/// <summary>
/// Diagonalizes the inertia matrix.
/// </summary>
/// <param name="inertia">The inertia matrix.</param>
/// <param name="inertiaDiagonal">The inertia of the principal axes.</param>
/// <param name="rotation">
/// The rotation that rotates from principal axis space to parent/world space.
/// </param>
/// <remarks>
/// All valid inertia matrices can be transformed into a coordinate space where all elements
/// non-diagonal matrix elements are 0. The axis of this special space are the principal axes.
/// </remarks>
internal static void DiagonalizeInertia(Matrix33F inertia, out Vector3F inertiaDiagonal, out Matrix33F rotation)
{
// Alternatively we could use Jacobi transformation (iterative method, see Bullet/btMatrix3x3.diagonalize()
// and Numerical Recipes book) or we could find the eigenvalues using the characteristic
// polynomial which is a cubic polynomial and then solve for the eigenvectors (see Numeric
// Recipes and "Mathematics for 3D Game Programming and Computer Graphics" chapter ray-tracing
// for cubic equations and computation of bounding boxes.
// Perform eigenvalue decomposition.
var eigenValueDecomposition = new EigenvalueDecompositionF(inertia.ToMatrixF());
inertiaDiagonal = eigenValueDecomposition.RealEigenvalues.ToVector3F();
rotation = eigenValueDecomposition.V.ToMatrix33F();
if (!rotation.IsRotation)
{
// V is orthogonal but not necessarily a rotation. If it is no rotation
// we have to swap two columns.
MathHelper.Swap(ref inertiaDiagonal.Y, ref inertiaDiagonal.Z);
Vector3F dummy = rotation.GetColumn(1);
rotation.SetColumn(1, rotation.GetColumn(2));
rotation.SetColumn(2, dummy);
Debug.Assert(rotation.IsRotation);
}
}
/// <inheritdoc/>
protected override void OnSetup()
{
// Get anchor pose/position in world space.
Pose anchorPoseA = BodyA.Pose * AnchorPoseALocal;
Vector3F anchorPositionB = BodyB.Pose.ToWorldPosition(AnchorPositionBLocal); // TODO: We could store rALocal and use ToWorldDirection instead of ToWorldPosition.
// Compute anchor position on B relative to anchor pose of A.
Vector3F relativePosition = anchorPoseA.ToLocalPosition(anchorPositionB);
// The linear constraint axes are the fixed anchor axes of A!
Matrix33F anchorOrientation = anchorPoseA.Orientation;
Vector3F rA = anchorPoseA.Position - BodyA.PoseCenterOfMass.Position;
Vector3F rB = anchorPositionB - BodyB.PoseCenterOfMass.Position;
// Remember old states.
LimitState oldXLimitState = _limitStates[0];
LimitState oldYLimitState = _limitStates[1];
LimitState oldZLimitState = _limitStates[2];
SetupConstraint(0, relativePosition.X, anchorOrientation.GetColumn(0), rA, rB);
SetupConstraint(1, relativePosition.Y, anchorOrientation.GetColumn(1), rA, rB);
SetupConstraint(2, relativePosition.Z, anchorOrientation.GetColumn(2), rA, rB);
Warmstart(0, oldXLimitState);
Warmstart(1, oldYLimitState);
Warmstart(2, oldZLimitState);
}
/// <summary>
/// Diagonalizes the inertia matrix.
/// </summary>
/// <param name="inertia">The inertia matrix.</param>
/// <param name="inertiaDiagonal">The inertia of the principal axes.</param>
/// <param name="rotation">
/// The rotation that rotates from principal axis space to parent/world space.
/// </param>
/// <remarks>
/// All valid inertia matrices can be transformed into a coordinate space where all elements
/// non-diagonal matrix elements are 0. The axis of this special space are the principal axes.
/// </remarks>
internal static void DiagonalizeInertia(Matrix33F inertia, out Vector3F inertiaDiagonal, out Matrix33F rotation)
{
// Alternatively we could use Jacobi transformation (iterative method, see Bullet/btMatrix3x3.diagonalize()
// and Numerical Recipes book) or we could find the eigenvalues using the characteristic
// polynomial which is a cubic polynomial and then solve for the eigenvectors (see Numeric
// Recipes and "Mathematics for 3D Game Programming and Computer Graphics" chapter ray-tracing
// for cubic equations and computation of bounding boxes.
// Perform eigenvalue decomposition.
var eigenValueDecomposition = new EigenvalueDecompositionF(inertia.ToMatrixF());
inertiaDiagonal = eigenValueDecomposition.RealEigenvalues.ToVector3F();
rotation = eigenValueDecomposition.V.ToMatrix33F();
if (!rotation.IsRotation)
{
// V is orthogonal but not necessarily a rotation. If it is no rotation
// we have to swap two columns.
