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>();
// 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;
}
}
}
}
/// Compute the collision manifold between a polygon and a circle.
public static void CollidePolygonAndCircle(ref Manifold manifold,
PolygonShape polygon, ref XForm xf1,
CircleShape circle, ref XForm xf2)
{
manifold._pointCount = 0;
// Compute circle position in the frame of the polygon.
Vector2 c = MathUtils.Multiply(ref xf2, circle._p);
Vector2 cLocal = MathUtils.MultiplyT(ref xf1, c);
// Find the min separating edge.
int normalIndex = 0;
float separation = -Settings.b2_FLT_MAX;
float radius = polygon._radius + circle._radius;
int vertexCount = polygon._vertexCount;
for (int i = 0; i < vertexCount; ++i)
{
float s = Vector2.Dot(polygon._normals[i], cLocal - polygon._vertices[i]);
if (s > radius)
{
// Early out.
return;
}
if (s > separation)
{
separation = s;
normalIndex = i;
}
}
// Vertices that subtend the incident face.
int vertIndex1 = normalIndex;
int vertIndex2 = vertIndex1 + 1 < vertexCount ? vertIndex1 + 1 : 0;
Vector2 v1 = polygon._vertices[vertIndex1];
Vector2 v2 = polygon._vertices[vertIndex2];
// If the center is inside the polygon ...
if (separation < Settings.b2_FLT_EPSILON)
{
manifold._pointCount = 1;
manifold._type = ManifoldType.FaceA;
manifold._localPlaneNormal = polygon._normals[normalIndex];
manifold._localPoint = 0.5f * (v1 + v2);
var p0 = manifold._points[0];
p0.LocalPoint = circle._p;
p0.Id.Key = 0;
manifold._points[0] = p0;
return;
}
// Compute barycentric coordinates
float u1 = Vector2.Dot(cLocal - v1, v2 - v1);
float u2 = Vector2.Dot(cLocal - v2, v1 - v2);
if (u1 <= 0.0f)
{
if (Vector2.DistanceSquared(cLocal, v1) > radius * radius)
{
return;
}
manifold._pointCount = 1;
manifold._type = ManifoldType.FaceA;
manifold._localPlaneNormal = cLocal - v1;
manifold._localPlaneNormal.Normalize();
manifold._localPoint = v1;
var p0b = manifold._points[0];
p0b.LocalPoint = circle._p;
p0b.Id.Key = 0;
manifold._points[0] = p0b;
}
else if (u2 <= 0.0f)
{
if (Vector2.DistanceSquared(cLocal, v2) > radius * radius)
{
return;
}
manifold._pointCount = 1;
manifold._type = ManifoldType.FaceA;
manifold._localPlaneNormal = cLocal - v2;
manifold._localPlaneNormal.Normalize();
manifold._localPoint = v2;
var p0c = manifold._points[0];
p0c.LocalPoint = circle._p;
p0c.Id.Key = 0;
manifold._points[0] = p0c;
}
else
{
Vector2 faceCenter = 0.5f * (v1 + v2);
float separation2 = Vector2.Dot(cLocal - faceCenter, polygon._normals[vertIndex1]);
if (separation2 > radius)
{
return;
}
manifold._pointCount = 1;
manifold._type = ManifoldType.FaceA;
manifold._localPlaneNormal = polygon._normals[vertIndex1];
manifold._localPoint = faceCenter;
var p0d = manifold._points[0];
p0d.LocalPoint = circle._p;
p0d.Id.Key = 0;
manifold._points[0] = p0d;
}
}
/// Compute the collision manifold between two polygons.
