void TryToEscape(TriangleShape triangle, ref Vector3 position)
{
if (++escapeAttempts == EscapeAttemptPeriod && GetVoronoiRegion(triangle, ref position) == VoronoiRegion.ABC)
{
escapeAttempts = 0;
state = CollisionState.Plane;
}
}
/// <summary>
/// Returns a resource to the pool.
/// </summary>
/// <param name="triangle">Triangle to return.</param>
public static void GiveBack(TriangleShape triangle)
{
if (SubPoolTriangleShape == null)
{
SubPoolTriangleShape = new UnsafeResourcePool <TriangleShape>();
}
triangle.collisionMargin = 0;
triangle.sidedness = TriangleSidedness.DoubleSided;
SubPoolTriangleShape.GiveBack(triangle);
}
private bool DoExternalSeparated(TriangleShape triangle, out TinyStructList <ContactData> contactList)
{
if (GJKToolbox.AreShapesIntersecting(convex, triangle, ref Toolbox.RigidIdentity, ref Toolbox.RigidIdentity, ref localSeparatingAxis))
{
state = CollisionState.ExternalNear;
return(DoExternalNear(triangle, out contactList));
}
TryToEscape();
contactList = new TinyStructList <ContactData>();
return(false);
}
protected override bool ConfigureLocalTriangle(int i, TriangleShape localTriangleShape, out TriangleIndices indices)
{
var data = mesh.Shape.TriangleMesh.Data;
int triangleIndex = overlappedTriangles.Elements[i];
TriangleSidedness sidedness;
//TODO: Note superhack; don't do this in v2.
if (IsQuery)
{
sidedness = TriangleSidedness.DoubleSided;
}
else
{
switch (mesh.Shape.solidity)
{
case MobileMeshSolidity.Clockwise:
sidedness = TriangleSidedness.Clockwise;
break;
case MobileMeshSolidity.Counterclockwise:
sidedness = TriangleSidedness.Counterclockwise;
break;
case MobileMeshSolidity.DoubleSided:
sidedness = TriangleSidedness.DoubleSided;
break;
default:
sidedness = mesh.Shape.SidednessWhenSolid;
break;
}
}
localTriangleShape.sidedness = sidedness;
localTriangleShape.collisionMargin = 0;
indices = new TriangleIndices
{
A = data.indices[triangleIndex],
B = data.indices[triangleIndex + 1],
C = data.indices[triangleIndex + 2]
};
localTriangleShape.vA = data.vertices[indices.A];
localTriangleShape.vB = data.vertices[indices.B];
localTriangleShape.vC = data.vertices[indices.C];
return(true);
}
protected override bool ConfigureLocalTriangle(int i, TriangleShape localTriangleShape, out TriangleIndices indices)
{
int triangleIndex = overlappedTriangles.Elements[i];
var data = mesh.Mesh.Data;
localTriangleShape.vA = data.vertices[data.indices[triangleIndex]];
localTriangleShape.vB = data.vertices[data.indices[triangleIndex + 1]];
localTriangleShape.vC = data.vertices[data.indices[triangleIndex + 2]];
//TODO: Note the IsQuery hack to avoid missing contacts. Avoid doing this in v2.
localTriangleShape.sidedness = IsQuery ? TriangleSidedness.DoubleSided : mesh.sidedness;
localTriangleShape.collisionMargin = 0;
indices = new TriangleIndices
{
A = data.indices[triangleIndex],
B = data.indices[triangleIndex + 1],
C = data.indices[triangleIndex + 2]
};
return(true);
}
protected override bool ConfigureLocalTriangle(int i, TriangleShape localTriangleShape, out TriangleIndices indices)
{
TerrainVertexIndices a, b, c;
terrain.Shape.GetLocalIndices(overlappedTriangles[i], out a, out b, out c);
int terrainWidth = terrain.Shape.Heights.GetLength(0);
indices.A = a.ToSequentialIndex(terrainWidth);
indices.B = b.ToSequentialIndex(terrainWidth);
indices.C = c.ToSequentialIndex(terrainWidth);
terrain.Shape.GetLocalPosition(a.ColumnIndex, a.RowIndex, out localTriangleShape.vA);
terrain.Shape.GetLocalPosition(b.ColumnIndex, b.RowIndex, out localTriangleShape.vB);
terrain.Shape.GetLocalPosition(c.ColumnIndex, c.RowIndex, out localTriangleShape.vC);
localTriangleShape.collisionMargin = 0;
localTriangleShape.sidedness = terrain.sidedness;
//Unlike other 'instanced' geometries, terrains are almost always axis aligned in some way and/or have low triangle density relative to what they are colliding with.
//Instead of performing additional tests, just assume that it's a fairly regular situation.
return(true);
}
//Relies on the triangle being located in the local space of the convex object. The convex transform is used to transform the
//contact points back from the convex's local space into world space.
///<summary>
/// Generates a contact between the triangle and convex.
///</summary>
/// <param name="triangle">Triangle to test the convex against. The input triangle should be transformed into the local space of the convex.</param>
///<param name="contactList">Contact between the shapes, if any.</param>
///<returns>Whether or not the shapes are colliding.</returns>
public override bool GenerateContactCandidates(TriangleShape triangle, out TinyStructList <ContactData> contactList)
{
switch (state)
{
case CollisionState.Plane:
return(DoPlaneTest(triangle, out contactList));
case CollisionState.ExternalSeparated:
return(DoExternalSeparated(triangle, out contactList));
case CollisionState.ExternalNear:
return(DoExternalNear(triangle, out contactList));
case CollisionState.Deep:
return(DoDeepContact(triangle, out contactList));
default:
contactList = new TinyStructList <ContactData>();
return(false);
}
}
protected void GetNormal(ref Vector3 uncorrectedNormal, TriangleShape localTriangleShape, out Vector3 normal)
{
//Compute the normal of the triangle in the current convex's local space.