MathHelper.Swap(ref inertiaDiagonal.Y, ref inertiaDiagonal.Z);
Vector3F dummy = rotation.GetColumn(1);
rotation.SetColumn(1, rotation.GetColumn(2));
rotation.SetColumn(2, dummy);
Debug.Assert(rotation.IsRotation);
}
}
public void GetColumn()
{
Matrix33F m = new Matrix33F(columnMajor, MatrixOrder.ColumnMajor);
Assert.AreEqual(new Vector3F(1.0f, 4.0f, 7.0f), m.GetColumn(0));
Assert.AreEqual(new Vector3F(2.0f, 5.0f, 8.0f), m.GetColumn(1));
Assert.AreEqual(new Vector3F(3.0f, 6.0f, 9.0f), m.GetColumn(2));
}
/// <inheritdoc/>
protected override void OnSetup()
{
// Get anchor orientations in world space.
Matrix33F anchorOrientationA = BodyA.Pose.Orientation * AnchorOrientationALocal;
Matrix33F anchorOrientationB = BodyB.Pose.Orientation * AnchorOrientationBLocal;
// Get anchor orientation of B relative to A.
Matrix33F relativeOrientation = anchorOrientationA.Transposed * anchorOrientationB;
Vector3F angles = ConstraintHelper.GetEulerAngles(relativeOrientation);
// The constraint axes: See OneNote for a detailed derivation of these non-intuitive axes.
var xA = anchorOrientationA.GetColumn(0); // Anchor x-axis on A.
var zB = anchorOrientationB.GetColumn(2); // Anchor z-axis on B.
Vector3F constraintAxisY = Vector3F.Cross(zB, xA);
Vector3F constraintAxisX = Vector3F.Cross(constraintAxisY, zB);
Vector3F constraintAxisZ = Vector3F.Cross(xA, constraintAxisY);
// Remember old states.
LimitState oldXLimitState = _limitStates[0];
LimitState oldYLimitState = _limitStates[1];
LimitState oldZLimitState = _limitStates[2];
SetupConstraint(0, angles.X, constraintAxisX);
SetupConstraint(1, angles.Y, constraintAxisY);
SetupConstraint(2, angles.Z, constraintAxisZ);
Warmstart(0, oldXLimitState);
Warmstart(1, oldYLimitState);
Warmstart(2, oldZLimitState);
}
public void MultiplyMatrix()
{
Matrix33F m = new Matrix33F(12, 23, 45,
67, 89, 90,
43, 65, 87);
Assert.AreEqual(Matrix33F.Zero, Matrix33F.Multiply(m, Matrix33F.Zero));
Assert.AreEqual(Matrix33F.Zero, Matrix33F.Multiply(Matrix33F.Zero, m));
Assert.AreEqual(m, Matrix33F.Multiply(m, Matrix33F.Identity));
Assert.AreEqual(m, Matrix33F.Multiply(Matrix33F.Identity, m));
Assert.IsTrue(Matrix33F.AreNumericallyEqual(Matrix33F.Identity, Matrix33F.Multiply(m, m.Inverse)));
Assert.IsTrue(Matrix33F.AreNumericallyEqual(Matrix33F.Identity, Matrix33F.Multiply(m.Inverse, m)));
Matrix33F m1 = new Matrix33F(columnMajor, MatrixOrder.ColumnMajor);
Matrix33F m2 = new Matrix33F(12, 23, 45,
67, 89, 90,
43, 65, 87);
Matrix33F result = Matrix33F.Multiply(m1, m2);
for (int column = 0; column < 3; column++)
{
for (int row = 0; row < 3; row++)
{
Assert.AreEqual(Vector3F.Dot(m1.GetRow(row), m2.GetColumn(column)), result[row, column]);
}
}
}
//--------------------------------------------------------------
#region Creation & Cleanup
//--------------------------------------------------------------
#endregion
//--------------------------------------------------------------
#region Methods
//--------------------------------------------------------------
/// <inheritdoc/>
protected override void OnSetup()
{
var deltaTime = Simulation.Settings.Timing.FixedTimeStep;
float errorReduction = ConstraintHelper.ComputeErrorReduction(deltaTime, SpringConstant, DampingConstant);
float softness = ConstraintHelper.ComputeSoftness(deltaTime, SpringConstant, DampingConstant);
// Get anchor orientations in world space.
Matrix33F anchorOrientationA = BodyA.Pose.Orientation * AnchorOrientationALocal;
Matrix33F anchorOrientationB = BodyB.Pose.Orientation * AnchorOrientationBLocal;
Matrix33F relativeOrientation = anchorOrientationA.Transposed * anchorOrientationB;
Vector3F angles = ConstraintHelper.GetEulerAngles(relativeOrientation);
// The constraint axes: See OneNote for a detailed derivation of these non-intuitive axes.
var xA = anchorOrientationA.GetColumn(0); // Anchor x-axis on A.
var zB = anchorOrientationB.GetColumn(2); // Anchor z-axis on B.
