public static void CollideEdgeAndPolygon(ref Manifold manifold, EdgeShape edgeA, ref Transform xfA, PolygonShape polygonB, ref Transform xfB)
{
manifold.PointCount = 0;
Transform xf = MathUtils.MulT(xfA, xfB);
Vector2 centroidB = MathUtils.Mul(ref xf, polygonB.MassData.Centroid);
Vector2 v1 = edgeA._vertex1;
Vector2 v2 = edgeA._vertex2;
Vector2 edge1 = v2 - v1;
edge1.Normalize();
// Normal points to the right for a CCW winding
Vector2 normal1 = new Vector2(edge1.Y, -edge1.X);
float offset1 = MathUtils.Dot(normal1, centroidB - v1);
bool oneSided = edgeA._oneSided;
if (oneSided && offset1 < 0.0f)
{
return;
}
// Get polygonB in frameA
TempPolygon tempPolygonB = new TempPolygon();
tempPolygonB.Count = polygonB.Vertices.Count;
for (int i = 0; i < polygonB.Vertices.Count; ++i)
{
tempPolygonB.Vertices[i] = MathUtils.Mul(ref xf, polygonB._vertices[i]);
tempPolygonB.Normals[i] = MathUtils.Mul(xf.q, polygonB._normals[i]);
}
float radius = polygonB._radius + edgeA._radius;
EPAxis edgeAxis = ComputeEdgeSeparation(tempPolygonB, v1, normal1);
if (edgeAxis.Separation > radius)
{
return;
}
EPAxis polygonAxis = ComputePolygonSeparation(tempPolygonB, v1, v2);
if (polygonAxis.Separation > radius)
{
return;
}
// Use hysteresis for jitter reduction.
const float k_relativeTol = 0.98f;
const float k_absoluteTol = 0.001f;
EPAxis primaryAxis;
if (polygonAxis.Separation - radius > k_relativeTol * (edgeAxis.Separation - radius) + k_absoluteTol)
{
primaryAxis = polygonAxis;
}
else
{
primaryAxis = edgeAxis;
}
if (oneSided)
{
// Smooth collision
// See https://box2d.org/posts/2020/06/ghost-collisions/
Vector2 edge0 = v1 - edgeA._vertex0;
edge0.Normalize();
Vector2 normal0 = new Vector2(edge0.Y, -edge0.X);
bool convex1 = MathUtils.Cross(edge0, edge1) >= 0.0f;
Vector2 edge2 = edgeA._vertex3 - v2;
edge2.Normalize();
Vector2 normal2 = new Vector2(edge2.Y, -edge2.X);
bool convex2 = MathUtils.Cross(edge1, edge2) >= 0.0f;
const float sinTol = 0.1f;
bool side1 = MathUtils.Dot(primaryAxis.Normal, edge1) <= 0.0f;
// Check Gauss Map
if (side1)
{
if (convex1)
{
if (MathUtils.Cross(primaryAxis.Normal, normal0) > sinTol)
{
// Skip region
return;
}
// Admit region
}
else
{
// Snap region
primaryAxis = edgeAxis;
}
}
else
{
if (convex2)
{
if (MathUtils.Cross(normal2, primaryAxis.Normal) > sinTol)
{
// Skip region
return;
}
// Admit region
}
else
{
// Snap region
primaryAxis = edgeAxis;
}
}
}
FixedArray2 <ClipVertex> clipPoints = new FixedArray2 <ClipVertex>();
ReferenceFace ref1;
if (primaryAxis.Type == EPAxisType.EdgeA)
{
manifold.Type = ManifoldType.FaceA;
// Search for the polygon normal that is most anti-parallel to the edge normal.
