& xfA,
+ const b2PolygonShape* polyB, const b2Transform& xfB)
+{
+ manifold->pointCount = 0;
+ float totalRadius = polyA->m_radius + polyB->m_radius;
+
+ int32 edgeA = 0;
+ float separationA = b2FindMaxSeparation(&edgeA, polyA, xfA, polyB, xfB);
+ if (separationA > totalRadius)
+ return;
+
+ int32 edgeB = 0;
+ float separationB = b2FindMaxSeparation(&edgeB, polyB, xfB, polyA, xfA);
+ if (separationB > totalRadius)
+ return;
+
+ const b2PolygonShape* poly1; // reference polygon
+ const b2PolygonShape* poly2; // incident polygon
+ b2Transform xf1, xf2;
+ int32 edge1; // reference edge
+ uint8 flip;
+ const float k_tol = 0.1f * b2_linearSlop;
+
+ if (separationB > separationA + k_tol)
+ {
+ poly1 = polyB;
+ poly2 = polyA;
+ xf1 = xfB;
+ xf2 = xfA;
+ edge1 = edgeB;
+ manifold->type = b2Manifold::e_faceB;
+ flip = 1;
+ }
+ else
+ {
+ poly1 = polyA;
+ poly2 = polyB;
+ xf1 = xfA;
+ xf2 = xfB;
+ edge1 = edgeA;
+ manifold->type = b2Manifold::e_faceA;
+ flip = 0;
+ }
+
+ b2ClipVertex incidentEdge[2];
+ b2FindIncidentEdge(incidentEdge, poly1, xf1, edge1, poly2, xf2);
+
+ int32 count1 = poly1->m_count;
+ const b2Vec2* vertices1 = poly1->m_vertices;
+
+ int32 iv1 = edge1;
+ int32 iv2 = edge1 + 1 < count1 ? edge1 + 1 : 0;
+
+ b2Vec2 v11 = vertices1[iv1];
+ b2Vec2 v12 = vertices1[iv2];
+
+ b2Vec2 localTangent = v12 - v11;
+ localTangent.Normalize();
+
+ b2Vec2 localNormal = b2Cross(localTangent, 1.0f);
+ b2Vec2 planePoint = 0.5f * (v11 + v12);
+
+ b2Vec2 tangent = b2Mul(xf1.q, localTangent);
+ b2Vec2 normal = b2Cross(tangent, 1.0f);
+
+ v11 = b2Mul(xf1, v11);
+ v12 = b2Mul(xf1, v12);
+
+ // Face offset.
+ float frontOffset = b2Dot(normal, v11);
+
+ // Side offsets, extended by polytope skin thickness.
+ float sideOffset1 = -b2Dot(tangent, v11) + totalRadius;
+ float sideOffset2 = b2Dot(tangent, v12) + totalRadius;
+
+ // Clip incident edge against extruded edge1 side edges.
+ b2ClipVertex clipPoints1[2];
+ b2ClipVertex clipPoints2[2];
+ int np;
+
+ // Clip to box side 1
+ np = b2ClipSegmentToLine(clipPoints1, incidentEdge, -tangent, sideOffset1, iv1);
+
+ if (np < 2)
+ return;
+
+ // Clip to negative box side 1
+ np = b2ClipSegmentToLine(clipPoints2, clipPoints1, tangent, sideOffset2, iv2);
+
+ if (np < 2)
+ {
+ return;
+ }
+
+ // Now clipPoints2 contains the clipped points.
+ manifold->localNormal = localNormal;
+ manifold->localPoint = planePoint;
+
+ int32 pointCount = 0;
+ for (int32 i = 0; i < b2_maxManifoldPoints; ++i)
+ {
+ float separation = b2Dot(normal, clipPoints2[i].v) - frontOffset;
+
+ if (separation <= totalRadius)
+ {
+ b2ManifoldPoint* cp = manifold->points + pointCount;
+ cp->localPoint = b2MulT(xf2, clipPoints2[i].v);
+ cp->id = clipPoints2[i].id;
+ if (flip)
+ {
+ // Swap features
+ b2ContactFeature cf = cp->id.cf;
+ cp->id.cf.indexA = cf.indexB;
+ cp->id.cf.indexB = cf.indexA;
+ cp->id.cf.typeA = cf.typeB;
+ cp->id.cf.typeB = cf.typeA;
+ }
+ ++pointCount;
+ }
+ }
+
+ manifold->pointCount = pointCount;
+}