//Note its reliance on the local triangle shape. It must be initialized to the correct values before this is called.
Vector3 AB, AC;
Vector3.Subtract(ref localTriangleShape.vB, ref localTriangleShape.vA, out AB);
Vector3.Subtract(ref localTriangleShape.vC, ref localTriangleShape.vA, out AC);
//Compute the normal based on the sidedness.
switch (localTriangleShape.sidedness)
{
case TriangleSidedness.DoubleSided:
//If it's double sided, then pick the triangle normal which points in the same direction
//as the contact normal that's going to be corrected.
float dot;
Vector3.Cross(ref AB, ref AC, out normal);
Vector3.Dot(ref normal, ref uncorrectedNormal, out dot);
if (dot < 0)
{
Vector3.Negate(ref normal, out normal);
}
break;
case TriangleSidedness.Clockwise:
//If it's clockwise, always use ACxAB.
Vector3.Cross(ref AC, ref AB, out normal);
break;
default:
//If it's counterclockwise, always use ABxAC.
Vector3.Cross(ref AB, ref AC, out normal);
break;
}
//If the normal is degenerate, just use the uncorrected normal.
if (normal.LengthSquared() < Toolbox.Epsilon)
{
normal = uncorrectedNormal;
}
}
protected abstract bool ConfigureLocalTriangle(int i, TriangleShape localTriangleShape, out TriangleIndices indices);
bool AnalyzeCandidate(ref TriangleIndices indices, TriangleShape triangle, TrianglePairTester pairTester, ref ContactData contact, ref BoundarySets sets)
{
switch (pairTester.GetRegion(triangle, ref contact))
{
case VoronoiRegion.A:
//Add the contact.
VertexContact vertexContact;
GetNormal(ref contact.Normal, triangle, out vertexContact.CorrectedNormal);
vertexContact.ContactData = contact;
vertexContact.Vertex = indices.A;
vertexContact.ShouldCorrect = pairTester.ShouldCorrectContactNormal;
sets.VertexContacts.Add(ref vertexContact);
//Block all of the other voronoi regions.
sets.BlockedEdgeRegions.Add(new Edge(indices.A, indices.B));
sets.BlockedEdgeRegions.Add(new Edge(indices.B, indices.C));
sets.BlockedEdgeRegions.Add(new Edge(indices.A, indices.C));
sets.BlockedVertexRegions.Add(indices.B);
sets.BlockedVertexRegions.Add(indices.C);
break;
case VoronoiRegion.B:
//Add the contact.
GetNormal(ref contact.Normal, triangle, out vertexContact.CorrectedNormal);
vertexContact.ContactData = contact;
vertexContact.Vertex = indices.B;
vertexContact.ShouldCorrect = pairTester.ShouldCorrectContactNormal;
sets.VertexContacts.Add(ref vertexContact);
//Block all of the other voronoi regions.
sets.BlockedEdgeRegions.Add(new Edge(indices.A, indices.B));
sets.BlockedEdgeRegions.Add(new Edge(indices.B, indices.C));
sets.BlockedEdgeRegions.Add(new Edge(indices.A, indices.C));
sets.BlockedVertexRegions.Add(indices.A);
sets.BlockedVertexRegions.Add(indices.C);
break;
case VoronoiRegion.C:
//Add the contact.
GetNormal(ref contact.Normal, triangle, out vertexContact.CorrectedNormal);
vertexContact.ContactData = contact;
vertexContact.Vertex = indices.C;
vertexContact.ShouldCorrect = pairTester.ShouldCorrectContactNormal;
sets.VertexContacts.Add(ref vertexContact);
//Block all of the other voronoi regions.
sets.BlockedEdgeRegions.Add(new Edge(indices.A, indices.B));
sets.BlockedEdgeRegions.Add(new Edge(indices.B, indices.C));
sets.BlockedEdgeRegions.Add(new Edge(indices.A, indices.C));
sets.BlockedVertexRegions.Add(indices.A);
sets.BlockedVertexRegions.Add(indices.B);
break;
case VoronoiRegion.AB:
//Add the contact.
EdgeContact edgeContact;
GetNormal(ref contact.Normal, triangle, out edgeContact.CorrectedNormal);
edgeContact.Edge = new Edge(indices.A, indices.B);
edgeContact.ContactData = contact;
edgeContact.ShouldCorrect = pairTester.ShouldCorrectContactNormal;
sets.EdgeContacts.Add(ref edgeContact);
//Block all of the other voronoi regions.
sets.BlockedEdgeRegions.Add(new Edge(indices.B, indices.C));
sets.BlockedEdgeRegions.Add(new Edge(indices.A, indices.C));
sets.BlockedVertexRegions.Add(indices.A);
sets.BlockedVertexRegions.Add(indices.B);
sets.BlockedVertexRegions.Add(indices.C);
break;
case VoronoiRegion.AC:
//Add the contact.
GetNormal(ref contact.Normal, triangle, out edgeContact.CorrectedNormal);
edgeContact.Edge = new Edge(indices.A, indices.C);
edgeContact.ContactData = contact;
edgeContact.ShouldCorrect = pairTester.ShouldCorrectContactNormal;
sets.EdgeContacts.Add(ref edgeContact);
//Block all of the other voronoi regions.
sets.BlockedEdgeRegions.Add(new Edge(indices.A, indices.B));
sets.BlockedEdgeRegions.Add(new Edge(indices.B, indices.C));
sets.BlockedVertexRegions.Add(indices.A);
sets.BlockedVertexRegions.Add(indices.B);
sets.BlockedVertexRegions.Add(indices.C);
break;
case VoronoiRegion.BC:
//Add the contact.