Vector3F constraintAxisY = Vector3F.Cross(zB, xA);
Vector3F constraintAxisX = Vector3F.Cross(constraintAxisY, zB);
Vector3F constraintAxisZ = Vector3F.Cross(xA, constraintAxisY);
SetupConstraint(0, angles[0], TargetAngles[0], constraintAxisX, deltaTime, errorReduction, softness);
SetupConstraint(1, angles[1], TargetAngles[1], constraintAxisY, deltaTime, errorReduction, softness);
SetupConstraint(2, angles[2], TargetAngles[2], constraintAxisZ, deltaTime, errorReduction, softness);
// No warmstarting.
_constraints[0].ConstraintImpulse = 0;
_constraints[1].ConstraintImpulse = 0;
_constraints[2].ConstraintImpulse = 0;
}
//--------------------------------------------------------------
#region Creation & Cleanup
//--------------------------------------------------------------
#endregion
//--------------------------------------------------------------
#region Methods
//--------------------------------------------------------------
/// <inheritdoc/>
protected override void OnSetup()
{
// Anchor pose/position in world space.
Pose anchorPoseA = BodyA.Pose * AnchorPoseALocal;
Vector3F anchorPositionB = BodyB.Pose.ToWorldPosition(AnchorPositionBLocal);
// Compute anchor pose of B relative to anchor pose of A.
Vector3F relativePosition = anchorPoseA.ToLocalPosition(anchorPositionB);
// The linear constraint axes are the fixed anchor axes of A!
Matrix33F anchorOrientation = anchorPoseA.Orientation;
Vector3F rA = anchorPoseA.Position - BodyA.PoseCenterOfMass.Position;
Vector3F rB = anchorPositionB - BodyB.PoseCenterOfMass.Position;
var deltaTime = Simulation.Settings.Timing.FixedTimeStep;
float errorReduction = ConstraintHelper.ComputeErrorReduction(deltaTime, SpringConstant, DampingConstant);
float softness = ConstraintHelper.ComputeSoftness(deltaTime, SpringConstant, DampingConstant);
if (!UseSingleAxisMode)
{
SetupConstraint(0, relativePosition.X, TargetPosition.X, anchorOrientation.GetColumn(0), rA, rB, deltaTime, errorReduction, softness);
SetupConstraint(1, relativePosition.Y, TargetPosition.Y, anchorOrientation.GetColumn(1), rA, rB, deltaTime, errorReduction, softness);
SetupConstraint(2, relativePosition.Z, TargetPosition.Z, anchorOrientation.GetColumn(2), rA, rB, deltaTime, errorReduction, softness);
}
else
{
var axis = TargetPosition - relativePosition;
var deviation = axis.Length;
if (Numeric.IsZero(deviation))
{
axis = Vector3F.UnitX;
}
else
{
axis.Normalize();
}
SetupConstraint(0, -deviation, 0, axis, rA, rB, deltaTime, errorReduction, softness);
}
// No warmstarting.
_constraints[0].ConstraintImpulse = 0;
_constraints[1].ConstraintImpulse = 0;
_constraints[2].ConstraintImpulse = 0;
}
//--------------------------------------------------------------
#region Creation & Cleanup
//--------------------------------------------------------------
#endregion
//--------------------------------------------------------------
#region Methods
//--------------------------------------------------------------
/// <inheritdoc/>
protected override void OnSetup()
{
Pose anchorPoseA = BodyA.Pose;
Vector3F anchorPositionB = BodyB.Pose.ToWorldPosition(AnchorPositionBLocal);
// The linear constraint axes are the fixed anchor axes of A!
Matrix33F anchorOrientation = anchorPoseA.Orientation;
Vector3F rA = anchorPoseA.Position - BodyA.PoseCenterOfMass.Position;
Vector3F rB = anchorPositionB - BodyB.PoseCenterOfMass.Position;
var deltaTime = Simulation.Settings.Timing.FixedTimeStep;
var axis = BodyA.Pose.Orientation * AxisALocal;
if (!UseSingleAxisMode)
{
// One constraint for each axis fixed on A.
var targetVelocityVector = axis * TargetVelocity;
SetupConstraint(0, targetVelocityVector.X, anchorOrientation.GetColumn(0), rA, rB, deltaTime);
SetupConstraint(1, targetVelocityVector.Y, anchorOrientation.GetColumn(1), rA, rB, deltaTime);
SetupConstraint(2, targetVelocityVector.Z, anchorOrientation.GetColumn(2), rA, rB, deltaTime);
}
else
{
// One constraint in direction of the velocity.
if (axis.IsNumericallyZero)
{
// TODO: We could have a separate Axis property if the motor should be able to constrain to velocity 0 in Single Axis Mode.
// No velocity axis.
_minImpulseLimits[0] = 0;
}
else
{
SetupConstraint(0, TargetVelocity, axis, rA, rB, deltaTime);
}
}
// No warmstarting.