int bestIndex = 0;
float bestValue = MathUtils.Dot(primaryAxis.Normal, tempPolygonB.Normals[0]);
for (int i = 1; i < tempPolygonB.Count; ++i)
{
float value = MathUtils.Dot(primaryAxis.Normal, tempPolygonB.Normals[i]);
if (value < bestValue)
{
bestValue = value;
bestIndex = i;
}
}
int i1 = bestIndex;
int i2 = i1 + 1 < tempPolygonB.Count ? i1 + 1 : 0;
clipPoints.Value0.V = tempPolygonB.Vertices[i1];
clipPoints.Value0.Id.ContactFeature.IndexA = 0;
clipPoints.Value0.Id.ContactFeature.IndexB = (byte)i1;
clipPoints.Value0.Id.ContactFeature.TypeA = ContactFeatureType.Face;
clipPoints.Value0.Id.ContactFeature.TypeB = ContactFeatureType.Vertex;
clipPoints.Value1.V = tempPolygonB.Vertices[i2];
clipPoints.Value1.Id.ContactFeature.IndexA = 0;
clipPoints.Value1.Id.ContactFeature.IndexB = (byte)i2;
clipPoints.Value1.Id.ContactFeature.TypeA = ContactFeatureType.Face;
clipPoints.Value1.Id.ContactFeature.TypeB = ContactFeatureType.Vertex;
ref1.i1 = 0;
ref1.i2 = 1;
ref1.v1 = v1;
ref1.v2 = v2;
ref1.Normal = primaryAxis.Normal;
ref1.SideNormal1 = -edge1;
ref1.SideNormal2 = edge1;
}
else
{
manifold.Type = ManifoldType.FaceB;
clipPoints.Value0.V = v2;
clipPoints.Value0.Id.ContactFeature.IndexA = 1;
clipPoints.Value0.Id.ContactFeature.IndexB = (byte)primaryAxis.Index;
clipPoints.Value0.Id.ContactFeature.TypeA = ContactFeatureType.Vertex;
clipPoints.Value0.Id.ContactFeature.TypeB = ContactFeatureType.Face;
clipPoints.Value1.V = v1;
clipPoints.Value1.Id.ContactFeature.IndexA = 0;
clipPoints.Value1.Id.ContactFeature.IndexB = (byte)primaryAxis.Index;
clipPoints.Value1.Id.ContactFeature.TypeA = ContactFeatureType.Vertex;
clipPoints.Value1.Id.ContactFeature.TypeB = ContactFeatureType.Face;
ref1.i1 = primaryAxis.Index;
ref1.i2 = ref1.i1 + 1 < tempPolygonB.Count ? ref1.i1 + 1 : 0;
ref1.v1 = tempPolygonB.Vertices[ref1.i1];
ref1.v2 = tempPolygonB.Vertices[ref1.i2];
ref1.Normal = tempPolygonB.Normals[ref1.i1];
// CCW winding
ref1.SideNormal1 = new Vector2(ref1.Normal.Y, -ref1.Normal.X);
ref1.SideNormal2 = -ref1.SideNormal1;
}
ref1.SideOffset1 = MathUtils.Dot(ref1.SideNormal1, ref1.v1);
ref1.SideOffset2 = MathUtils.Dot(ref1.SideNormal2, ref1.v2);
// Clip incident edge against reference face side planes
FixedArray2 <ClipVertex> clipPoints1;
FixedArray2 <ClipVertex> clipPoints2;
int np;
// Clip to side 1
np = Collision.ClipSegmentToLine(out clipPoints1, ref clipPoints, ref1.SideNormal1, ref1.SideOffset1, ref1.i1);
if (np < Settings.MaxManifoldPoints)
{
return;
}
// Clip to side 2
np = Collision.ClipSegmentToLine(out clipPoints2, ref clipPoints1, ref1.SideNormal2, ref1.SideOffset2, ref1.i2);
if (np < Settings.MaxManifoldPoints)
{
return;
}
// Now clipPoints2 contains the clipped points.
if (primaryAxis.Type == EPAxisType.EdgeA)
{
manifold.LocalNormal = ref1.Normal;
manifold.LocalPoint = ref1.v1;
}
else
{
manifold.LocalNormal = polygonB._normals[ref1.i1];
manifold.LocalPoint = polygonB._vertices[ref1.i1];
}
int pointCount = 0;
for (int i = 0; i < Settings.MaxManifoldPoints; ++i)
{
float separation = MathUtils.Dot(ref1.Normal, clipPoints2[i].V - ref1.v1);
if (separation <= radius)
{
ManifoldPoint cp = manifold.Points[pointCount];
if (primaryAxis.Type == EPAxisType.EdgeA)
{
cp.LocalPoint = MathUtils.MulT(xf, clipPoints2[i].V);
cp.Id = clipPoints2[i].Id;
}
else
{
cp.LocalPoint = clipPoints2[i].V;
cp.Id.ContactFeature.TypeA = clipPoints2[i].Id.ContactFeature.TypeB;
cp.Id.ContactFeature.TypeB = clipPoints2[i].Id.ContactFeature.TypeA;
cp.Id.ContactFeature.IndexA = clipPoints2[i].Id.ContactFeature.IndexB;
cp.Id.ContactFeature.IndexB = clipPoints2[i].Id.ContactFeature.IndexA;
}
manifold.Points[pointCount] = cp;
++pointCount;
}
}
manifold.PointCount = pointCount;
}
/// <summary>Compute the collision manifold between two polygons.</summary>
public static void CollidePolygons(ref Manifold manifold, PolygonShape polyA, ref Transform xfA, PolygonShape polyB, ref Transform xfB)
{
// 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
manifold.PointCount = 0;
float totalRadius = polyA._radius + polyB._radius;