GetNormal(ref contact.Normal, triangle, out edgeContact.CorrectedNormal);
edgeContact.Edge = new Edge(indices.B, indices.C);
edgeContact.ContactData = contact;
edgeContact.ShouldCorrect = pairTester.ShouldCorrectContactNormal;
sets.EdgeContacts.Add(ref edgeContact);
//Block all of the other voronoi regions.
sets.BlockedEdgeRegions.Add(new Edge(indices.A, indices.B));
sets.BlockedEdgeRegions.Add(new Edge(indices.A, indices.C));
sets.BlockedVertexRegions.Add(indices.A);
sets.BlockedVertexRegions.Add(indices.B);
sets.BlockedVertexRegions.Add(indices.C);
break;
default:
//Block all of the other voronoi regions.
sets.BlockedEdgeRegions.Add(new Edge(indices.A, indices.B));
sets.BlockedEdgeRegions.Add(new Edge(indices.B, indices.C));
sets.BlockedEdgeRegions.Add(new Edge(indices.A, indices.C));
sets.BlockedVertexRegions.Add(indices.A);
sets.BlockedVertexRegions.Add(indices.B);
sets.BlockedVertexRegions.Add(indices.C);
//Should add the contact.
return(true);
}
return(false);
}
///<summary>
/// Determines what voronoi region a given point is in.
///</summary>
///<param name="p">Point to test.</param>
///<returns>Voronoi region containing the point.</returns>
private VoronoiRegion GetVoronoiRegion(TriangleShape triangle, ref Vector3 p)
{
//The point we are comparing against the triangle is 0,0,0, so instead of storing an "A->P" vector,
//just use -A.
//Same for B->, C->P...
Vector3 ab, ac, ap;
Vector3.Subtract(ref triangle.vB, ref triangle.vA, out ab);
Vector3.Subtract(ref triangle.vC, ref triangle.vA, out ac);
Vector3.Subtract(ref p, ref triangle.vA, out ap);
//Check to see if it's outside A.
float APdotAB, APdotAC;
Vector3.Dot(ref ap, ref ab, out APdotAB);
Vector3.Dot(ref ap, ref ac, out APdotAC);
if (APdotAC <= 0f && APdotAB <= 0)
{
//It is A!
return(VoronoiRegion.A);
}
//Check to see if it's outside B.
float BPdotAB, BPdotAC;
Vector3 bp;
Vector3.Subtract(ref p, ref triangle.vB, out bp);
Vector3.Dot(ref ab, ref bp, out BPdotAB);
Vector3.Dot(ref ac, ref bp, out BPdotAC);
if (BPdotAB >= 0f && BPdotAC <= BPdotAB)
{
//It is B!
return(VoronoiRegion.B);
}
//Check to see if it's outside AB.
float vc = APdotAB * BPdotAC - BPdotAB * APdotAC;
if (vc <= 0 && APdotAB > 0 && BPdotAB < 0) //Note > and < instead of => <=; avoids possibly division by zero
{
return(VoronoiRegion.AB);
}
//Check to see if it's outside C.
float CPdotAB, CPdotAC;
Vector3 cp;
Vector3.Subtract(ref p, ref triangle.vC, out cp);
Vector3.Dot(ref ab, ref cp, out CPdotAB);
Vector3.Dot(ref ac, ref cp, out CPdotAC);
if (CPdotAC >= 0f && CPdotAB <= CPdotAC)
{
//It is C!
return(VoronoiRegion.C);
}
//Check if it's outside AC.
float vb = CPdotAB * APdotAC - APdotAB * CPdotAC;
if (vb <= 0f && APdotAC > 0f && CPdotAC < 0f) //Note > instead of >= and < instead of <=; prevents bad denominator
{
return(VoronoiRegion.AC);
}
//Check if it's outside BC.
float va = BPdotAB * CPdotAC - CPdotAB * BPdotAC;
if (va <= 0f && (BPdotAC - BPdotAB) > 0f && (CPdotAB - CPdotAC) > 0f)//Note > instead of >= and < instead of <=; prevents bad denominator
{
return(VoronoiRegion.BC);
}
//On the face of the triangle.
return(VoronoiRegion.ABC);
}
private bool TryInnerSphereContact(TriangleShape triangle, out ContactData contact)
{
Vector3 closestPoint;
Toolbox.GetClosestPointOnTriangleToPoint(ref triangle.vA, ref triangle.vB, ref triangle.vC, ref Toolbox.ZeroVector, out closestPoint);
float length = closestPoint.LengthSquared();
float minimumRadius = convex.MinimumRadius * (MotionSettings.CoreShapeScaling + .01f);
if (length < minimumRadius * minimumRadius)
{
Vector3 triangleNormal, ab, ac;
Vector3.Subtract(ref triangle.vB, ref triangle.vA, out ab);
Vector3.Subtract(ref triangle.vC, ref triangle.vA, out ac);
Vector3.Cross(ref ab, ref ac, out triangleNormal);
float dot;
Vector3.Dot(ref closestPoint, ref triangleNormal, out dot);
if ((triangle.sidedness == TriangleSidedness.Clockwise && dot > 0) || (triangle.sidedness == TriangleSidedness.Counterclockwise && dot < 0))
{
//Normal was facing the wrong way.
contact = new ContactData();
return(false);
}
length = (float)Math.Sqrt(length);
contact.Position = closestPoint;
if (length > Toolbox.Epsilon) //Watch out for NaN's!