_constraints[0].ConstraintImpulse = 0;
_constraints[1].ConstraintImpulse = 0;
_constraints[2].ConstraintImpulse = 0;
}
public void SetColumn()
{
Matrix33F m = new Matrix33F(columnMajor, MatrixOrder.ColumnMajor);
m.SetColumn(0, new Vector3F(0.1f, 0.2f, 0.3f));
Assert.AreEqual(new Vector3F(0.1f, 0.2f, 0.3f), m.GetColumn(0));
Assert.AreEqual(new Vector3F(2.0f, 5.0f, 8.0f), m.GetColumn(1));
Assert.AreEqual(new Vector3F(3.0f, 6.0f, 9.0f), m.GetColumn(2));
m.SetColumn(1, new Vector3F(0.4f, 0.5f, 0.6f));
Assert.AreEqual(new Vector3F(0.1f, 0.2f, 0.3f), m.GetColumn(0));
Assert.AreEqual(new Vector3F(0.4f, 0.5f, 0.6f), m.GetColumn(1));
Assert.AreEqual(new Vector3F(3.0f, 6.0f, 9.0f), m.GetColumn(2));
m.SetColumn(2, new Vector3F(0.7f, 0.8f, 0.9f));
Assert.AreEqual(new Vector3F(0.1f, 0.2f, 0.3f), m.GetColumn(0));
Assert.AreEqual(new Vector3F(0.4f, 0.5f, 0.6f), m.GetColumn(1));
Assert.AreEqual(new Vector3F(0.7f, 0.8f, 0.9f), m.GetColumn(2));
}
public void MultiplyMatrixOperator()
{
Matrix33F m = new Matrix33F(12, 23, 45,
67, 89, 90,
43, 65, 87);
Assert.AreEqual(Matrix33F.Zero, m * Matrix33F.Zero);
Assert.AreEqual(Matrix33F.Zero, Matrix33F.Zero * m);
Assert.AreEqual(m, m * Matrix33F.Identity);
Assert.AreEqual(m, Matrix33F.Identity * m);
Assert.IsTrue(Matrix33F.AreNumericallyEqual(Matrix33F.Identity, m * m.Inverse));
Assert.IsTrue(Matrix33F.AreNumericallyEqual(Matrix33F.Identity, m.Inverse * m));
Matrix33F m1 = new Matrix33F(columnMajor, MatrixOrder.ColumnMajor);
Matrix33F m2 = new Matrix33F(12, 23, 45,
67, 89, 90,
43, 65, 87);
Matrix33F result = m1 * m2;
for (int column = 0; column < 3; column++)
for (int row = 0; row < 3; row++)
Assert.AreEqual(Vector3F.Dot(m1.GetRow(row), m2.GetColumn(column)), result[row, column]);
}
public void GetColumnException2()
{
Matrix33F m = new Matrix33F(columnMajor, MatrixOrder.ColumnMajor);
m.GetColumn(3);
}
public void GetColumn()
{
Matrix33F m = new Matrix33F(columnMajor, MatrixOrder.ColumnMajor);
Assert.AreEqual(new Vector3F(1.0f, 4.0f, 7.0f), m.GetColumn(0));
Assert.AreEqual(new Vector3F(2.0f, 5.0f, 8.0f), m.GetColumn(1));
Assert.AreEqual(new Vector3F(3.0f, 6.0f, 9.0f), m.GetColumn(2));
}
public void SetColumn()
{
Matrix33F m = new Matrix33F(columnMajor, MatrixOrder.ColumnMajor);
m.SetColumn(0, new Vector3F(0.1f, 0.2f, 0.3f));
Assert.AreEqual(new Vector3F(0.1f, 0.2f, 0.3f), m.GetColumn(0));
Assert.AreEqual(new Vector3F(2.0f, 5.0f, 8.0f), m.GetColumn(1));
Assert.AreEqual(new Vector3F(3.0f, 6.0f, 9.0f), m.GetColumn(2));
m.SetColumn(1, new Vector3F(0.4f, 0.5f, 0.6f));
Assert.AreEqual(new Vector3F(0.1f, 0.2f, 0.3f), m.GetColumn(0));
Assert.AreEqual(new Vector3F(0.4f, 0.5f, 0.6f), m.GetColumn(1));
Assert.AreEqual(new Vector3F(3.0f, 6.0f, 9.0f), m.GetColumn(2));
m.SetColumn(2, new Vector3F(0.7f, 0.8f, 0.9f));
Assert.AreEqual(new Vector3F(0.1f, 0.2f, 0.3f), m.GetColumn(0));
Assert.AreEqual(new Vector3F(0.4f, 0.5f, 0.6f), m.GetColumn(1));
Assert.AreEqual(new Vector3F(0.7f, 0.8f, 0.9f), m.GetColumn(2));
}
public override void Render(IList <SceneNode> nodes, RenderContext context, RenderOrder order)
{
if (nodes == null)
{
throw new ArgumentNullException("nodes");
}
if (context == null)
{
throw new ArgumentNullException("context");
}
if (context.Scene == null)
{
throw new ArgumentException("Scene needs to be set in render context.", "context");
}
if (context.CameraNode == null)
{
throw new ArgumentException("Camera needs to be set in render context.", "context");
}
if (!(context.CameraNode.Camera.Projection is PerspectiveProjection))
{
throw new ArgumentException("The camera in the render context must use a perspective projection.", "context");
}
int numberOfNodes = nodes.Count;
if (numberOfNodes == 0)
{
return;
}
var graphicsDevice = context.GraphicsService.GraphicsDevice;
int frame = context.Frame;
var savedRenderState = new RenderStateSnapshot(graphicsDevice);
var originalRenderTarget = context.RenderTarget;
var originalViewport = context.Viewport;
var originalCameraNode = context.CameraNode;
var originalLodCameraNode = context.LodCameraNode;
float originalLodBias = context.LodBias;
var originalReferenceNode = context.ReferenceNode;
Pose originalCameraPose = originalCameraNode.PoseWorld;
Vector3F originalCameraPosition = originalCameraPose.Position;
Matrix33F originalCameraOrientation = originalCameraPose.Orientation;
Vector3F right = originalCameraOrientation.GetColumn(0);
Vector3F up = originalCameraOrientation.GetColumn(1);
Vector3F back = originalCameraOrientation.GetColumn(2);
try
{
// Use foreach instead of for-loop to catch InvalidOperationExceptions in
// case the collection is modified.