public static void CollidePolygons(ref Manifold manifold,
PolygonShape polyA, ref XForm xfA,
PolygonShape polyB, ref XForm xfB)
{
manifold._pointCount = 0;
float totalRadius = polyA._radius + polyB._radius;
int edgeA = 0;
float separationA = FindMaxSeparation(out edgeA, polyA, ref xfA, polyB, ref xfB);
if (separationA > totalRadius)
return;
int edgeB = 0;
float separationB = FindMaxSeparation(out edgeB, polyB, ref xfB, polyA, ref xfA);
if (separationB > totalRadius)
return;
PolygonShape poly1; // reference polygon
PolygonShape poly2; // incident polygon
XForm xf1, xf2;
int edge1; // reference edge
byte flip;
float k_relativeTol = 0.98f;
float k_absoluteTol = 0.001f;
if (separationB > k_relativeTol * separationA + k_absoluteTol)
{
poly1 = polyB;
poly2 = polyA;
xf1 = xfB;
xf2 = xfA;
edge1 = edgeB;
manifold._type = ManifoldType.FaceB;
flip = 1;
}
else
{
poly1 = polyA;
poly2 = polyB;
xf1 = xfA;
xf2 = xfB;
edge1 = edgeA;
manifold._type = ManifoldType.FaceA;
flip = 0;
}
FixedArray2<ClipVertex> incidentEdge;
FindIncidentEdge(out incidentEdge, poly1, ref xf1, edge1, poly2, ref xf2);
int count1 = poly1._vertexCount;
Vector2 v11 = poly1._vertices[edge1];
Vector2 v12 = edge1 + 1 < count1 ? poly1._vertices[edge1+1] : poly1._vertices[0];
Vector2 dv = v12 - v11;
Vector2 localNormal = MathUtils.Cross(dv, 1.0f);
localNormal.Normalize();
Vector2 planePoint = 0.5f * (v11 + v12);
Vector2 sideNormal = MathUtils.Multiply(ref xf1.R, v12 - v11);
sideNormal.Normalize();
Vector2 frontNormal = MathUtils.Cross(sideNormal, 1.0f);
v11 = MathUtils.Multiply(ref xf1, v11);
v12 = MathUtils.Multiply(ref xf1, v12);
float frontOffset = Vector2.Dot(frontNormal, v11);
float sideOffset1 = -Vector2.Dot(sideNormal, v11);
float sideOffset2 = Vector2.Dot(sideNormal, v12);
// Clip incident edge against extruded edge1 side edges.
FixedArray2<ClipVertex> clipPoints1;
FixedArray2<ClipVertex> clipPoints2;
int np;
// Clip to box side 1
np = ClipSegmentToLine(out clipPoints1, ref incidentEdge, -sideNormal, sideOffset1);
if (np < 2)
return;
// Clip to negative box side 1
np = ClipSegmentToLine(out clipPoints2, ref clipPoints1, sideNormal, sideOffset2);
if (np < 2)
{
return;
}
// Now clipPoints2 contains the clipped points.
manifold._localPlaneNormal = localNormal;
manifold._localPoint = planePoint;
int pointCount = 0;
for (int i = 0; i < Settings.b2_maxManifoldPoints; ++i)
{
float separation = Vector2.Dot(frontNormal, clipPoints2[i].v) - frontOffset;
if (separation <= totalRadius)
{
ManifoldPoint cp = manifold._points[pointCount];
cp.LocalPoint = MathUtils.MultiplyT(ref xf2, clipPoints2[i].v);
cp.Id = clipPoints2[i].id;
cp.Id.Features.Flip = flip;
manifold._points[pointCount] = cp;
++pointCount;
}
}
manifold._pointCount = pointCount;
}
/// Compute the collision manifold between two circles.
public static void CollideCircles(ref Manifold manifold,
CircleShape circle1, ref XForm xf1,
CircleShape circle2, ref XForm xf2)
{
manifold._pointCount = 0;
Vector2 p1 = MathUtils.Multiply(ref xf1, circle1._p);
Vector2 p2 = MathUtils.Multiply(ref xf2, circle2._p);
Vector2 d = p2 - p1;
float distSqr = Vector2.Dot(d, d);
float radius = circle1._radius + circle2._radius;
if (distSqr > radius * radius)
{
return;
}
manifold._type = ManifoldType.Circles;
manifold._localPoint = circle1._p;
manifold._localPlaneNormal = Vector2.Zero;
manifold._pointCount = 1;
var p0 = manifold._points[0];
p0.LocalPoint = circle2._p;
p0.Id.Key = 0;
manifold._points[0] = p0;
}
public FixedArray2<Vector2> _points; ///< world contact point (point of intersection)
#endregion Fields
#region Constructors
/// Evaluate the manifold with supplied transforms. This assumes
/// modest motion from the original state. This does not change the
/// point count, impulses, etc. The radii must come from the shapes
/// that generated the manifold.