{
Vector3.Divide(ref closestPoint, length, out contact.Normal);
}
else
{
//The direction is undefined. Use the triangle's normal.
//One sided triangles can only face in the appropriate direction.
float normalLength = triangleNormal.LengthSquared();
if (triangleNormal.LengthSquared() > Toolbox.Epsilon)
{
Vector3.Divide(ref triangleNormal, (float)Math.Sqrt(normalLength), out triangleNormal);
if (triangle.sidedness == TriangleSidedness.Clockwise)
{
contact.Normal = triangleNormal;
}
else
{
Vector3.Negate(ref triangleNormal, out contact.Normal);
}
}
else
{
//Degenerate triangle!
contact = new ContactData();
return(false);
}
}
//Compute the actual depth of the contact.
//This is conservative; the minimum radius is guaranteed to be no larger than the shape itself.
//But that's ok- this is strictly a deep contact protection scheme. Other contacts will make the objects separate.
contact.PenetrationDepth = convex.MinimumRadius - length;
contact.Id = -1;
return(true);
}
contact = new ContactData();
return(false);
}
private bool DoPlaneTest(TriangleShape triangle, out TinyStructList <ContactData> contactList)
{
//Find closest point between object and plane.
Vector3 reverseNormal;
Vector3 ab, ac;
Vector3.Subtract(ref triangle.vB, ref triangle.vA, out ab);
Vector3.Subtract(ref triangle.vC, ref triangle.vA, out ac);
Vector3.Cross(ref ac, ref ab, out reverseNormal);
//Convex position dot normal is ALWAYS zero. The thing to look at is the plane's 'd'.
//If the distance along the normal is positive, then the convex is 'behind' that normal.
float dotA;
Vector3.Dot(ref triangle.vA, ref reverseNormal, out dotA);
contactList = new TinyStructList <ContactData>();
switch (triangle.sidedness)
{
case TriangleSidedness.DoubleSided:
if (dotA < 0)
{
//The reverse normal is pointing towards the convex.
//It needs to point away from the convex so that the direction
//will get the proper extreme point.
Vector3.Negate(ref reverseNormal, out reverseNormal);
dotA = -dotA;
}
break;
case TriangleSidedness.Clockwise:
//if (dotA < 0)
//{
// //The reverse normal is pointing towards the convex.
// return false;
//}
break;
case TriangleSidedness.Counterclockwise:
//if (dotA > 0)
//{
// //The reverse normal is pointing away from the convex.
// return false;
//}
//The reverse normal is pointing towards the convex.
//It needs to point away from the convex so that the direction
//will get the proper extreme point.
Vector3.Negate(ref reverseNormal, out reverseNormal);
dotA = -dotA;
break;
}
Vector3 extremePoint;
convex.GetLocalExtremePointWithoutMargin(ref reverseNormal, out extremePoint);
//See if the extreme point is within the face or not.
//It might seem like the easy "depth" test should come first, since a barycentric
//calculation takes a bit more time. However, transferring from plane to depth is 'rare'
//(like all transitions), and putting this test here is logically closer to its requirements'
//computation.
if (GetVoronoiRegion(triangle, ref extremePoint) != VoronoiRegion.ABC)
{
state = CollisionState.ExternalSeparated;
return(DoExternalSeparated(triangle, out contactList));
}
float dotE;
Vector3.Dot(ref extremePoint, ref reverseNormal, out dotE);
float t = (dotA - dotE) / reverseNormal.LengthSquared();
Vector3 offset;
Vector3.Multiply(ref reverseNormal, t, out offset);
//Compare the distance from the plane to the convex object.
float distanceSquared = offset.LengthSquared();
float marginSum = triangle.collisionMargin + convex.collisionMargin;
//TODO: Could just normalize early and avoid computing point plane before it's necessary.
//Exposes a sqrt but...
if (t <= 0 || distanceSquared < marginSum * marginSum)
{
//The convex object is in the margin of the plane.
//All that's left is to create the contact.
var contact = new ContactData();
//Displacement is from A to B. point = A + t * AB, where t = marginA / margin.
if (marginSum > Toolbox.Epsilon) //This can be zero! It would cause a NaN is unprotected.
{
Vector3.Multiply(ref offset, convex.collisionMargin / marginSum, out contact.Position); //t * AB
}
else
{
contact.Position = new Vector3();
}
Vector3.Add(ref extremePoint, ref contact.Position, out contact.Position); //A + t * AB.
float normalLength = reverseNormal.Length();
Vector3.Divide(ref reverseNormal, normalLength, out contact.Normal);
float distance = normalLength * t;
contact.PenetrationDepth = marginSum - distance;
if (contact.PenetrationDepth > marginSum)
{
//Check to see if the inner sphere is touching the plane.
//This does not override other tests; there can be more than one contact from a single triangle.
ContactData alternateContact;
if (TryInnerSphereContact(triangle, out alternateContact))// && alternateContact.PenetrationDepth > contact.PenetrationDepth)
{
contactList.Add(ref alternateContact);
}
//The convex object is stuck deep in the plane!
//The most problematic case for this is when
//an object is right on top of a cliff.
//The lower, vertical triangle may occasionally detect
//a contact with the object, but would compute an extremely
//deep depth if the normal plane test was used.
//Verify that the depth is correct by trying another approach.
CollisionState previousState = state;
state = CollisionState.ExternalNear;
TinyStructList <ContactData> alternateContacts;
if (DoExternalNear(triangle, out alternateContacts))
{
alternateContacts.Get(0, out alternateContact);
if (alternateContact.PenetrationDepth + .01f < contact.PenetrationDepth) //Bias against the subtest's result, since the plane version will probably have a better position.
