public void MultiplyTransposed()
{
var m = RandomHelper.Random.NextMatrix33F(1, 10);
var v = RandomHelper.Random.NextVector3F(1, 10);
Assert.AreEqual(m.Transposed * v, Matrix33F.MultiplyTransposed(m, v));
}
public override void ComputeCollision(ContactSet contactSet, CollisionQueryType type)
{
// Invoke GJK for closest points.
if (type == CollisionQueryType.ClosestPoints)
{
throw new GeometryException("This collision algorithm cannot handle closest-point queries. Use GJK instead.");
}
CollisionObject collisionObjectA = contactSet.ObjectA;
CollisionObject collisionObjectB = contactSet.ObjectB;
IGeometricObject geometricObjectA = collisionObjectA.GeometricObject;
IGeometricObject geometricObjectB = collisionObjectB.GeometricObject;
BoxShape boxA = geometricObjectA.Shape as BoxShape;
BoxShape boxB = geometricObjectB.Shape as BoxShape;
// Check if collision objects shapes are correct.
if (boxA == null || boxB == null)
{
throw new ArgumentException("The contact set must contain box shapes.", "contactSet");
}
Vector3F scaleA = Vector3F.Absolute(geometricObjectA.Scale);
Vector3F scaleB = Vector3F.Absolute(geometricObjectB.Scale);
Pose poseA = geometricObjectA.Pose;
Pose poseB = geometricObjectB.Pose;
// We perform the separating axis test in the local space of A.
// The following variables are in local space of A.
// Center of box B.
Vector3F cB = poseA.ToLocalPosition(poseB.Position);
// Orientation matrix of box B
Matrix33F mB = poseA.Orientation.Transposed * poseB.Orientation;
// Absolute of mB.
Matrix33F aMB = Matrix33F.Absolute(mB);
// Half extent vectors of the boxes.
Vector3F eA = 0.5f * boxA.Extent * scaleA;
Vector3F eB = 0.5f * boxB.Extent * scaleB;
// ----- Separating Axis tests
// If the boxes are separated, we immediately return.
// For the case of interpenetration, we store the smallest penetration depth.
float smallestPenetrationDepth = float.PositiveInfinity;
int separatingAxisNumber = 0;
Vector3F normal = Vector3F.UnitX;
bool isNormalInverted = false;
contactSet.HaveContact = false; // Assume no contact.
#region ----- Case 1: Separating Axis: (1, 0, 0) -----
float separation = Math.Abs(cB.X) - (eA.X + eB.X * aMB.M00 + eB.Y * aMB.M01 + eB.Z * aMB.M02);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean && -separation < smallestPenetrationDepth)
{
normal = Vector3F.UnitX;
smallestPenetrationDepth = -separation;
isNormalInverted = cB.X < 0;
separatingAxisNumber = 1;
}
#endregion
#region ----- Case 2: Separating Axis: (0, 1, 0) -----
separation = Math.Abs(cB.Y) - (eA.Y + eB.X * aMB.M10 + eB.Y * aMB.M11 + eB.Z * aMB.M12);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean && -separation < smallestPenetrationDepth)
{
normal = Vector3F.UnitY;
smallestPenetrationDepth = -separation;
isNormalInverted = cB.Y < 0;
separatingAxisNumber = 2;
}
#endregion
#region ----- Case 3: Separating Axis: (0, 0, 1) -----
separation = Math.Abs(cB.Z) - (eA.Z + eB.X * aMB.M20 + eB.Y * aMB.M21 + eB.Z * aMB.M22);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean && -separation < smallestPenetrationDepth)
{
normal = Vector3F.UnitZ;
smallestPenetrationDepth = -separation;
isNormalInverted = cB.Z < 0;
separatingAxisNumber = 3;
}
#endregion
#region ----- Case 4: Separating Axis: OrientationB * (1, 0, 0) -----
float expression = cB.X * mB.M00 + cB.Y * mB.M10 + cB.Z * mB.M20;
separation = Math.Abs(expression) - (eB.X + eA.X * aMB.M00 + eA.Y * aMB.M10 + eA.Z * aMB.M20);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean && -separation < smallestPenetrationDepth)
{
normal = mB.GetColumn(0);
smallestPenetrationDepth = -separation;
isNormalInverted = expression < 0;
separatingAxisNumber = 4;
}
#endregion
#region ----- Case 5: Separating Axis: OrientationB * (0, 1, 0) -----
expression = cB.X * mB.M01 + cB.Y * mB.M11 + cB.Z * mB.M21;
separation = Math.Abs(expression) - (eB.Y + eA.X * aMB.M01 + eA.Y * aMB.M11 + eA.Z * aMB.M21);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean && -separation < smallestPenetrationDepth)
{
normal = mB.GetColumn(1);
smallestPenetrationDepth = -separation;
isNormalInverted = expression < 0;
separatingAxisNumber = 5;
}
#endregion
#region ----- Case 6: Separating Axis: OrientationB * (0, 0, 1) -----
expression = cB.X * mB.M02 + cB.Y * mB.M12 + cB.Z * mB.M22;
separation = Math.Abs(expression) - (eB.Z + eA.X * aMB.M02 + eA.Y * aMB.M12 + eA.Z * aMB.M22);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean && -separation < smallestPenetrationDepth)
{
normal = mB.GetColumn(2);
smallestPenetrationDepth = -separation;
isNormalInverted = expression < 0;
separatingAxisNumber = 6;
}
#endregion
// The next 9 tests are edge-edge cases. The normal vector has to be normalized
// to get the right penetration depth.