for (int i = 0; i < numberOfNodes; i++)
{
var node = nodes[i] as PlanarReflectionNode;
if (node == null)
{
continue;
}
// Update each node only once per frame.
if (node.LastFrame == frame)
{
continue;
}
node.LastFrame = frame;
var texture = node.RenderToTexture.Texture;
if (texture == null)
{
continue;
}
var renderTarget = texture as RenderTarget2D;
if (renderTarget == null)
{
throw new GraphicsException(
"PlanarReflectionNode.RenderToTexture.Texture is invalid. The texture must be a RenderTarget2D.");
}
// RenderToTexture instances can be shared. --> Update them only once per frame.
if (node.RenderToTexture.LastFrame == frame)
{
continue;
}
// Do not render if we look at the back of the reflection plane.
Vector3F planeNormal = node.NormalWorld;
Vector3F planePosition = node.PoseWorld.Position;
Vector3F planeToCamera = originalCameraPosition - planePosition;
if (Vector3F.Dot(planeNormal, planeToCamera) < 0)
{
continue;
}
var cameraNode = node.CameraNode;
// Reflect camera pose.
Pose cameraPose;
cameraPose.Position = planePosition + Reflect(planeToCamera, planeNormal);
cameraPose.Orientation = new Matrix33F();
cameraPose.Orientation.SetColumn(0, Reflect(right, planeNormal));
cameraPose.Orientation.SetColumn(1, -Reflect(up, planeNormal));
cameraPose.Orientation.SetColumn(2, Reflect(back, planeNormal));
cameraNode.PoseWorld = cameraPose;
// The projection of the player camera.
var originalProjection = originalCameraNode.Camera.Projection;
// The projection of the reflected camera.
var projection = (PerspectiveProjection)cameraNode.Camera.Projection;
// Choose optimal projection. We get the screen-space bounds of the reflection node.
// Then we make the FOV so small that it exactly contains the node.
projection.Set(originalProjection);
var bounds = GraphicsHelper.GetBounds(cameraNode, node);
// Abort if the bounds are empty.
if (Numeric.AreEqual(bounds.X, bounds.Z) || Numeric.AreEqual(bounds.Y, bounds.W))
{
continue;
}
// Apply FOV scale to bounds.
float fovScale = node.FieldOfViewScale;
float deltaX = (bounds.Z - bounds.X) * (fovScale - 1) / 2;
bounds.X -= deltaX;
bounds.Z += deltaX;
float deltaY = (bounds.W - bounds.Y) * (fovScale - 1) / 2;
bounds.Y -= deltaY;
bounds.W += deltaY;
// Update projection to contain only the node bounds.
projection.Left = projection.Left + bounds.X * projection.Width;
projection.Right = projection.Left + bounds.Z * projection.Width;
projection.Top = projection.Top - bounds.Y * projection.Height;
projection.Bottom = projection.Top - bounds.W * projection.Height;
// Set far clip plane.
if (node.Far.HasValue)
{
projection.Far = node.Far.Value;
}
// Set near clip plane.