float separationA = FindMaxSeparation(out int edgeA, polyA, ref xfA, polyB, ref xfB);
if (separationA > totalRadius)
{
return;
}
float separationB = FindMaxSeparation(out int edgeB, polyB, ref xfB, polyA, ref xfA);
if (separationB > totalRadius)
{
return;
}
PolygonShape poly1; // reference polygon
PolygonShape poly2; // incident polygon
Transform xf1, xf2;
int edge1; // reference edge
bool flip;
float k_tol = 0.1f * Settings.LinearSlop;
if (separationB > separationA + k_tol)
{
poly1 = polyB;
poly2 = polyA;
xf1 = xfB;
xf2 = xfA;
edge1 = edgeB;
manifold.Type = ManifoldType.FaceB;
flip = true;
}
else
{
poly1 = polyA;
poly2 = polyB;
xf1 = xfA;
xf2 = xfB;
edge1 = edgeA;
manifold.Type = ManifoldType.FaceA;
flip = false;
}
FindIncidentEdge(out FixedArray2 <ClipVertex> incidentEdge, poly1, ref xf1, edge1, poly2, ref xf2);
int count1 = poly1._vertices.Count;
Vertices vertices1 = poly1._vertices;
int iv1 = edge1;
int iv2 = edge1 + 1 < count1 ? edge1 + 1 : 0;
Vector2 v11 = vertices1[iv1];
Vector2 v12 = vertices1[iv2];
Vector2 localTangent = v12 - v11;
localTangent.Normalize();
Vector2 localNormal = MathUtils.Cross(localTangent, 1.0f);
Vector2 planePoint = 0.5f * (v11 + v12);
Vector2 tangent = MathUtils.Mul(ref xf1.q, localTangent);
Vector2 normal = MathUtils.Cross(tangent, 1.0f);
v11 = MathUtils.Mul(ref xf1, v11);
v12 = MathUtils.Mul(ref xf1, v12);
// Face offset.
float frontOffset = Vector2.Dot(normal, v11);
// Side offsets, extended by polytope skin thickness.
float sideOffset1 = -Vector2.Dot(tangent, v11) + totalRadius;
float sideOffset2 = Vector2.Dot(tangent, v12) + totalRadius;
// Clip incident edge against extruded edge1 side edges.
// Clip to box side 1
int np = Collision.ClipSegmentToLine(out FixedArray2 <ClipVertex> clipPoints1, ref incidentEdge, -tangent, sideOffset1, iv1);
if (np < 2)
{
return;
}
// Clip to negative box side 1
np = Collision.ClipSegmentToLine(out FixedArray2 <ClipVertex> clipPoints2, ref clipPoints1, tangent, sideOffset2, iv2);
if (np < 2)
{
return;
}
// Now clipPoints2 contains the clipped points.
manifold.LocalNormal = localNormal;
manifold.LocalPoint = planePoint;
int pointCount = 0;
for (int i = 0; i < Settings.MaxManifoldPoints; ++i)
{
float separation = Vector2.Dot(normal, clipPoints2[i].V) - frontOffset;
if (separation <= totalRadius)
{
ManifoldPoint cp = manifold.Points[pointCount];
cp.LocalPoint = MathUtils.MulT(ref xf2, clipPoints2[i].V);
cp.Id = clipPoints2[i].Id;
if (flip)
{
// Swap features
ContactFeature cf = cp.Id.ContactFeature;
cp.Id.ContactFeature.IndexA = cf.IndexB;
cp.Id.ContactFeature.IndexB = cf.IndexA;
cp.Id.ContactFeature.TypeA = cf.TypeB;
cp.Id.ContactFeature.TypeB = cf.TypeA;
}
manifold.Points[pointCount] = cp;
++pointCount;
}
}
manifold.PointCount = pointCount;
}
/// <summary>Compute contact points for edge versus circle. This accounts for edge connectivity.</summary>
/// <param name="manifold">The manifold.</param>
/// <param name="edgeA">The edge A.</param>
/// <param name="transformA">The transform A.</param>
/// <param name="circleB">The circle B.</param>
/// <param name="transformB">The transform B.</param>
public static void CollideEdgeAndCircle(ref Manifold manifold, EdgeShape edgeA, ref Transform transformA, CircleShape circleB, ref Transform transformB)
{
manifold.PointCount = 0;
// Compute circle in frame of edge
Vector2 Q = MathUtils.MulT(ref transformA, MathUtils.Mul(ref transformB, ref circleB._position));
Vector2 A = edgeA.Vertex1, B = edgeA.Vertex2;
Vector2 e = B - A;
// Normal points to the right for a CCW winding
Vector2 n = new Vector2(e.Y, -e.X);
float offset = MathUtils.Dot(n, Q - A);
bool oneSided = edgeA.OneSided;
if (oneSided && offset < 0.0f)
{
return;
}
// Barycentric coordinates
float u = Vector2.Dot(e, B - Q);
float v = Vector2.Dot(e, Q - A);
float radius = edgeA.Radius + circleB.Radius;
ContactFeature cf;
cf.IndexB = 0;
cf.TypeB = ContactFeatureType.Vertex;
// Region A
if (v <= 0.0f)
{
Vector2 P1 = A;
Vector2 d1 = Q - P1;
float dd1 = Vector2.Dot(d1, d1);
if (dd1 > radius * radius)
{
return;
}
// Is there an edge connected to A?