// normal = Normalize(edgeA x edgeB)
Vector3F separatingAxis;
float length;
#region ----- Case 7: Separating Axis: (1, 0, 0) x (OrientationB * (1, 0, 0)) -----
expression = cB.Z * mB.M10 - cB.Y * mB.M20;
separation = Math.Abs(expression) - (eA.Y * aMB.M20 + eA.Z * aMB.M10 + eB.Y * aMB.M02 + eB.Z * aMB.M01);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean)
{
separatingAxis = new Vector3F(0, -mB.M20, mB.M10);
length = separatingAxis.Length;
separation /= length;
if (-separation < smallestPenetrationDepth)
{
normal = separatingAxis / length;
smallestPenetrationDepth = -separation;
isNormalInverted = expression < 0;
separatingAxisNumber = 7;
}
}
#endregion
#region ----- Case 8: Separating Axis: (1, 0, 0) x (OrientationB * (0, 1, 0)) -----
expression = cB.Z * mB.M11 - cB.Y * mB.M21;
separation = Math.Abs(expression) - (eA.Y * aMB.M21 + eA.Z * aMB.M11 + eB.X * aMB.M02 + eB.Z * aMB.M00);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean)
{
separatingAxis = new Vector3F(0, -mB.M21, mB.M11);
length = separatingAxis.Length;
separation /= length;
if (-separation < smallestPenetrationDepth)
{
normal = separatingAxis / length;
smallestPenetrationDepth = -separation;
isNormalInverted = expression < 0;
separatingAxisNumber = 8;
}
}
#endregion
#region ----- Case 9: Separating Axis: (1, 0, 0) x (OrientationB * (0, 0, 1)) -----
expression = cB.Z * mB.M12 - cB.Y * mB.M22;
separation = Math.Abs(expression) - (eA.Y * aMB.M22 + eA.Z * aMB.M12 + eB.X * aMB.M01 + eB.Y * aMB.M00);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean)
{
separatingAxis = new Vector3F(0, -mB.M22, mB.M12);
length = separatingAxis.Length;
separation /= length;
if (-separation < smallestPenetrationDepth)
{
normal = separatingAxis / length;
smallestPenetrationDepth = -separation;
isNormalInverted = expression < 0;
separatingAxisNumber = 9;
}
}
#endregion
#region ----- Case 10: Separating Axis: (0, 1, 0) x (OrientationB * (1, 0, 0)) -----
expression = cB.X * mB.M20 - cB.Z * mB.M00;
separation = Math.Abs(expression) - (eA.X * aMB.M20 + eA.Z * aMB.M00 + eB.Y * aMB.M12 + eB.Z * aMB.M11);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean)
{
separatingAxis = new Vector3F(mB.M20, 0, -mB.M00);
length = separatingAxis.Length;
separation /= length;
if (-separation < smallestPenetrationDepth)
{
normal = separatingAxis / length;
smallestPenetrationDepth = -separation;
isNormalInverted = expression < 0;
separatingAxisNumber = 10;
}
}
#endregion
#region ----- Case 11: Separating Axis: (0, 1, 0) x (OrientationB * (0, 1, 0)) -----
expression = cB.X * mB.M21 - cB.Z * mB.M01;
separation = Math.Abs(expression) - (eA.X * aMB.M21 + eA.Z * aMB.M01 + eB.X * aMB.M12 + eB.Z * aMB.M10);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean)
{
separatingAxis = new Vector3F(mB.M21, 0, -mB.M01);
length = separatingAxis.Length;
separation /= length;
if (-separation < smallestPenetrationDepth)
{
normal = separatingAxis / length;
smallestPenetrationDepth = -separation;
isNormalInverted = expression < 0;
separatingAxisNumber = 11;
}
}
#endregion