public WorldManifold(ref Manifold manifold,
ref XForm xfA, float radiusA,
ref XForm xfB, float radiusB)
{
_normal = Vector2.Zero;
_points = new FixedArray2<Vector2>();
if (manifold._pointCount == 0)
{
return;
}
switch (manifold._type)
{
case ManifoldType.Circles:
{
Vector2 pointA = MathUtils.Multiply(ref xfA, manifold._localPoint);
Vector2 pointB = MathUtils.Multiply(ref xfB, manifold._points[0].LocalPoint);
Vector2 normal = new Vector2(1.0f, 0.0f);
if (Vector2.DistanceSquared(pointA, pointB) > Settings.b2_FLT_EPSILON * Settings.b2_FLT_EPSILON)
{
normal = pointB - pointA;
normal.Normalize();
}
_normal = normal;
Vector2 cA = pointA + radiusA * normal;
Vector2 cB = pointB - radiusB * normal;
_points[0] = 0.5f * (cA + cB);
}
break;
case ManifoldType.FaceA:
{
Vector2 normal = MathUtils.Multiply(ref xfA.R, manifold._localPlaneNormal);
Vector2 planePoint = MathUtils.Multiply(ref xfA, manifold._localPoint);
// Ensure normal points from A to B.
_normal = normal;
for (int i = 0; i < manifold._pointCount; ++i)
{
Vector2 clipPoint = MathUtils.Multiply(ref xfB, manifold._points[i].LocalPoint);
Vector2 cA = clipPoint + (radiusA - Vector2.Dot(clipPoint - planePoint, normal)) * normal;
Vector2 cB = clipPoint - radiusB * normal;
_points[i] = 0.5f * (cA + cB);
}
}
break;
case ManifoldType.FaceB:
{
Vector2 normal = MathUtils.Multiply(ref xfB.R, manifold._localPlaneNormal);
Vector2 planePoint = MathUtils.Multiply(ref xfB, manifold._localPoint);
// Ensure normal points from A to B.
_normal = -normal;
for (int i = 0; i < manifold._pointCount; ++i)
{
Vector2 clipPoint = MathUtils.Multiply(ref xfA, manifold._points[i].LocalPoint);
Vector2 cA = clipPoint - radiusA * normal;
Vector2 cB = clipPoint + (radiusB - Vector2.Dot(clipPoint - planePoint, normal)) * normal;
_points[i] = 0.5f * (cA + cB);
}
}
break;
}
}
/// Compute the collision manifold between two polygons.
public static void CollidePolygons(ref Manifold manifold,
PolygonShape polyA, ref XForm xfA,
PolygonShape polyB, ref XForm xfB)
{
manifold._pointCount = 0;
float totalRadius = polyA._radius + polyB._radius;
int edgeA = 0;
float separationA = FindMaxSeparation(out edgeA, polyA, ref xfA, polyB, ref xfB);
if (separationA > totalRadius)
{
return;
}
int edgeB = 0;
float separationB = FindMaxSeparation(out edgeB, polyB, ref xfB, polyA, ref xfA);
if (separationB > totalRadius)
{
return;
}
PolygonShape poly1; // reference polygon
PolygonShape poly2; // incident polygon
XForm xf1, xf2;
int edge1; // reference edge
byte flip;
float k_relativeTol = 0.98f;
float k_absoluteTol = 0.001f;
if (separationB > k_relativeTol * separationA + k_absoluteTol)
{
poly1 = polyB;
poly2 = polyA;
xf1 = xfB;
xf2 = xfA;
edge1 = edgeB;
manifold._type = ManifoldType.FaceB;
flip = 1;
}
else
{
poly1 = polyA;
poly2 = polyB;
xf1 = xfA;
xf2 = xfB;
edge1 = edgeA;
manifold._type = ManifoldType.FaceA;
flip = 0;
}
FixedArray2 <ClipVertex> incidentEdge;
FindIncidentEdge(out incidentEdge, poly1, ref xf1, edge1, poly2, ref xf2);
int count1 = poly1._vertexCount;
Vector2 v11 = poly1._vertices[edge1];
Vector2 v12 = edge1 + 1 < count1 ? poly1._vertices[edge1 + 1] : poly1._vertices[0];
Vector2 dv = v12 - v11;
Vector2 localNormal = MathUtils.Cross(dv, 1.0f);
localNormal.Normalize();
Vector2 planePoint = 0.5f * (v11 + v12);
Vector2 sideNormal = MathUtils.Multiply(ref xf1.R, v12 - v11);
sideNormal.Normalize();
Vector2 frontNormal = MathUtils.Cross(sideNormal, 1.0f);
v11 = MathUtils.Multiply(ref xf1, v11);
v12 = MathUtils.Multiply(ref xf1, v12);
float frontOffset = Vector2.Dot(frontNormal, v11);
float sideOffset1 = -Vector2.Dot(sideNormal, v11);
float sideOffset2 = Vector2.Dot(sideNormal, v12);
// Clip incident edge against extruded edge1 side edges.
