// 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 public void Collide(out Manifold manifold, EdgeShape edgeA, Transform xfA, PolygonShape polygonB, Transform xfB){ manifold = new Manifold(); m_xf = Utilities.MulT(xfA, xfB); m_centroidB = Utilities.Mul(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; Vec2 edge1 = m_v2 - m_v1; edge1.Normalize(); m_normal1.Set(edge1.Y, -edge1.X); float offset1 = Utilities.Dot(m_normal1, m_centroidB - m_v1); float offset0 = 0.0f, offset2 = 0.0f; bool convex1 = false, convex2 = false; // Is there a preceding edge? if (hasVertex0) { Vec2 edge0 = m_v1 - m_v0; edge0.Normalize(); m_normal0.Set(edge0.Y, -edge0.X); convex1 = Utilities.Cross(edge0, edge1) >= 0.0f; offset0 = Utilities.Dot(m_normal0, m_centroidB - m_v0); } // Is there a following edge? if (hasVertex3) { Vec2 edge2 = m_v3 - m_v2; edge2.Normalize(); m_normal2.Set(edge2.Y, -edge2.X); convex2 = Utilities.Cross(edge1, edge2) > 0.0f; offset2 = Utilities.Dot(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 (int i = 0; i < polygonB.m_count; ++i) { m_polygonB.vertices[i] = Utilities.Mul(m_xf, polygonB.m_vertices[i]); m_polygonB.normals[i] = Utilities.Mul(m_xf.q, polygonB.m_normals[i]); } m_radius = 2.0f * Settings._polygonRadius; manifold.points.Clear(); EPAxis edgeAxis = ComputeEdgeSeparation(); // If no valid normal can be found than this edge should not collide. if (edgeAxis.type == EPAxisType.e_unknown) { return; } if (edgeAxis.separation > m_radius) { return; } EPAxis polygonAxis = ComputePolygonSeparation(); if (polygonAxis.type != EPAxisType.e_unknown && polygonAxis.separation > m_radius) { return; } // Use hysteresis for jitter reduction. const float k_relativeTol = 0.98f; const float k_absoluteTol = 0.001f; EPAxis primaryAxis; if (polygonAxis.type == EPAxisType.e_unknown) { primaryAxis = edgeAxis; } else if (polygonAxis.separation > k_relativeTol * edgeAxis.separation + k_absoluteTol) { primaryAxis = polygonAxis; } else { primaryAxis = edgeAxis; } ClipVertex[] ie = new ClipVertex[2]; ReferenceFace rf = new ReferenceFace(); if (primaryAxis.type == EPAxisType.e_edgeA) { manifold.type = Manifold.ManifoldType.e_faceA; // Search for the polygon normal that is most anti-parallel to the edge normal. int bestIndex = 0; float bestValue = Utilities.Dot(m_normal, m_polygonB.normals[0]); for (int i = 1; i < m_polygonB.count; ++i) { float value = Utilities.Dot(m_normal, m_polygonB.normals[i]); if (value < bestValue) { bestValue = value; bestIndex = i; } } int i1 = bestIndex; int 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 = (byte)i1; ie[0].id.cf.typeA = ContactFeature.FeatureType.e_face; ie[0].id.cf.typeB = ContactFeature.FeatureType.e_vertex; ie[1].v = m_polygonB.vertices[i2]; ie[1].id.cf.indexA = 0; ie[1].id.cf.indexB = (byte)i2; ie[1].id.cf.typeA = ContactFeature.FeatureType.e_face; ie[1].id.cf.typeB = ContactFeature.FeatureType.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 = Manifold.ManifoldType.e_faceB; ie[0].v = m_v1; ie[0].id.cf.indexA = 0; ie[0].id.cf.indexB = (byte)primaryAxis.index; ie[0].id.cf.typeA = ContactFeature.FeatureType.e_vertex; ie[0].id.cf.typeB = ContactFeature.FeatureType.e_face; ie[1].v = m_v2; ie[1].id.cf.indexA = 0; ie[1].id.cf.indexB = (byte)primaryAxis.index; ie[1].id.cf.typeA = ContactFeature.FeatureType.e_vertex; ie[1].id.cf.typeB = ContactFeature.FeatureType.