{
//It WAS a bad contact.
contactList.Add(ref alternateContact);
//DoDeepContact (which can be called from within DoExternalNear) can generate two contacts, but the second contact would just be an inner sphere (which we already generated).
//DoExternalNear can only generate one contact. So we only need the first contact!
//TODO: This is a fairly fragile connection between the two stages. Consider robustifying. (Also, the TryInnerSphereContact is done twice! This process is very rare for marginful pairs, though)
}
else
{
//Well, it really is just that deep.
contactList.Add(ref contact);
state = previousState;
}
}
else
{
//If the external near test finds that there was no collision at all,
//just return to plane testing. If the point turns up outside the face region
//next time, the system will adapt.
state = previousState;
return(false);
}
}
else
{
contactList.Add(ref contact);
}
return(true);
}
return(false);
}
private bool DoDeepContact(TriangleShape triangle, out TinyStructList <ContactData> contactList)
{
//Find the origin to triangle center offset.
Vector3 center;
Vector3.Add(ref triangle.vA, ref triangle.vB, out center);
Vector3.Add(ref center, ref triangle.vC, out center);
Vector3.Multiply(ref center, 1f / 3f, out center);
ContactData contact;
contactList = new TinyStructList <ContactData>();
if (MPRToolbox.AreLocalShapesOverlapping(convex, triangle, ref center, ref Toolbox.RigidIdentity))
{
float dot;
Vector3 triangleNormal, ab, ac;
Vector3.Subtract(ref triangle.vB, ref triangle.vA, out ab);
Vector3.Subtract(ref triangle.vC, ref triangle.vA, out ac);
Vector3.Cross(ref ab, ref ac, out triangleNormal);
float lengthSquared = triangleNormal.LengthSquared();
if (lengthSquared < Toolbox.Epsilon * .01f)
{
//Degenerate triangle! That's no good.
//Just use the direction pointing from A to B, "B" being the triangle. That direction is center - origin, or just center.
MPRToolbox.LocalSurfaceCast(convex, triangle, ref Toolbox.RigidIdentity, ref center, out contact.PenetrationDepth, out contact.Normal, out contact.Position);
}
else
{
//Normalize the normal.
Vector3.Divide(ref triangleNormal, (float)Math.Sqrt(lengthSquared), out triangleNormal);
//TODO: This tests all three edge axes with a full MPR raycast. That's not really necessary; the correct edge normal should be discoverable, resulting in a single MPR raycast.
//Find the edge directions that will be tested with MPR.
Vector3 AO, BO, CO;
Vector3 AB, BC, CA;
Vector3.Subtract(ref center, ref triangle.vA, out AO);
Vector3.Subtract(ref center, ref triangle.vB, out BO);
Vector3.Subtract(ref center, ref triangle.vC, out CO);
Vector3.Subtract(ref triangle.vB, ref triangle.vA, out AB);
Vector3.Subtract(ref triangle.vC, ref triangle.vB, out BC);
Vector3.Subtract(ref triangle.vA, ref triangle.vC, out CA);
//We don't have to worry about degenerate triangles here because we've already handled that possibility above.
Vector3 ABnormal, BCnormal, CAnormal;
//Project the center onto the edge to find the direction from the center to the edge AB.
Vector3.Dot(ref AO, ref AB, out dot);
Vector3.Multiply(ref AB, dot / AB.LengthSquared(), out ABnormal);
Vector3.Subtract(ref AO, ref ABnormal, out ABnormal);
ABnormal.Normalize();
//Project the center onto the edge to find the direction from the center to the edge BC.
Vector3.Dot(ref BO, ref BC, out dot);
Vector3.Multiply(ref BC, dot / BC.LengthSquared(), out BCnormal);
Vector3.Subtract(ref BO, ref BCnormal, out BCnormal);
BCnormal.Normalize();
//Project the center onto the edge to find the direction from the center to the edge BC.
Vector3.Dot(ref CO, ref CA, out dot);
Vector3.Multiply(ref CA, dot / CA.LengthSquared(), out CAnormal);
Vector3.Subtract(ref CO, ref CAnormal, out CAnormal);
CAnormal.Normalize();
MPRToolbox.LocalSurfaceCast(convex, triangle, ref Toolbox.RigidIdentity, ref ABnormal, out contact.PenetrationDepth, out contact.Normal);
//Check to see if the normal is facing in the proper direction, considering that this may not be a two-sided triangle.
Vector3.Dot(ref triangleNormal, ref contact.Normal, out dot);
if ((triangle.sidedness == TriangleSidedness.Clockwise && dot > 0) || (triangle.sidedness == TriangleSidedness.Counterclockwise && dot < 0))
{
//Normal was facing the wrong way.
//Instead of ignoring it entirely, correct the direction to as close as it can get by removing any component parallel to the triangle normal.
Vector3 previousNormal = contact.Normal;
Vector3.Dot(ref contact.Normal, ref triangleNormal, out dot);
Vector3 p;
Vector3.Multiply(ref contact.Normal, dot, out p);
Vector3.Subtract(ref contact.Normal, ref p, out contact.Normal);
float length = contact.Normal.LengthSquared();
if (length > Toolbox.Epsilon)
{
//Renormalize the corrected normal.
Vector3.Divide(ref contact.Normal, (float)Math.Sqrt(length), out contact.Normal);
Vector3.Dot(ref contact.Normal, ref previousNormal, out dot);
contact.PenetrationDepth *= dot;
}
else
{
contact.PenetrationDepth = float.MaxValue;
contact.Normal = new Vector3();
}
}
Vector3 candidateNormal;
float candidateDepth;
MPRToolbox.LocalSurfaceCast(convex, triangle, ref Toolbox.RigidIdentity, ref BCnormal, out candidateDepth, out candidateNormal);
//Check to see if the normal is facing in the proper direction, considering that this may not be a two-sided triangle.