FixedArray2 <ClipVertex> clipPoints1;
FixedArray2 <ClipVertex> clipPoints2;
int np;
// Clip to box side 1
np = ClipSegmentToLine(out clipPoints1, ref incidentEdge, -sideNormal, sideOffset1);
if (np < 2)
{
return;
}
// Clip to negative box side 1
np = ClipSegmentToLine(out clipPoints2, ref clipPoints1, sideNormal, sideOffset2);
if (np < 2)
{
return;
}
// Now clipPoints2 contains the clipped points.
manifold._localPlaneNormal = localNormal;
manifold._localPoint = planePoint;
int pointCount = 0;
for (int i = 0; i < Settings.b2_maxManifoldPoints; ++i)
{
float separation = Vector2.Dot(frontNormal, clipPoints2[i].v) - frontOffset;
if (separation <= totalRadius)
{
ManifoldPoint cp = manifold._points[pointCount];
cp.LocalPoint = MathUtils.MultiplyT(ref xf2, clipPoints2[i].v);
cp.Id = clipPoints2[i].id;
cp.Id.Features.Flip = flip;
manifold._points[pointCount] = cp;
++pointCount;
}
}
manifold._pointCount = pointCount;
}
/// Compute the collision manifold between a polygon and a circle.
public static void CollidePolygonAndCircle(ref Manifold manifold,
PolygonShape polygon, ref XForm xf1,
CircleShape circle, ref XForm xf2)
{
manifold._pointCount = 0;
// Compute circle position in the frame of the polygon.
Vector2 c = MathUtils.Multiply(ref xf2, circle._p);
Vector2 cLocal = MathUtils.MultiplyT(ref xf1, c);
// Find the min separating edge.
int normalIndex = 0;
float separation = -Settings.b2_FLT_MAX;
float radius = polygon._radius + circle._radius;
int vertexCount = polygon._vertexCount;
for (int i = 0; i < vertexCount; ++i)
{
float s = Vector2.Dot(polygon._normals[i], cLocal - polygon._vertices[i]);
if (s > radius)
{
// Early out.
return;
}
if (s > separation)
{
separation = s;
normalIndex = i;
}
}
// Vertices that subtend the incident face.
int vertIndex1 = normalIndex;
int vertIndex2 = vertIndex1 + 1 < vertexCount ? vertIndex1 + 1 : 0;
Vector2 v1 = polygon._vertices[vertIndex1];
Vector2 v2 = polygon._vertices[vertIndex2];
// If the center is inside the polygon ...