if (edgeA.OneSided)
{
Vector2 A1 = edgeA.Vertex0;
Vector2 B1 = A;
Vector2 e1 = B1 - A1;
float u1 = Vector2.Dot(e1, B1 - Q);
// Is the circle in Region AB of the previous edge?
if (u1 > 0.0f)
{
return;
}
}
cf.IndexA = 0;
cf.TypeA = ContactFeatureType.Vertex;
manifold.PointCount = 1;
manifold.Type = ManifoldType.Circles;
manifold.LocalNormal = Vector2.Zero;
manifold.LocalPoint = P1;
manifold.Points.Value0.Id.Key = 0;
manifold.Points.Value0.Id.ContactFeature = cf;
manifold.Points.Value0.LocalPoint = circleB.Position;
return;
}
// Region B
if (u <= 0.0f)
{
Vector2 P2 = B;
Vector2 d2 = Q - P2;
float dd2 = Vector2.Dot(d2, d2);
if (dd2 > radius * radius)
{
return;
}
// Is there an edge connected to B?
if (edgeA.OneSided)
{
Vector2 B2 = edgeA.Vertex3;
Vector2 A2 = B;
Vector2 e2 = B2 - A2;
float v2 = Vector2.Dot(e2, Q - A2);
// Is the circle in Region AB of the next edge?
if (v2 > 0.0f)
{
return;
}
}
cf.IndexA = 1;
cf.TypeA = (byte)ContactFeatureType.Vertex;
manifold.PointCount = 1;
manifold.Type = ManifoldType.Circles;
manifold.LocalNormal = Vector2.Zero;
manifold.LocalPoint = P2;
manifold.Points.Value0.Id.Key = 0;
manifold.Points.Value0.Id.ContactFeature = cf;
manifold.Points.Value0.LocalPoint = circleB.Position;
return;
}
// Region AB
float den = Vector2.Dot(e, e);
Debug.Assert(den > 0.0f);
Vector2 P = (1.0f / den) * (u * A + v * B);
Vector2 d = Q - P;
float dd = Vector2.Dot(d, d);
if (dd > radius * radius)
{
return;
}
if (offset < 0.0f)
{
n = new Vector2(-n.X, -n.Y);
}
n.Normalize();
cf.IndexA = 0;
cf.TypeA = ContactFeatureType.Face;
manifold.PointCount = 1;
manifold.Type = ManifoldType.FaceA;
manifold.LocalNormal = n;
manifold.LocalPoint = A;
manifold.Points.Value0.Id.Key = 0;
manifold.Points.Value0.Id.ContactFeature = cf;
manifold.Points.Value0.LocalPoint = circleB.Position;
}
public static void GetPointStates(out FixedArray2 <PointState> state1, out FixedArray2 <PointState> state2, ref Manifold manifold1, ref Manifold manifold2)
{
state1 = new FixedArray2 <PointState>();
state2 = new FixedArray2 <PointState>();
for (int i = 0; i < Settings.MaxManifoldPoints; ++i)
{
state1[i] = PointState.Null;
state2[i] = PointState.Null;
}
// Detect persists and removes.
for (int i = 0; i < manifold1.PointCount; ++i)
{
ContactId id = manifold1.Points[i].Id;
state1[i] = PointState.Remove;
for (int j = 0; j < manifold2.PointCount; ++j)
{
if (manifold2.Points[j].Id.Key == id.Key)
{
state1[i] = PointState.Persist;
break;
}
}
}
// Detect persists and adds.
for (int i = 0; i < manifold2.PointCount; ++i)
{
ContactId id = manifold2.Points[i].Id;
state2[i] = PointState.Add;
for (int j = 0; j < manifold1.PointCount; ++j)
{
if (manifold1.Points[j].Id.Key == id.Key)
{
state2[i] = PointState.Persist;
break;
}
}
}
}