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 = Utilities.Dot(rf.sideNormal1, rf.v1); rf.sideOffset2 = Utilities.Dot(rf.sideNormal2, rf.v2); // Clip incident edge against extruded edge1 side edges. ClipVertex[] clipPoints1 = new ClipVertex[2]; ClipVertex[] clipPoints2 = new ClipVertex[2]; int np; // Clip to box side 1 np = Collision.ClipSegmentToLine(clipPoints1, ie, rf.sideNormal1, rf.sideOffset1, rf.i1); if (np < Settings._maxManifoldPoints) { return; } // Clip to negative box side 1 np = Collision.ClipSegmentToLine(clipPoints2, clipPoints1, rf.sideNormal2, rf.sideOffset2, rf.i2); if (np < Settings._maxManifoldPoints) { return; } // Now clipPoints2 contains the clipped points. if (primaryAxis.type == EPAxisType.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]; } manifold.points.Clear(); for (int i = 0; i < Settings._maxManifoldPoints; ++i) { float separation; separation = Utilities.Dot(rf.normal, clipPoints2[i].v - rf.v1); if (separation <= m_radius) { ManifoldPoint cp = new ManifoldPoint(); if (primaryAxis.type == EPAxisType.e_edgeA) { cp.localPoint = Utilities.MulT(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; } manifold.points.Add(cp); } } }
/// Clipping for contact manifolds. // Sutherland-Hodgman clipping. public static int ClipSegmentToLine(ClipVertex[/*2*/] vOut, ClipVertex[/*2*/] vIn, Vec2 normal, float offset, int vertexIndexA){ // Start with no output points int numOut = 0; // Calculate the distance of end points to the line float distance0 = Utilities.Dot(normal, vIn[0].v) - offset; float distance1 = Utilities.Dot(normal, vIn[1].v) - offset; // If the points are behind the plane if (distance0 <= 0.0f) vOut[numOut++] = vIn[0]; if (distance1 <= 0.0f) vOut[numOut++] = vIn[1]; // If the points are on different sides of the plane if (distance0 * distance1 < 0.0f) { // Find intersection point of edge and plane float interp = distance0 / (distance0 - distance1); vOut[numOut].v = vIn[0].v + interp * (vIn[1].v - vIn[0].v); // VertexA is hitting edgeB. vOut[numOut].id.cf.indexA = (byte)vertexIndexA; vOut[numOut].id.cf.indexB = vIn[0].id.cf.indexB; vOut[numOut].id.cf.typeA = ContactFeature.FeatureType.e_vertex; vOut[numOut].id.cf.typeB = ContactFeature.FeatureType.e_face; ++numOut; } return numOut; }
// 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 /// Compute the collision manifold between two polygons. public static void CollidePolygons(out Manifold manifold, PolygonShape polyA, Transform xfA, PolygonShape polyB, Transform xfB) { manifold = new Manifold(); float totalRadius = polyA.m_radius + polyB.m_radius; int edgeA = 0; float separationA = FindMaxSeparation(out edgeA, polyA, xfA, polyB, xfB); if (separationA > totalRadius) return; int edgeB = 0; float separationB = FindMaxSeparation(out edgeB, polyB, xfB, polyA, xfA); if (separationB > totalRadius) return; PolygonShape poly1; // reference polygon PolygonShape poly2; // incident polygon Transform xf1, xf2; int edge1; // reference edge bool flip; const float k_relativeTol = 0.98f; const float k_absoluteTol = 0.001f; if (separationB > k_relativeTol * separationA + k_absoluteTol) { poly1 = polyB; poly2 = polyA; xf1 = xfB; xf2 = xfA; edge1 = edgeB; manifold.type = Manifold.ManifoldType.e_faceB; flip = true; } else { poly1 = polyA; poly2 = polyB; xf1 = xfA; xf2 = xfB; edge1 = edgeA; manifold.type = Manifold.ManifoldType.e_faceA; flip = false; } ClipVertex[] incidentEdge = new ClipVertex[2]; FindIncidentEdge(incidentEdge, poly1, xf1, edge1, poly2, xf2); int count1 = poly1.m_count; Vec2[] vertices1 = poly1.m_vertices; int iv1 = edge1; int iv2 = edge1 + 1 < count1 ? edge1 + 1 : 0; Vec2 v11 = vertices1[iv1]; Vec2 v12 = vertices1[iv2]; Vec2 localTangent = v12 - v11; localTangent.Normalize(); Vec2 localNormal = Utilities.Cross(localTangent, 1.0f); Vec2 planePoint = 0.5f * (v11 + v12); Vec2 tangent = Utilities.Mul(xf1.q, localTangent); Vec2 normal = Utilities.Cross(tangent, 1.0f); v11 = Utilities.Mul(xf1, v11); v12 = Utilities.Mul(xf1, v12); // Face offset. float frontOffset = Utilities.Dot(normal, v11); // Side offsets, extended by polytope skin thickness. float sideOffset1 = -Utilities.Dot(tangent, v11) + totalRadius; float sideOffset2 = Utilities.Dot(tangent, v12) + totalRadius; // Clip incident edge against extruded edge1 side edges. ClipVertex[] clipPoints1 = new ClipVertex[2]; ClipVertex[] clipPoints2 = new ClipVertex[2]; int np; // Clip to box side 1 np = ClipSegmentToLine(clipPoints1, incidentEdge, -tangent, sideOffset1, iv1); if (np < 2) return; // Clip to negative box side 1 np = ClipSegmentToLine(clipPoints2, clipPoints1, tangent, sideOffset2, iv2); if (np < 2) { return; } // Now clipPoints2 contains the clipped points. manifold.localNormal = localNormal; manifold.localPoint = planePoint; manifold.points.Clear(); for (int i = 0; i < Settings._maxManifoldPoints; ++i) { float separation = Utilities.Dot(normal, clipPoints2[i].v) - frontOffset; if (separation <= totalRadius) { ManifoldPoint cp = new ManifoldPoint(); cp.localPoint = Utilities.MulT(xf2, clipPoints2[i].v); cp.id = clipPoints2[i].id; if (flip) { // Swap features ContactFeature 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; } manifold.points.Add(cp); } } }
static void FindIncidentEdge(ClipVertex[/*2*/] c, PolygonShape poly1, Transform xf1, int edge1, PolygonShape poly2, Transform xf2) { Vec2[] normals1 = poly1.m_normals; int count2 = poly2.m_count; Vec2[] vertices2 = poly2.m_vertices; Vec2[] normals2 = poly2.m_normals; Utilities.Assert(0 <= edge1 && edge1 < poly1.m_count); // Get the normal of the reference edge in poly2's frame. Vec2 normal1 = Utilities.MulT(xf2.q, Utilities.Mul(xf1.q, normals1[edge1])); // Find the incident edge on poly2. int index = 0; float minDot = Single.MaxValue; for (int i = 0; i < count2; ++i) { float dot = Utilities.Dot(normal1, normals2[i]); if (dot < minDot) { minDot = dot; index = i; } } // Build the clip vertices for the incident edge. int i1 = index; int i2 = i1 + 1 < count2 ? i1 + 1 : 0; c[0].v = Utilities.Mul(xf2, vertices2[i1]); c[0].id.cf.indexA = (byte)edge1; c[0].id.cf.indexB = (byte)i1; c[0].id.cf.typeA = ContactFeature.FeatureType.e_face; c[0].id.cf.typeB = ContactFeature.FeatureType.e_vertex; c[1].v = Utilities.Mul(xf2, vertices2[i2]); c[1].id.cf.indexA = (byte)edge1; c[1].id.cf.indexB = (byte)i2; c[1].id.cf.typeA = ContactFeature.FeatureType.e_face; c[1].id.cf.typeB = ContactFeature.FeatureType.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 /// Compute the collision manifold between two polygons. public static void CollidePolygons(out Manifold manifold, PolygonShape polyA, Transform xfA, PolygonShape polyB, Transform xfB) { manifold = new Manifold(); float totalRadius = polyA.m_radius + polyB.m_radius; int edgeA = 0; float separationA = FindMaxSeparation(out edgeA, polyA, xfA, polyB, xfB); if (separationA > totalRadius) { return; } int edgeB = 0; float separationB = FindMaxSeparation(out edgeB, polyB, xfB, polyA, xfA); if (separationB > totalRadius) { return; } PolygonShape