if (separation < Settings.b2_FLT_EPSILON)
{
manifold._pointCount = 1;
manifold._type = ManifoldType.FaceA;
manifold._localPlaneNormal = polygon._normals[normalIndex];
manifold._localPoint = 0.5f * (v1 + v2);
var p0 = manifold._points[0];
p0.LocalPoint = circle._p;
p0.Id.Key = 0;
manifold._points[0] = p0;
return;
}
// Compute barycentric coordinates
float u1 = Vector2.Dot(cLocal - v1, v2 - v1);
float u2 = Vector2.Dot(cLocal - v2, v1 - v2);
if (u1 <= 0.0f)
{
if (Vector2.DistanceSquared(cLocal, v1) > radius * radius)
{
return;
}
manifold._pointCount = 1;
manifold._type = ManifoldType.FaceA;
manifold._localPlaneNormal = cLocal - v1;
manifold._localPlaneNormal.Normalize();
manifold._localPoint = v1;
var p0b = manifold._points[0];
p0b.LocalPoint = circle._p;
p0b.Id.Key = 0;
manifold._points[0] = p0b;
}
else if (u2 <= 0.0f)
{
if (Vector2.DistanceSquared(cLocal, v2) > radius * radius)
{
return;
}
manifold._pointCount = 1;
manifold._type = ManifoldType.FaceA;
manifold._localPlaneNormal = cLocal - v2;
manifold._localPlaneNormal.Normalize();
manifold._localPoint = v2;
var p0c = manifold._points[0];
p0c.LocalPoint = circle._p;
p0c.Id.Key = 0;
manifold._points[0] = p0c;
}
else
{
Vector2 faceCenter = 0.5f * (v1 + v2);
float separation2 = Vector2.Dot(cLocal - faceCenter, polygon._normals[vertIndex1]);
if (separation2 > radius)
{
return;
}
manifold._pointCount = 1;
manifold._type = ManifoldType.FaceA;
manifold._localPlaneNormal = polygon._normals[vertIndex1];
manifold._localPoint = faceCenter;
var p0d = manifold._points[0];
p0d.LocalPoint = circle._p;
p0d.Id.Key = 0;
manifold._points[0] = p0d;
}
}
/// Evaluate the manifold with supplied transforms. This assumes
/// modest motion from the original state. This does not change the
/// point count, impulses, etc. The radii must come from the shapes
/// that generated the manifold.
public WorldManifold(ref Manifold manifold,
ref XForm xfA, float radiusA,
ref XForm xfB, float radiusB)
{
_normal = Vector2.Zero;
_points = new FixedArray2 <Vector2>();
if (manifold._pointCount == 0)
{
return;
}
switch (manifold._type)
{
case ManifoldType.Circles:
{
Vector2 pointA = MathUtils.Multiply(ref xfA, manifold._localPoint);
Vector2 pointB = MathUtils.Multiply(ref xfB, manifold._points[0].LocalPoint);
Vector2 normal = new Vector2(1.0f, 0.0f);
if (Vector2.DistanceSquared(pointA, pointB) > Settings.b2_FLT_EPSILON * Settings.b2_FLT_EPSILON)
{
normal = pointB - pointA;
normal.Normalize();
}
_normal = normal;
Vector2 cA = pointA + radiusA * normal;
Vector2 cB = pointB - radiusB * normal;
_points[0] = 0.5f * (cA + cB);
}
break;
case ManifoldType.FaceA:
{
Vector2 normal = MathUtils.Multiply(ref xfA.R, manifold._localPlaneNormal);
Vector2 planePoint = MathUtils.Multiply(ref xfA, manifold._localPoint);
// Ensure normal points from A to B.
_normal = normal;
for (int i = 0; i < manifold._pointCount; ++i)
{
Vector2 clipPoint = MathUtils.Multiply(ref xfB, manifold._points[i].LocalPoint);
Vector2 cA = clipPoint + (radiusA - Vector2.Dot(clipPoint - planePoint, normal)) * normal;
Vector2 cB = clipPoint - radiusB * normal;
_points[i] = 0.5f * (cA + cB);
}
}
break;
case ManifoldType.FaceB:
{
Vector2 normal = MathUtils.Multiply(ref xfB.R, manifold._localPlaneNormal);
Vector2 planePoint = MathUtils.Multiply(ref xfB, manifold._localPoint);
// Ensure normal points from A to B.
_normal = -normal;
for (int i = 0; i < manifold._pointCount; ++i)
{
Vector2 clipPoint = MathUtils.Multiply(ref xfA, manifold._points[i].LocalPoint);
Vector2 cA = clipPoint - radiusA * normal;
Vector2 cB = clipPoint + (radiusB - Vector2.Dot(clipPoint - planePoint, normal)) * normal;
_points[i] = 0.5f * (cA + cB);
}
}
break;
}
}