#region ----- Case 12: Separating Axis: (0, 1, 0) x (OrientationB * (0, 0, 1)) -----
expression = cB.X * mB.M22 - cB.Z * mB.M02;
separation = Math.Abs(expression) - (eA.X * aMB.M22 + eA.Z * aMB.M02 + eB.X * aMB.M11 + eB.Y * aMB.M10);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean)
{
separatingAxis = new Vector3F(mB.M22, 0, -mB.M02);
length = separatingAxis.Length;
separation /= length;
if (-separation < smallestPenetrationDepth)
{
normal = separatingAxis / length;
smallestPenetrationDepth = -separation;
isNormalInverted = expression < 0;
separatingAxisNumber = 12;
}
}
#endregion
#region ----- Case 13: Separating Axis: (0, 0, 1) x (OrientationB * (1, 0, 0)) -----
expression = cB.Y * mB.M00 - cB.X * mB.M10;
separation = Math.Abs(expression) - (eA.X * aMB.M10 + eA.Y * aMB.M00 + eB.Y * aMB.M22 + eB.Z * aMB.M21);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean)
{
separatingAxis = new Vector3F(-mB.M10, mB.M00, 0);
length = separatingAxis.Length;
separation /= length;
if (-separation < smallestPenetrationDepth)
{
normal = separatingAxis / length;
smallestPenetrationDepth = -separation;
isNormalInverted = expression < 0;
separatingAxisNumber = 13;
}
}
#endregion
#region ----- Case 14: Separating Axis: (0, 0, 1) x (OrientationB * (0, 1, 0)) -----
expression = cB.Y * mB.M01 - cB.X * mB.M11;
separation = Math.Abs(expression) - (eA.X * aMB.M11 + eA.Y * aMB.M01 + eB.X * aMB.M22 + eB.Z * aMB.M20);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean)
{
separatingAxis = new Vector3F(-mB.M11, mB.M01, 0);
length = separatingAxis.Length;
separation /= length;
if (-separation < smallestPenetrationDepth)
{
normal = separatingAxis / length;
smallestPenetrationDepth = -separation;
isNormalInverted = expression < 0;
separatingAxisNumber = 14;
}
}
#endregion
#region ----- Case 15: Separating Axis: (0, 0, 1) x (OrientationB * (0, 0, 1)) -----
expression = cB.Y * mB.M02 - cB.X * mB.M12;
separation = Math.Abs(expression) - (eA.X * aMB.M12 + eA.Y * aMB.M02 + eB.X * aMB.M21 + eB.Y * aMB.M20);
if (separation > 0)
{
return;
}
if (type != CollisionQueryType.Boolean)
{
separatingAxis = new Vector3F(-mB.M12, mB.M02, 0);
length = separatingAxis.Length;
separation /= length;
if (-separation < smallestPenetrationDepth)
{
normal = separatingAxis / length;
smallestPenetrationDepth = -separation;
isNormalInverted = expression < 0;
separatingAxisNumber = 15;
}
}
#endregion
// We have a contact.
contactSet.HaveContact = true;
// HaveContact queries can exit here.
if (type == CollisionQueryType.Boolean)
{
return;
}
// Lets find the contact info.
Debug.Assert(smallestPenetrationDepth >= 0, "The smallest penetration depth should be greater than or equal to 0.");
if (isNormalInverted)
{
normal = -normal;
}
// Transform normal from local space of A to world space.
Vector3F normalWorld = poseA.ToWorldDirection(normal);
if (separatingAxisNumber > 6)
{
// The intersection was detected by an edge-edge test.
// Get the intersecting edges.
// Separating axes:
// 7 = x edge on A, x edge on B
// 8 = x edge on A, y edge on B
// 9 = x edge on A, Z edge on B
// 10 = y edge on A, x edge on B
// ...