Vector3.Dot(ref triangleNormal, ref candidateNormal, out dot);
if ((triangle.sidedness == TriangleSidedness.Clockwise && dot > 0) || (triangle.sidedness == TriangleSidedness.Counterclockwise && dot < 0))
{
//Normal was facing the wrong way.
//Instead of ignoring it entirely, correct the direction to as close as it can get by removing any component parallel to the triangle normal.
Vector3 previousNormal = candidateNormal;
Vector3.Dot(ref candidateNormal, ref triangleNormal, out dot);
Vector3 p;
Vector3.Multiply(ref candidateNormal, dot, out p);
Vector3.Subtract(ref candidateNormal, ref p, out candidateNormal);
float length = candidateNormal.LengthSquared();
if (length > Toolbox.Epsilon)
{
//Renormalize the corrected normal.
Vector3.Divide(ref candidateNormal, (float)Math.Sqrt(length), out candidateNormal);
Vector3.Dot(ref candidateNormal, ref previousNormal, out dot);
candidateDepth *= dot;
}
else
{
contact.PenetrationDepth = float.MaxValue;
contact.Normal = new Vector3();
}
}
if (candidateDepth < contact.PenetrationDepth)
{
contact.Normal = candidateNormal;
contact.PenetrationDepth = candidateDepth;
}
MPRToolbox.LocalSurfaceCast(convex, triangle, ref Toolbox.RigidIdentity, ref CAnormal, out candidateDepth, out candidateNormal);
//Check to see if the normal is facing in the proper direction, considering that this may not be a two-sided triangle.
Vector3.Dot(ref triangleNormal, ref candidateNormal, out dot);
if ((triangle.sidedness == TriangleSidedness.Clockwise && dot > 0) || (triangle.sidedness == TriangleSidedness.Counterclockwise && dot < 0))
{
//Normal was facing the wrong way.
//Instead of ignoring it entirely, correct the direction to as close as it can get by removing any component parallel to the triangle normal.
Vector3 previousNormal = candidateNormal;
Vector3.Dot(ref candidateNormal, ref triangleNormal, out dot);
Vector3 p;
Vector3.Multiply(ref candidateNormal, dot, out p);
Vector3.Subtract(ref candidateNormal, ref p, out candidateNormal);
float length = candidateNormal.LengthSquared();
if (length > Toolbox.Epsilon)
{
//Renormalize the corrected normal.
Vector3.Divide(ref candidateNormal, (float)Math.Sqrt(length), out candidateNormal);
Vector3.Dot(ref candidateNormal, ref previousNormal, out dot);
candidateDepth *= dot;
}
else
{
contact.PenetrationDepth = float.MaxValue;
contact.Normal = new Vector3();
}
}
if (candidateDepth < contact.PenetrationDepth)
{
contact.Normal = candidateNormal;
contact.PenetrationDepth = candidateDepth;
}
//Try the depth along the positive triangle normal.
//If it's clockwise, this direction is unnecessary (the resulting normal would be invalidated by the onesidedness of the triangle).
if (triangle.sidedness != TriangleSidedness.Clockwise)
{
MPRToolbox.LocalSurfaceCast(convex, triangle, ref Toolbox.RigidIdentity, ref triangleNormal, out candidateDepth, out candidateNormal);
if (candidateDepth < contact.PenetrationDepth)
{
contact.Normal = candidateNormal;
contact.PenetrationDepth = candidateDepth;
}
}
//Try the depth along the negative triangle normal.
//If it's counterclockwise, this direction is unnecessary (the resulting normal would be invalidated by the onesidedness of the triangle).
if (triangle.sidedness != TriangleSidedness.Counterclockwise)
{
Vector3.Negate(ref triangleNormal, out triangleNormal);
MPRToolbox.LocalSurfaceCast(convex, triangle, ref Toolbox.RigidIdentity, ref triangleNormal, out candidateDepth, out candidateNormal);
if (candidateDepth < contact.PenetrationDepth)
{
contact.Normal = candidateNormal;
contact.PenetrationDepth = candidateDepth;
}
}
}
MPRToolbox.RefinePenetration(convex, triangle, ref Toolbox.RigidIdentity, contact.PenetrationDepth, ref contact.Normal, out contact.PenetrationDepth, out contact.Normal, out contact.Position);
//It's possible for the normal to still face the 'wrong' direction according to one sided triangles.
if (triangle.sidedness != TriangleSidedness.DoubleSided)
{
Vector3.Dot(ref triangleNormal, ref contact.Normal, out dot);
if (dot < 0)
{
//Skip the add process.
goto InnerSphere;
}
}
contact.Id = -1;
if (contact.PenetrationDepth < convex.collisionMargin + triangle.collisionMargin)
{
state = CollisionState.ExternalNear; //If it's emerged from the deep contact, we can go back to using the preferred GJK method.
}
contactList.Add(ref contact);
}
InnerSphere:
if (TryInnerSphereContact(triangle, out contact))
{
contactList.Add(ref contact);
}
if (contactList.Count > 0)
{
return(true);
}
state = CollisionState.ExternalSeparated;
return(false);
}
private bool DoExternalNear(TriangleShape triangle, out TinyStructList <ContactData> contactList)
{
Vector3 closestA, closestB;
//Don't bother trying to do any clever caching. The continually transforming simplex makes it very rarely useful.
//TODO: Initialize the simplex of the GJK method using the 'true' center of the triangle.