Vector3F planeNormalCamera = cameraPose.ToLocalDirection(-node.NormalWorld);
Vector3F planePointCamera = cameraPose.ToLocalPosition(node.PoseWorld.Position);
projection.NearClipPlane = new Plane(planeNormalCamera, planePointCamera);
context.CameraNode = cameraNode;
context.LodCameraNode = cameraNode;
context.LodBias = node.LodBias ?? originalLodBias;
context.ReferenceNode = node;
context.RenderTarget = renderTarget;
context.Viewport = new Viewport(0, 0, renderTarget.Width, renderTarget.Height);
RenderCallback(context);
// Update other properties of RenderToTexture.
node.RenderToTexture.LastFrame = frame;
node.RenderToTexture.TextureMatrix = GraphicsHelper.ProjectorBiasMatrix
* cameraNode.Camera.Projection
* cameraNode.PoseWorld.Inverse;
}
}
catch (InvalidOperationException exception)
{
throw new GraphicsException(
"InvalidOperationException was raised in PlanarReflectionRenderer.Render(). "
+ "This can happen if a SceneQuery instance that is currently in use is modified in the "
+ "RenderCallback. --> Use different SceneQuery types in the method which calls "
+ "SceneCaptureRenderer.Render() and in the RenderCallback method.",
exception);
}
graphicsDevice.SetRenderTarget(null);
savedRenderState.Restore();
context.RenderTarget = originalRenderTarget;
context.Viewport = originalViewport;
context.CameraNode = originalCameraNode;
context.LodCameraNode = originalLodCameraNode;
context.LodBias = originalLodBias;
context.ReferenceNode = originalReferenceNode;
}
public override void Render(IList <SceneNode> nodes, RenderContext context, RenderOrder order)
{
if (nodes == null)
{
throw new ArgumentNullException("nodes");
}
if (context == null)
{
throw new ArgumentNullException("context");
}
int numberOfNodes = nodes.Count;
if (numberOfNodes == 0)
{
return;
}
context.ThrowIfCameraMissing();
context.ThrowIfSceneMissing();
var originalRenderTarget = context.RenderTarget;
var originalViewport = context.Viewport;
var originalReferenceNode = context.ReferenceNode;
// Camera properties
var cameraNode = context.CameraNode;
var cameraPose = cameraNode.PoseWorld;
var projection = cameraNode.Camera.Projection;
if (!(projection is PerspectiveProjection))
{
throw new NotImplementedException(
"Cascaded shadow maps not yet implemented for scenes with orthographic camera.");
}
float fieldOfViewY = projection.FieldOfViewY;
float aspectRatio = projection.AspectRatio;
// Update SceneNode.LastFrame for all visible nodes.
int frame = context.Frame;
cameraNode.LastFrame = frame;
// The scene node renderer should use the light camera instead of the player camera.
context.CameraNode = _orthographicCameraNode;
context.Technique = "Directional";
var graphicsService = context.GraphicsService;
var graphicsDevice = graphicsService.GraphicsDevice;
var savedRenderState = new RenderStateSnapshot(graphicsDevice);
for (int i = 0; i < numberOfNodes; i++)
{
var lightNode = nodes[i] as LightNode;
if (lightNode == null)
{
continue;
}
var shadow = lightNode.Shadow as CascadedShadow;
if (shadow == null)
{
continue;
}
// LightNode is visible in current frame.
lightNode.LastFrame = frame;
var format = new RenderTargetFormat(
shadow.PreferredSize * shadow.NumberOfCascades,
shadow.PreferredSize,
false,
shadow.Prefer16Bit ? SurfaceFormat.HalfSingle : SurfaceFormat.Single,
DepthFormat.Depth24);
bool allLocked = shadow.IsCascadeLocked[0] && shadow.IsCascadeLocked[1] && shadow.IsCascadeLocked[2] && shadow.IsCascadeLocked[3];
if (shadow.ShadowMap == null)
{
shadow.ShadowMap = graphicsService.RenderTargetPool.Obtain2D(format);
allLocked = false; // Need to render shadow map.
}
// If we can reuse the whole shadow map texture, abort early.
if (allLocked)
{
continue;
}
_csmSplitDistances[0] = projection.Near;
_csmSplitDistances[1] = shadow.Distances.X;
_csmSplitDistances[2] = shadow.Distances.Y;
_csmSplitDistances[3] = shadow.Distances.Z;
_csmSplitDistances[4] = shadow.Distances.W;
// (Re-)Initialize the array for cached matrices in the CascadedShadow.
if (shadow.ViewProjections == null || shadow.ViewProjections.Length < shadow.NumberOfCascades)
{
shadow.ViewProjections = new Matrix[shadow.NumberOfCascades];
}
// Initialize the projection matrices to an empty matrix.
// The unused matrices should not contain valid projections because
// CsmComputeSplitOptimized in CascadedShadowMask.fxh should not choose
// the wrong cascade.
for (int j = 0; j < shadow.ViewProjections.Length; j++)
{
if (!shadow.IsCascadeLocked[j]) // Do not delete cached info for cached cascade.