// 15 = z edge on A, z edge on B
var edgeA = boxA.GetEdge((separatingAxisNumber - 7) / 3, normal, scaleA);
var edgeB = boxB.GetEdge((separatingAxisNumber - 7) % 3, Matrix33F.MultiplyTransposed(mB, -normal), scaleB);
edgeB.Start = mB * edgeB.Start + cB;
edgeB.End = mB * edgeB.End + cB;
Vector3F position;
Vector3F dummy;
GeometryHelper.GetClosestPoints(edgeA, edgeB, out position, out dummy);
position = position - normal * (smallestPenetrationDepth / 2); // Position is between the positions of the box surfaces.
// Convert back position from local space of A to world space;
position = poseA.ToWorldPosition(position);
Contact contact = ContactHelper.CreateContact(contactSet, position, normalWorld, smallestPenetrationDepth, false);
ContactHelper.Merge(contactSet, contact, type, CollisionDetection.ContactPositionTolerance);
}
else if (1 <= separatingAxisNumber && separatingAxisNumber <= 6)
{
// The intersection was detected by a face vs. * test.
// The separating axis is perpendicular to a face.
#region ----- Credits -----
// The face vs. * test is based on the algorithm of the Bullet Continuous Collision
// Detection and Physics Library. DigitalRune Geometry contains a new and improved
// implementation of the original algorithm.
//
// The box-box detector in Bullet contains the following remarks:
//
// Box-Box collision detection re-distributed under the ZLib license with permission from Russell L. Smith
// Original version is from Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith.
// All rights reserved. Email: [email protected] Web: www.q12.org
//
// Bullet Continuous Collision Detection and Physics Library
// Copyright (c) 2003-2006 Erwin Coumans http://continuousphysics.com/Bullet/
//
// This software is provided 'as-is', without any express or implied warranty.
// In no event will the authors be held liable for any damages arising from the use of this software.
// Permission is granted to anyone to use this software for any purpose,
// including commercial applications, and to alter it and redistribute it freely,
// subject to the following restrictions:
//
// 1. The origin of this software must not be misrepresented; you must not claim that you wrote the
// original software. If you use this software in a product, an acknowledgment in the product
// documentation would be appreciated but is not required.
// 2. Altered source versions must be plainly marked as such, and must not be misrepresented as being
// the original software.
// 3. This notice may not be removed or altered from any source distribution.
#endregion
// We define the face perpendicular to the separating axis to be the "reference face".
// The face of the other box closest to the reference face is called the "incident face".
// Accordingly, we will call the box containing the reference face the "reference box" and
// the box containing the incident face the "incident box".
//
// We will transform the incident face into the 2D space of reference face. Then we will
// clip the incident face against the reference face. The polygon resulting from the
// intersection will be transformed back into world space and the points of the polygon will
// be the candidates for the contact points.
Pose poseR; // Pose of reference box.
Pose poseI; // Pose of incident box.
Vector3F boxExtentR; // Half extent of reference box.
Vector3F boxExtentI; // Half extent of incident box.
// Contact normal (= normal of reference face) in world space.
if (separatingAxisNumber <= 3)
{
poseR = poseA;
poseI = poseB;
boxExtentR = eA;
boxExtentI = eB;
isNormalInverted = false;
}
else
{
poseR = poseB;
poseI = poseA;
boxExtentR = eB;
boxExtentI = eA;
normalWorld = -normalWorld;
isNormalInverted = true;
}
// Contact normal in local space of incident box.
Vector3F normalI = poseI.ToLocalDirection(normalWorld);
Vector3F absNormal = normalI;
absNormal.Absolute();
Vector3F xAxisInc, yAxisInc; // The basis of the incident-face space.
float absFaceOffsetI; // The offset of the incident face to the center of the box.
Vector2F faceExtentI; // The half extent of the incident face.
Vector3F faceNormal; // The normal of the incident face in world space.
float faceDirection; // A value indicating the direction of the incident face.
// Find the largest component of the normal. The largest component indicates which face is
// the incident face.