//If left unmodified, the simplex that is used in GJK will just be a point at 0,0,0, which of course is at the origin.
//This causes an instant-out, always. Not good!
//By giving the contributing simplex the average centroid, it has a better guess.
Vector3 triangleCentroid;
Vector3.Add(ref triangle.vA, ref triangle.vB, out triangleCentroid);
Vector3.Add(ref triangleCentroid, ref triangle.vC, out triangleCentroid);
Vector3.Multiply(ref triangleCentroid, .33333333f, out triangleCentroid);
var initialSimplex = new CachedSimplex {
State = SimplexState.Point, LocalSimplexB = { A = triangleCentroid }
};
if (GJKToolbox.GetClosestPoints(convex, triangle, ref Toolbox.RigidIdentity, ref Toolbox.RigidIdentity, ref initialSimplex, out closestA, out closestB))
{
state = CollisionState.Deep;
return(DoDeepContact(triangle, out contactList));
}
Vector3 displacement;
Vector3.Subtract(ref closestB, ref closestA, out displacement);
float distanceSquared = displacement.LengthSquared();
float margin = convex.collisionMargin + triangle.collisionMargin;
contactList = new TinyStructList <ContactData>();
if (distanceSquared < margin * margin)
{
//Try to generate a contact.
var contact = new ContactData();
//Determine if the normal points in the appropriate direction given the sidedness of the triangle.
if (triangle.sidedness != TriangleSidedness.DoubleSided)
{
Vector3 triangleNormal, ab, ac;
Vector3.Subtract(ref triangle.vB, ref triangle.vA, out ab);
Vector3.Subtract(ref triangle.vC, ref triangle.vA, out ac);
Vector3.Cross(ref ab, ref ac, out triangleNormal);
float dot;
Vector3.Dot(ref triangleNormal, ref displacement, out dot);
if (triangle.sidedness == TriangleSidedness.Clockwise && dot > 0)
{
return(false);
}
if (triangle.sidedness == TriangleSidedness.Counterclockwise && dot < 0)
{
return(false);
}
}
//Displacement is from A to B. point = A + t * AB, where t = marginA / margin.
if (margin > Toolbox.Epsilon) //This can be zero! It would cause a NaN if unprotected.
{
Vector3.Multiply(ref displacement, convex.collisionMargin / margin, out contact.Position); //t * AB
}
else
{
contact.Position = new Vector3();
}
Vector3.Add(ref closestA, ref contact.Position, out contact.Position); //A + t * AB.
contact.Normal = displacement;
float distance = (float)Math.Sqrt(distanceSquared);
Vector3.Divide(ref contact.Normal, distance, out contact.Normal);
contact.PenetrationDepth = margin - distance;
contactList.Add(ref contact);
TryToEscape(triangle, ref contact.Position);
return(true);
}
//Too far to make a contact- move back to separation.
state = CollisionState.ExternalSeparated;
return(false);
}
public override VoronoiRegion GetRegion(TriangleShape triangle, ref ContactData contact)
{
return(lastRegion);
}
//Relies on the triangle being located in the local space of the convex object. The convex transform is used to transform the
//contact points back from the convex's local space into world space.
///<summary>
/// Generates a contact between the triangle and convex.
///</summary>
///<param name="contactList">Contact between the shapes, if any.</param>
///<returns>Whether or not the shapes are colliding.</returns>
public override bool GenerateContactCandidates(TriangleShape triangle, out TinyStructList <ContactData> contactList)
{
contactList = new TinyStructList <ContactData>();
Vector3 ab, ac;
Vector3.Subtract(ref triangle.vB, ref triangle.vA, out ab);
Vector3.Subtract(ref triangle.vC, ref triangle.vA, out ac);
Vector3 triangleNormal;
Vector3.Cross(ref ab, ref ac, out triangleNormal);
if (triangleNormal.LengthSquared() < Toolbox.Epsilon * .01f)
{
//If the triangle is degenerate, use the offset between its center and the sphere.
Vector3.Add(ref triangle.vA, ref triangle.vB, out triangleNormal);
Vector3.Add(ref triangleNormal, ref triangle.vC, out triangleNormal);
Vector3.Multiply(ref triangleNormal, 1 / 3f, out triangleNormal);
if (triangleNormal.LengthSquared() < Toolbox.Epsilon * .01f)
{
triangleNormal = Toolbox.UpVector; //Alrighty then! Pick a random direction.
}
}
float dot;
Vector3.Dot(ref triangleNormal, ref triangle.vA, out dot);
switch (triangle.sidedness)
{
case TriangleSidedness.DoubleSided:
if (dot < 0)
{
Vector3.Negate(ref triangleNormal, out triangleNormal); //Normal must face outward.
}
break;
case TriangleSidedness.Clockwise:
if (dot > 0)
{
return(false); //Wrong side, can't have a contact pointing in a reasonable direction.
}
break;
case TriangleSidedness.Counterclockwise:
if (dot < 0)
{
return(false); //Wrong side, can't have a contact pointing in a reasonable direction.
}
break;
}
Vector3 closestPoint;
//Could optimize this process a bit. The 'point' being compared is always zero. Additionally, since the triangle normal is available,
//there is a little extra possible optimization.
lastRegion = Toolbox.GetClosestPointOnTriangleToPoint(ref triangle.vA, ref triangle.vB, ref triangle.vC, ref Toolbox.ZeroVector, out closestPoint);
float lengthSquared = closestPoint.LengthSquared();
float marginSum = triangle.collisionMargin + sphere.collisionMargin;
if (lengthSquared <= marginSum * marginSum)
{
var contact = new ContactData();
if (lengthSquared < Toolbox.Epsilon)
{
//Super close to the triangle. Normalizing would be dangerous.