{
shadow.ViewProjections[j] = new Matrix();
}
}
// If some cascades are cached, we have to create a new shadow map and copy
// the old cascades into the new shadow map.
if (shadow.IsCascadeLocked[0] || shadow.IsCascadeLocked[1] || shadow.IsCascadeLocked[2] || shadow.IsCascadeLocked[3])
{
var oldShadowMap = shadow.ShadowMap;
shadow.ShadowMap = graphicsService.RenderTargetPool.Obtain2D(new RenderTargetFormat(oldShadowMap));
graphicsDevice.SetRenderTarget(shadow.ShadowMap);
graphicsDevice.Clear(Color.White);
var spriteBatch = graphicsService.GetSpriteBatch();
spriteBatch.Begin(SpriteSortMode.Deferred, BlendState.Opaque, SamplerState.PointClamp, DepthStencilState.None, RasterizerState.CullNone);
for (int cascade = 0; cascade < shadow.NumberOfCascades; cascade++)
{
if (shadow.IsCascadeLocked[cascade])
{
var viewport = GetViewport(shadow, cascade);
var rectangle = new Rectangle(viewport.X, viewport.Y, viewport.Width, viewport.Height);
spriteBatch.Draw(oldShadowMap, rectangle, rectangle, Color.White);
}
}
spriteBatch.End();
graphicsService.RenderTargetPool.Recycle(oldShadowMap);
}
else
{
graphicsDevice.SetRenderTarget(shadow.ShadowMap);
graphicsDevice.Clear(Color.White);
}
context.RenderTarget = shadow.ShadowMap;
graphicsDevice.DepthStencilState = DepthStencilState.Default;
graphicsDevice.RasterizerState = RasterizerState.CullCounterClockwise;
graphicsDevice.BlendState = BlendState.Opaque;
context.ReferenceNode = lightNode;
context.Object = shadow;
context.ShadowNear = 0; // Obsolete: Only kept for backward compatibility.
bool shadowMapContainsSomething = false;
for (int split = 0; split < shadow.NumberOfCascades; split++)
{
if (shadow.IsCascadeLocked[split])
{
continue;
}
context.Data[RenderContextKeys.ShadowTileIndex] = CubeMapShadowMapRenderer.BoxedIntegers[split];
// near/far of this split.
float near = _csmSplitDistances[split];
float far = Math.Max(_csmSplitDistances[split + 1], near + Numeric.EpsilonF);
// Create a view volume for this split.
_splitVolume.SetFieldOfView(fieldOfViewY, aspectRatio, near, far);
// Find the bounding sphere of the split camera frustum.
Vector3F center;
float radius;
GetBoundingSphere(_splitVolume, out center, out radius);
// Extend radius to get enough border for filtering.
int shadowMapSize = shadow.ShadowMap.Height;
// We could extend by (ShadowMapSize + BorderTexels) / ShadowMapSize;
// Add at least 1 texel. (This way, shadow mask shader can clamp uv to
// texture rect in without considering half texel border to avoid sampling outside..)
radius *= (float)(shadowMapSize + 1) / shadowMapSize;
// Convert center to light space.
Pose lightPose = lightNode.PoseWorld;
center = cameraPose.ToWorldPosition(center);
center = lightPose.ToLocalPosition(center);
// Snap center to texel positions to avoid shadow swimming.
SnapPositionToTexels(ref center, 2 * radius, shadowMapSize);
// Convert center back to world space.
center = lightPose.ToWorldPosition(center);
Matrix33F orientation = lightPose.Orientation;
Vector3F backward = orientation.GetColumn(2);
var orthographicProjection = (OrthographicProjection)_orthographicCameraNode.Camera.Projection;
// Create a tight orthographic frustum around the cascade's bounding sphere.
orthographicProjection.SetOffCenter(-radius, radius, -radius, radius, 0, 2 * radius);
Vector3F cameraPosition = center + radius * backward;
Pose frustumPose = new Pose(cameraPosition, orientation);
Pose view = frustumPose.Inverse;
shadow.ViewProjections[split] = (Matrix)view * orthographicProjection;
// Convert depth bias from "texel" to light space [0, 1] depth.
// Minus sign to move receiver depth closer to light. Divide by depth to normalize.
float unitsPerTexel = orthographicProjection.Width / shadow.ShadowMap.Height;
shadow.EffectiveDepthBias[split] = -shadow.DepthBias[split] * unitsPerTexel / orthographicProjection.Depth;
// Convert normal offset from "texel" to world space.
shadow.EffectiveNormalOffset[split] = shadow.NormalOffset[split] * unitsPerTexel;
// For rendering the shadow map, move near plane back by MinLightDistance
// to catch occluders in front of the cascade.
orthographicProjection.Near = -shadow.MinLightDistance;
_orthographicCameraNode.PoseWorld = frustumPose;
// Set a viewport to render a tile in the texture atlas.
graphicsDevice.Viewport = GetViewport(shadow, split);
context.Viewport = graphicsDevice.Viewport;
shadowMapContainsSomething |= RenderCallback(context);
}
// Recycle shadow map if empty.
if (!shadowMapContainsSomething)
{
graphicsService.RenderTargetPool.Recycle(shadow.ShadowMap);
shadow.ShadowMap = null;
}
}
graphicsDevice.SetRenderTarget(null);
savedRenderState.Restore();
context.CameraNode = cameraNode;
context.ShadowNear = float.NaN;
context.Technique = null;
context.RenderTarget = originalRenderTarget;
context.Viewport = originalViewport;
context.ReferenceNode = originalReferenceNode;
context.Object = null;
context.Data[RenderContextKeys.ShadowTileIndex] = null;
}
public void GetColumnException2()
{
Matrix33F m = new Matrix33F(columnMajor, MatrixOrder.ColumnMajor);
m.GetColumn(3);
}
/// <summary>
/// Estimates the size of an object in pixels.