switch (Vector3F.Absolute(normalI).IndexOfLargestComponent)
{
case 0:
faceExtentI.X = boxExtentI.Y;
faceExtentI.Y = boxExtentI.Z;
absFaceOffsetI = boxExtentI.X;
faceNormal = poseI.Orientation.GetColumn(0);
xAxisInc = poseI.Orientation.GetColumn(1);
yAxisInc = poseI.Orientation.GetColumn(2);
faceDirection = normalI.X;
break;
case 1:
faceExtentI.X = boxExtentI.X;
faceExtentI.Y = boxExtentI.Z;
absFaceOffsetI = boxExtentI.Y;
faceNormal = poseI.Orientation.GetColumn(1);
xAxisInc = poseI.Orientation.GetColumn(0);
yAxisInc = poseI.Orientation.GetColumn(2);
faceDirection = normalI.Y;
break;
// case 2:
default:
faceExtentI.X = boxExtentI.X;
faceExtentI.Y = boxExtentI.Y;
absFaceOffsetI = boxExtentI.Z;
faceNormal = poseI.Orientation.GetColumn(2);
xAxisInc = poseI.Orientation.GetColumn(0);
yAxisInc = poseI.Orientation.GetColumn(1);
faceDirection = normalI.Z;
break;
}
// Compute center of incident face relative to the center of the reference box in world space.
float faceOffset = (faceDirection < 0) ? absFaceOffsetI : -absFaceOffsetI;
Vector3F centerOfFaceI = faceNormal * faceOffset + poseI.Position - poseR.Position;
// (Note: We will use the center of the incident face to compute the points of the incident
// face and transform the points into the reference-face frame. The center of the incident
// face is relative to the center of the reference box. We could also get center of the
// incident face relative to the center of the reference face. But since we are projecting
// the points from 3D to 2D this does not matter.)
Vector3F xAxisR, yAxisR; // The basis of the reference-face space.
float faceOffsetR; // The offset of the reference face to the center of the box.
Vector2F faceExtentR; // The half extent of the reference face.
switch (separatingAxisNumber)
{
case 1:
case 4:
faceExtentR.X = boxExtentR.Y;
faceExtentR.Y = boxExtentR.Z;
faceOffsetR = boxExtentR.X;
xAxisR = poseR.Orientation.GetColumn(1);
yAxisR = poseR.Orientation.GetColumn(2);
break;
case 2:
case 5:
faceExtentR.X = boxExtentR.X;
faceExtentR.Y = boxExtentR.Z;
faceOffsetR = boxExtentR.Y;
xAxisR = poseR.Orientation.GetColumn(0);
yAxisR = poseR.Orientation.GetColumn(2);
break;
// case 3:
// case 6:
default:
faceExtentR.X = boxExtentR.X;
faceExtentR.Y = boxExtentR.Y;
faceOffsetR = boxExtentR.Z;
xAxisR = poseR.Orientation.GetColumn(0);
yAxisR = poseR.Orientation.GetColumn(1);
break;
}
// Compute the center of the incident face in the reference-face frame.
// We can simply project centerOfFaceI onto the x- and y-axis of the reference
// face.
Vector2F centerOfFaceIInR;
//centerOfFaceIInR.X = Vector3F.Dot(centerOfFaceI, xAxisR);
// ----- Optimized version:
centerOfFaceIInR.X = centerOfFaceI.X * xAxisR.X + centerOfFaceI.Y * xAxisR.Y + centerOfFaceI.Z * xAxisR.Z;
//centerOfFaceIInR.Y = Vector3F.Dot(centerOfFaceI, yAxisR);
// ----- Optimized version:
centerOfFaceIInR.Y = centerOfFaceI.X * yAxisR.X + centerOfFaceI.Y * yAxisR.Y + centerOfFaceI.Z * yAxisR.Z;
// Now, we have the center of the incident face in reference-face coordinates.
// To compute the corners of the incident face in reference-face coordinates, we need
// transform faceExtentI (the half extent vector of the incident face) from the incident-
// face frame to the reference-face frame to compute the corners.
//
// The reference-face frame has the basis
// mR = (xAxisR, yAxisR, ?)
//
// The incident-face frame has the basis
// mI = (xAxisI, yAxisI, ?)
//
// Rotation from incident-face frame to reference-face frame is
// mIToR = mR^-1 * mI
//
// The corner offsets in incident-face space is are vectors (x, y, 0). To transform these
// vectors from incident-face space to reference-face space we need to calculate:
// mIToR * v
//
// Since the z-components are 0 and we are only interested in the resulting x, y coordinates
// in reference-space when can reduce the rotation to a 2 x 2 matrix. (The other components
// are not needed.)