Vector3.Negate(ref triangleNormal, out contact.Normal);
contact.Normal.Normalize();
contact.PenetrationDepth = marginSum;
contactList.Add(ref contact);
return(true);
}
lengthSquared = (float)Math.Sqrt(lengthSquared);
Vector3.Divide(ref closestPoint, lengthSquared, out contact.Normal);
contact.PenetrationDepth = marginSum - lengthSquared;
contact.Position = closestPoint;
contactList.Add(ref contact);
return(true);
}
return(false);
}
public override VoronoiRegion GetRegion(TriangleShape triangle, ref ContactData contact)
{
//Deep contact can produce non-triangle normals while still being within the triangle.
//To solve this problem, find the voronoi region to which the contact belongs using its normal.
//The voronoi region will be either the most extreme vertex, or the edge that includes
//the first and second most extreme vertices.
//If the normal dotted with an extreme edge direction is near 0, then it belongs to the edge.
//Otherwise, it belongs to the vertex.
//MPR tends to produce 'approximate' normals, though.
//Use a fairly forgiving epsilon.
float dotA, dotB, dotC;
Vector3.Dot(ref triangle.vA, ref contact.Normal, out dotA);
Vector3.Dot(ref triangle.vB, ref contact.Normal, out dotB);
Vector3.Dot(ref triangle.vC, ref contact.Normal, out dotC);
//Since normal points from convex to triangle always, reverse dot signs.
dotA = -dotA;
dotB = -dotB;
dotC = -dotC;
float faceEpsilon = .01f;
const float edgeEpsilon = .01f;
float edgeDot;
Vector3 edgeDirection;
if (dotA > dotB && dotA > dotC)
{
//A is extreme.
if (dotB > dotC)
{
//B is second most extreme.
if (Math.Abs(dotA - dotC) < faceEpsilon)
{
//The normal is basically a face normal. This can happen at the edges occasionally.
return(VoronoiRegion.ABC);
}
else
{
Vector3.Subtract(ref triangle.vB, ref triangle.vA, out edgeDirection);
Vector3.Dot(ref edgeDirection, ref contact.Normal, out edgeDot);
if (edgeDot * edgeDot < edgeDirection.LengthSquared() * edgeEpsilon)
{
return(VoronoiRegion.AB);
}
else
{
return(VoronoiRegion.A);
}
}
}
else
{
//C is second most extreme.
if (Math.Abs(dotA - dotB) < faceEpsilon)
{
//The normal is basically a face normal. This can happen at the edges occasionally.
return(VoronoiRegion.ABC);
}
else
{
Vector3.Subtract(ref triangle.vC, ref triangle.vA, out edgeDirection);
Vector3.Dot(ref edgeDirection, ref contact.Normal, out edgeDot);
if (edgeDot * edgeDot < edgeDirection.LengthSquared() * edgeEpsilon)
{
return(VoronoiRegion.AC);
}
else
{
return(VoronoiRegion.A);
}
}
}
}
else if (dotB > dotC)
{
//B is extreme.
if (dotC > dotA)
{
//C is second most extreme.
if (Math.Abs(dotB - dotA) < faceEpsilon)
{
//The normal is basically a face normal. This can happen at the edges occasionally.
return(VoronoiRegion.ABC);
}
else
{
Vector3.Subtract(ref triangle.vC, ref triangle.vB, out edgeDirection);
Vector3.Dot(ref edgeDirection, ref contact.Normal, out edgeDot);
if (edgeDot * edgeDot < edgeDirection.LengthSquared() * edgeEpsilon)
{
return(VoronoiRegion.BC);
}
else
{
return(VoronoiRegion.B);
}
}
}
else
{
//A is second most extreme.
if (Math.Abs(dotB - dotC) < faceEpsilon)
{
//The normal is basically a face normal. This can happen at the edges occasionally.
return(VoronoiRegion.ABC);
}
else
{
Vector3.Subtract(ref triangle.vA, ref triangle.vB, out edgeDirection);
Vector3.Dot(ref edgeDirection, ref contact.Normal, out edgeDot);
if (edgeDot * edgeDot < edgeDirection.LengthSquared() * edgeEpsilon)
{
return(VoronoiRegion.AB);
}
else
{
return(VoronoiRegion.B);
}
}
}
}
else
{
//C is extreme.
if (dotA > dotB)
{
//A is second most extreme.
if (Math.Abs(dotC - dotB) < faceEpsilon)
{
//The normal is basically a face normal. This can happen at the edges occasionally.
return(VoronoiRegion.ABC);
}
else
{
Vector3.Subtract(ref triangle.vA, ref triangle.vC, out edgeDirection);
Vector3.Dot(ref edgeDirection, ref contact.Normal, out edgeDot);
if (edgeDot * edgeDot < edgeDirection.LengthSquared() * edgeEpsilon)
{
return(VoronoiRegion.AC);
}
else
{
return(VoronoiRegion.C);
}
}
}
else
{
//B is second most extreme.
if (Math.Abs(dotC - dotA) < faceEpsilon)
{
//The normal is basically a face normal. This can happen at the edges occasionally.
return(VoronoiRegion.ABC);
}
else
{
Vector3.Subtract(ref triangle.vB, ref triangle.vC, out edgeDirection);
Vector3.Dot(ref edgeDirection, ref contact.Normal, out edgeDot);
if (edgeDot * edgeDot < edgeDirection.LengthSquared() * edgeEpsilon)
{
return(VoronoiRegion.BC);
}
else
{
return(VoronoiRegion.C);
}
}
}
}
}