poly1; // reference polygon PolygonShape poly2; // incident polygon Transform xf1, xf2; int edge1; // reference edge bool flip; const float k_relativeTol = 0.98f; const float k_absoluteTol = 0.001f; if (separationB > k_relativeTol * separationA + k_absoluteTol) { poly1 = polyB; poly2 = polyA; xf1 = xfB; xf2 = xfA; edge1 = edgeB; manifold.type = Manifold.ManifoldType.e_faceB; flip = true; } else { poly1 = polyA; poly2 = polyB; xf1 = xfA; xf2 = xfB; edge1 = edgeA; manifold.type = Manifold.ManifoldType.e_faceA; flip = false; } ClipVertex[] incidentEdge = new ClipVertex[2]; FindIncidentEdge(incidentEdge, poly1, xf1, edge1, poly2, xf2); int count1 = poly1.m_count; Vec2[] vertices1 = poly1.m_vertices; int iv1 = edge1; int iv2 = edge1 + 1 < count1 ? edge1 + 1 : 0; Vec2 v11 = vertices1[iv1]; Vec2 v12 = vertices1[iv2]; Vec2 localTangent = v12 - v11; localTangent.Normalize(); Vec2 localNormal = Utilities.Cross(localTangent, 1.0f); Vec2 planePoint = 0.5f * (v11 + v12); Vec2 tangent = Utilities.Mul(xf1.q, localTangent); Vec2 normal = Utilities.Cross(tangent, 1.0f); v11 = Utilities.Mul(xf1, v11); v12 = Utilities.Mul(xf1, v12); // Face offset. float frontOffset = Utilities.Dot(normal, v11); // Side offsets, extended by polytope skin thickness. float sideOffset1 = -Utilities.Dot(tangent, v11) + totalRadius; float sideOffset2 = Utilities.Dot(tangent, v12) + totalRadius; // Clip incident edge against extruded edge1 side edges. ClipVertex[] clipPoints1 = new ClipVertex[2]; ClipVertex[] clipPoints2 = new ClipVertex[2]; int np; // Clip to box side 1 np = ClipSegmentToLine(clipPoints1, incidentEdge, -tangent, sideOffset1, iv1); if (np < 2) { return; } // Clip to negative box side 1 np = ClipSegmentToLine(clipPoints2, clipPoints1, tangent, sideOffset2, iv2); if (np < 2) { return; } // Now clipPoints2 contains the clipped points. manifold.localNormal = localNormal; manifold.localPoint = planePoint; manifold.points.Clear(); for (int i = 0; i < Settings._maxManifoldPoints; ++i) { float separation = Utilities.Dot(normal, clipPoints2[i].v) - frontOffset; if (separation <= totalRadius) { ManifoldPoint cp = new ManifoldPoint(); cp.localPoint = Utilities.MulT(xf2, clipPoints2[i].v); cp.id = clipPoints2[i].id; if (flip) { // Swap features ContactFeature 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; } manifold.points.Add(cp); } } }
// 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 public void Collide(out Manifold manifold, EdgeShape edgeA, Transform xfA, PolygonShape polygonB, Transform xfB) { manifold = new Manifold(); m_xf = Utilities.MulT(xfA, xfB); m_centroidB = Utilities.Mul(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; Vec2 edge1 = m_v2 - m_v1; edge1.Normalize(); m_normal1.Set(edge1.Y, -edge1.X); float offset1 = Utilities.Dot(m_normal1, m_centroidB - m_v1); float offset0 = 0.0f, offset2 = 0.0f; bool convex1 = false, convex2 = false; // Is there a preceding edge? if (hasVertex0) { Vec2 edge0 = m_v1 - m_v0; edge0.Normalize(); m_normal0.Set(edge0.Y, -edge0.X); convex1 = Utilities.Cross(edge0, edge1) >= 0.0f; offset0 = Utilities.Dot(m_normal0, m_centroidB - m_v0); } // Is there a following edge? if (hasVertex3) { Vec2 edge2 = m_v3 - m_v2; edge2.Normalize(); m_normal2.Set(edge2.Y, -edge2.X); convex2 = Utilities.Cross(edge1, edge2) > 0.0f; offset2 = Utilities.Dot(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 (int i = 0; i < polygonB.m_count; ++i) { m_polygonB.vertices[i] = Utilities.Mul(m_xf, polygonB.m_vertices[i]); m_polygonB.normals[i] = Utilities.Mul(m_xf.q, polygonB.m_normals[i]); } m_radius = 2.0f * Settings._polygonRadius; manifold.points.Clear(); EPAxis edgeAxis = ComputeEdgeSeparation(); // If no valid normal can be found than this edge should not collide. if (edgeAxis.type == EPAxisType.e_unknown) { return; } if (edgeAxis.separation > m_radius) { return; } EPAxis polygonAxis = ComputePolygonSeparation(); if (polygonAxis.type != EPAxisType.e_unknown && polygonAxis.separation > m_radius) { return; } // Use hysteresis for jitter reduction. const float k_relativeTol = 0.98f; const float k_absoluteTol = 0.001f; EPAxis primaryAxis; if (polygonAxis.type == EPAxisType.e_unknown) { primaryAxis = edgeAxis; } else if (polygonAxis.separation > k_relativeTol * edgeAxis.separation + k_absoluteTol) { primaryAxis = polygonAxis; } else { primaryAxis = edgeAxis; } ClipVertex[] ie = new ClipVertex[2]; ReferenceFace rf = new ReferenceFace(); if (primaryAxis.type == EPAxisType.e_edgeA) { manifold.type = Manifold.ManifoldType.e_faceA; // Search for the polygon normal that is most anti-parallel to the edge normal. int bestIndex = 0; float bestValue = Utilities.Dot(m_normal, m_polygonB.normals[0]); for (int i = 1; i < m_polygonB.count; ++i) { float value = Utilities.Dot(m_normal, m_polygonB.normals[i]); if (value < bestValue) { bestValue = value; bestIndex = i; } } int i1 = bestIndex; int 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 = (byte)i1; ie[0].id.cf.typeA = ContactFeature.FeatureType.e_face; ie[0].id.cf.typeB = ContactFeature.FeatureType.e_vertex; ie[1].v = m_polygonB.vertices[i2]; ie[1].id.cf.indexA = 0; ie[1].id.cf.indexB = (byte)i2; ie[1].id.cf.typeA = ContactFeature.FeatureType.e_face; ie[1].id.cf.typeB = ContactFeature.FeatureType.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 = Manifold.ManifoldType.e_faceB; ie[0].v = m_v1; ie[0].id.cf.indexA = 0; ie[0].id.cf.indexB = (byte)primaryAxis.index; ie[0].id.cf.typeA = ContactFeature.FeatureType.e_vertex; ie[0].id.cf.typeB = ContactFeature.FeatureType.e_face; ie[1].v = m_v2; ie[1].id.cf.indexA = 0; ie[1].id.cf.indexB = (byte)primaryAxis.index; ie[1].id.cf.typeA = ContactFeature.FeatureType.e_vertex; ie[1].id.cf.typeB = ContactFeature.FeatureType.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 = Utilities.Dot(rf.sideNormal1, rf.v1); rf.sideOffset2 = Utilities.Dot(rf.sideNormal2, rf.v2); // Clip incident edge against extruded edge1 side edges. ClipVertex[] clipPoints1 = new ClipVertex[2]; ClipVertex[] clipPoints2 = new ClipVertex[2]; int np; // Clip to box side 1 np = Collision.ClipSegmentToLine(clipPoints1, ie, rf.sideNormal1, rf.sideOffset1, rf.i1); if (np < Settings._maxManifoldPoints) { return; } // Clip to negative box side 1 np = Collision.ClipSegmentToLine(clipPoints2, clipPoints1, rf.sideNormal2, rf.sideOffset2, rf.i2); if (np < Settings._maxManifoldPoints) { return; } // Now clipPoints2 contains the clipped points. if (primaryAxis.type == EPAxisType.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]; } manifold.points.Clear(); for (int i = 0; i < Settings._maxManifoldPoints; ++i) { float separation; separation = Utilities.Dot(rf.normal, clipPoints2[i].v - rf.v1); if (separation <= m_radius) { ManifoldPoint cp = new ManifoldPoint(); if (primaryAxis.type == EPAxisType.e_edgeA) { cp.localPoint = Utilities.MulT(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; } manifold.points.Add(cp); } } }