// ----- Optimized version: (Original on the right)
Matrix22F mIToR;
mIToR.M00 = xAxisR.X * xAxisInc.X + xAxisR.Y * xAxisInc.Y + xAxisR.Z * xAxisInc.Z; // mIToR.M00 = Vector3F.Dot(xAxisR, xAxisInc);
mIToR.M01 = xAxisR.X * yAxisInc.X + xAxisR.Y * yAxisInc.Y + xAxisR.Z * yAxisInc.Z; // mIToR.M01 = Vector3F.Dot(xAxisR, yAxisInc);
mIToR.M10 = yAxisR.X * xAxisInc.X + yAxisR.Y * xAxisInc.Y + yAxisR.Z * xAxisInc.Z; // mIToR.M10 = Vector3F.Dot(yAxisR, xAxisInc);
mIToR.M11 = yAxisR.X * yAxisInc.X + yAxisR.Y * yAxisInc.Y + yAxisR.Z * yAxisInc.Z; // mIToR.M11 = Vector3F.Dot(yAxisR, yAxisInc);
// The corner offsets in incident-face space are:
// (-faceExtentI.X, -faceExtentI.Y) ... left, bottom corner
// ( faceExtentI.X, -faceExtentI.Y) ... right, bottom corner
// ( faceExtentI.X, faceExtentI.Y) ... right, top corner
// (-faceExtentI.X, faceExtentI.Y) ... left, top corner
//
// Instead of transforming each corner offset, we can optimize the computation: Do the
// matrix-vector multiplication once, keep the intermediate products, apply the sign
// of the components when adding the intermediate results.
float k1 = mIToR.M00 * faceExtentI.X; // Products of matrix-vector multiplication.
float k2 = mIToR.M01 * faceExtentI.Y;
float k3 = mIToR.M10 * faceExtentI.X;
float k4 = mIToR.M11 * faceExtentI.Y;
List <Vector2F> quad = DigitalRune.ResourcePools <Vector2F> .Lists.Obtain();
quad.Add(new Vector2F(centerOfFaceIInR.X - k1 - k2, centerOfFaceIInR.Y - k3 - k4));
quad.Add(new Vector2F(centerOfFaceIInR.X + k1 - k2, centerOfFaceIInR.Y + k3 - k4));
quad.Add(new Vector2F(centerOfFaceIInR.X + k1 + k2, centerOfFaceIInR.Y + k3 + k4));
quad.Add(new Vector2F(centerOfFaceIInR.X - k1 + k2, centerOfFaceIInR.Y - k3 + k4));
// Clip incident face (quadrilateral) against reference face (rectangle).
List <Vector2F> contacts2D = ClipQuadrilateralAgainstRectangle(faceExtentR, quad);
// Transform contact points back to world space and compute penetration depths.
int numberOfContacts = contacts2D.Count;
List <Vector3F> contacts3D = DigitalRune.ResourcePools <Vector3F> .Lists.Obtain();
List <float> penetrationDepths = DigitalRune.ResourcePools <float> .Lists.Obtain();
Matrix22F mRToI = mIToR.Inverse;
for (int i = numberOfContacts - 1; i >= 0; i--)
{
Vector2F contact2DR = contacts2D[i]; // Contact in reference-face space.
Vector2F contact2DI = mRToI * (contact2DR - centerOfFaceIInR); // Contact in incident-face space.
// Transform point in incident-face space to world (relative to center of reference box).
// contact3D = mI * (x, y, 0) + centerOfFaceI
Vector3F contact3D;
contact3D.X = xAxisInc.X * contact2DI.X + yAxisInc.X * contact2DI.Y + centerOfFaceI.X;
contact3D.Y = xAxisInc.Y * contact2DI.X + yAxisInc.Y * contact2DI.Y + centerOfFaceI.Y;
contact3D.Z = xAxisInc.Z * contact2DI.X + yAxisInc.Z * contact2DI.Y + centerOfFaceI.Z;
// Compute penetration depth.
//float penetrationDepth = faceOffsetR - Vector3F.Dot(normalWorld, contact3D);
// ----- Optimized version:
float penetrationDepth = faceOffsetR - (normalWorld.X * contact3D.X + normalWorld.Y * contact3D.Y + normalWorld.Z * contact3D.Z);
if (penetrationDepth >= 0)
{
// Valid contact.
contacts3D.Add(contact3D);
penetrationDepths.Add(penetrationDepth);
}
else
{
// Remove bad contacts from the 2D contacts.
// (We might still need the 2D contacts, if we need to reduce the contacts.)
contacts2D.RemoveAt(i);
}
}
numberOfContacts = contacts3D.Count;
if (numberOfContacts == 0)
{
return; // Should never happen.
}
// Revert normal back to original direction.
normal = (isNormalInverted) ? -normalWorld : normalWorld;
// Note: normal ........ contact normal pointing from box A to B.
// normalWorld ... contact normal pointing from reference box to incident box.
if (numberOfContacts <= MaxNumberOfContacts)
{
// Add all contacts to contact set.
for (int i = 0; i < numberOfContacts; i++)
{
float penetrationDepth = penetrationDepths[i];
// Position is between the positions of the box surfaces.
Vector3F position = contacts3D[i] + poseR.Position + normalWorld * (penetrationDepth / 2);
Contact contact = ContactHelper.CreateContact(contactSet, position, normal, penetrationDepth, false);
ContactHelper.Merge(contactSet, contact, type, CollisionDetection.ContactPositionTolerance);
}
}
else
{
// Reduce number of contacts, keep the contact with the max penetration depth.
int indexOfDeepest = 0;
float maxPenetrationDepth = penetrationDepths[0];
for (int i = 1; i < numberOfContacts; i++)
{
float penetrationDepth = penetrationDepths[i];
if (penetrationDepth > maxPenetrationDepth)
{
maxPenetrationDepth = penetrationDepth;
indexOfDeepest = i;
}
}
List <int> indicesOfContacts = ReduceContacts(contacts2D, indexOfDeepest, MaxNumberOfContacts);
// Add selected contacts to contact set.
numberOfContacts = indicesOfContacts.Count;
for (int i = 0; i < numberOfContacts; i++)
{
int index = indicesOfContacts[i];
float penetrationDepth = penetrationDepths[index];
// Position is between the positions of the box surfaces.
Vector3F position = contacts3D[index] + poseR.Position + normalWorld * (penetrationDepth / 2);
Contact contact = ContactHelper.CreateContact(contactSet, position, normal, penetrationDepths[index], false);
ContactHelper.Merge(contactSet, contact, type, CollisionDetection.ContactPositionTolerance);
}
DigitalRune.ResourcePools <int> .Lists.Recycle(indicesOfContacts);
}
DigitalRune.ResourcePools <Vector2F> .Lists.Recycle(contacts2D);
DigitalRune.ResourcePools <Vector3F> .Lists.Recycle(contacts3D);
DigitalRune.ResourcePools <float> .Lists.Recycle(penetrationDepths);
}
}
//public Vector3F RelativePosition
//{
// get
// {
// if (BodyA == null)
// throw new PhysicsException("BodyA must not be null.");
// if (BodyB == null)
// throw new PhysicsException("BodyB must not be null.");
// // Anchor orientation in world space.
// Matrix33F anchorOrientationA = BodyA.Pose.Orientation * AnchorOrientationALocal;
// Matrix33F anchorOrientationB = BodyB.Pose.Orientation * AnchorOrientationBLocal;
// // Anchor orientation of B relative to A.
// Matrix33F relativeOrientation = anchorOrientationA.Transposed * anchorOrientationB;
// // The Euler angles.
// Vector3F angles = GetAngles(relativeOrientation);
// return angles;
// }
//}
#endregion
//--------------------------------------------------------------
#region Creation & Cleanup
//--------------------------------------------------------------
#endregion
//--------------------------------------------------------------
#region Methods
//--------------------------------------------------------------
/// <inheritdoc/>
protected override void OnSetup()
{
// Get anchor orientations in world space.
Matrix33F anchorOrientationA = BodyA.Pose.Orientation * AnchorOrientationALocal;
Matrix33F anchorOrientationB = BodyB.Pose.Orientation * AnchorOrientationBLocal;
// Get the quaternion that rotates something from anchor orientation A to
// anchor orientation B:
// QB = QTotal * QA
// => QTotal = QB * QA.Inverse
QuaternionF total = QuaternionF.CreateRotation(anchorOrientationB * anchorOrientationA.Transposed);
// Compute swing axis and angle.
Vector3F xAxisA = anchorOrientationA.GetColumn(0);
Vector3F yAxisA = anchorOrientationA.GetColumn(1);
Vector3F xAxisB = anchorOrientationB.GetColumn(0);
QuaternionF swing = QuaternionF.CreateRotation(xAxisA, xAxisB);
Vector3F swingAxis = new Vector3F(swing.X, swing.Y, swing.Z);
if (!swingAxis.TryNormalize())
{
swingAxis = yAxisA;
}
float swingAngle = swing.Angle;
Debug.Assert(
0 <= swingAngle && swingAngle <= ConstantsF.Pi,
"QuaternionF.CreateRotation(Vector3F, Vector3F) should only create rotations along the \"short arc\".");
// The swing limits create a deformed cone. If we look onto the x-axis of A:
// y-axis goes to the right. z-axis goes up.
Vector3F xAxisBInAnchorA = Matrix33F.MultiplyTransposed(anchorOrientationA, xAxisB);
float directionY = xAxisBInAnchorA.Y;
float directionZ = xAxisBInAnchorA.Z;
// In this plane, we have an ellipse with the formula:
// y²/a² + z²/b² = 1, where a and b are the ellipse radii.
// We don't know the exact radii. We can compute them from the swing min/max angles.
// To make it simpler, we do not use a flat ellipse. We use the swing z limit for a.
// And the swing y limit for b.
// We have a different ellipse for each quarter.
float ellipseA = (directionY > 0) ? Maximum.Z : -Minimum.Z;
float ellipseB = (directionZ > 0) ? -Minimum.Y : Maximum.Y;
// The angles are in radians: angle = bow/radius. So our a and b are on the unit sphere.
// This creates an elliptic thing on the unit sphere - not in a plane. We don't care because
// we only need a smooth interpolation between the swing y and z limits.
// No we look for the swing angle in the direction of xAxisB.
// The next step can derived from following formulas:
// y²/a² + z²/b² = 1 The ellipse formula.
// slope = directionZ / directionY The direction in which we need the limit.
// slope = z/y The (y,z) is the point on the ellipse in the given direction.
// swingLimit = sqrt(y² + z²) This is the distance of (y,z) from the center.
// Since our ellipse is on a sphere, swingLimit is an angle (= bow / radius).
float swingLimit = ellipseB;
if (!Numeric.IsZero(directionY))
{
float slope = directionZ / directionY;
float slopeSquared = slope * slope;
float ellipseASquared = ellipseA * ellipseA;
float ellipseBSquared = ellipseB * ellipseB;
swingLimit = (float)Math.Sqrt((1 + slopeSquared) / (1 / ellipseASquared + slopeSquared / ellipseBSquared));
// The ellipse normal would give us a better swing axis. But our computed swingAngle
// is not correct for this axis...
// Create a swing axis from the ellipse normal.
//float k = ellipseASquared / ellipseBSquared * directionZ / directionY;
//var normal = anchorOrientationA * new Vector3F(0, -k, 1).Normalized;
//if (Vector3F.Dot(normal, swingAxis) < 0)
// swingAxis = -normal;
//else
// swingAxis = normal;
}
#if DEBUG
//Debug.Assert(QuaternionF.Dot(swing, total) >= 0);
var swingAxisALocal = Matrix33F.MultiplyTransposed(anchorOrientationA, swingAxis);
Debug.Assert(Numeric.IsZero(swingAxisALocal.X));
#endif
// We define our rotations like this:
// First we twist around the x-axis of A. Then we swing.
// QTotal = QSwing * QTwist
// => QSwing.Inverse * QTotal = QTwist
QuaternionF twist = swing.Conjugated * total;
twist.Normalize();
// The quaternion returns an angle in the range [0, 2π].
float twistAngle = twist.Angle;
// The minimum and maximum twist limits are in the range [-π, π].
if (twistAngle > ConstantsF.Pi)
{
// Convert the twistAngle to the range used by the twist limits.
twistAngle = -(ConstantsF.TwoPi - twistAngle);
Debug.Assert(-ConstantsF.TwoPi < twistAngle && twistAngle <= ConstantsF.TwoPi);
}
// The axis of the twist quaternion is parallel to xAxisA.
Vector3F twistAxis = new Vector3F(twist.X, twist.Y, twist.Z);
if (Vector3F.Dot(twistAxis, xAxisA) < 0)
{
// The axis of the twist quaternion points in the opposite direction of xAxisA.
// The twist angle need to be inverted.
twistAngle = -twistAngle;
}
// Remember old states.
LimitState oldXLimitState = _limitStates[0];
LimitState oldYLimitState = _limitStates[1];
// Note: All axes between xAxisA and xAxisB should be valid twist axes.
SetupConstraint(0, twistAngle, xAxisB, Minimum[0], Maximum[0]);
SetupConstraint(1, swingAngle, swingAxis, -swingLimit, swingLimit);
// Warm-start the constraints if the previous limit state matches the new limit state.
Warmstart(0, oldXLimitState);
Warmstart(1, oldYLimitState);
}