/// </summary>
/// <param name="cameraNode">The camera node with perspective projection.</param>
/// <param name="viewport">The viewport.</param>
/// <param name="geometricObject">The geometric object.</param>
/// <returns>
/// The estimated width and height of <paramref name="geometricObject"/> in pixels.
/// </returns>
/// <remarks>
/// The method assumes that the object is fully visible by the camera, i.e. it does not perform
/// frustum culling. It estimates the size of <paramref name="geometricObject"/> based on its
/// bounding shape.
/// </remarks>
/// <exception cref="ArgumentNullException">
/// <paramref name="cameraNode"/> or <paramref name="geometricObject"/> is
/// <see langword="null"/>.
/// </exception>
internal static Vector2F GetScreenSize(CameraNode cameraNode, Viewport viewport, IGeometricObject geometricObject)
{
// This implementation is just for reference. (It is preferable to optimize
// and inline the code when needed.)
if (cameraNode == null)
{
throw new ArgumentNullException("cameraNode");
}
if (geometricObject == null)
{
throw new ArgumentNullException("geometricObject");
}
// Use bounding sphere of AABB in world space.
var aabb = geometricObject.Aabb;
float diameter = aabb.Extent.Length;
float width = diameter;
float height = diameter;
Matrix44F proj = cameraNode.Camera.Projection;
bool isOrthographic = (proj.M33 != 0);
// ----- xScale, yScale:
// Orthographic Projection:
// proj.M00 = 2 / (right - left)
// proj.M11 = 2 / (top - bottom)
//
// Perspective Projection:
// proj.M00 = 2 * zNear / (right - left) = 1 / tan(fovX/2)
// proj.M11 = 2 * zNear / (top - bottom) = 1 / tan(fovY/2)
float xScale = Math.Abs(proj.M00);
float yScale = Math.Abs(proj.M11);
// Screen size [px].
Vector2F screenSize;
if (isOrthographic)
{
// ----- Orthographic Projection
// sizeX = viewportWidth * width / (right - left)
// = viewportWidth * width * xScale / 2
screenSize.X = viewport.Width * width * xScale / 2;
// sizeY = viewportHeight* height / (top - bottom)
// = viewportHeight* height * xScale / 2
screenSize.Y = viewport.Height * height * yScale / 2;
}
else
{
// ----- Perspective Projection
// Camera properties.
Pose cameraPose = cameraNode.PoseWorld;
Vector3F cameraPosition = cameraPose.Position;
Matrix33F cameraOrientation = cameraPose.Orientation;
Vector3F cameraForward = -cameraOrientation.GetColumn(2);
// Get planar distance from camera to object by projecting the distance
// vector onto the look direction.
Vector3F cameraToObject = aabb.Center - cameraPosition;
float distance = Vector3F.Dot(cameraToObject, cameraForward);
// Assume that object is in front of camera (no frustum culling).
distance = Math.Abs(distance);
// Avoid division by zero.
if (distance < Numeric.EpsilonF)
{
distance = Numeric.EpsilonF;
}
// sizeX = viewportWidth * width / (objectDistance * 2 * tan(fovX/2))
// = viewportWidth * width * zNear / (objectDistance * (right - left))
// = viewportWidth * width * xScale / (2 * objectDistance)
screenSize.X = viewport.Width * width * xScale / (2 * distance);
// sizeY = viewportHeight * height / (objectDistance * 2 * tan(fovY/2))
// = viewportHeight * height * zNear / (objectDistance * (top - bottom))
// = viewportHeight * height * yScale / (2 * objectDistance)
screenSize.Y = viewport.Height * height * yScale / (2 * distance);
}
return(screenSize);
}
public override void Render(IList <SceneNode> nodes, RenderContext context, RenderOrder order)
{
ThrowIfDisposed();
if (nodes == null)
{
throw new ArgumentNullException("nodes");
}
if (context == null)
{
throw new ArgumentNullException("context");
}
int numberOfNodes = nodes.Count;
if (nodes.Count == 0)
{
return;
}
context.Validate(_effect);
context.ThrowIfCameraMissing();
var graphicsDevice = context.GraphicsService.GraphicsDevice;
var savedRenderState = new RenderStateSnapshot(graphicsDevice);
graphicsDevice.RasterizerState = RasterizerState.CullNone;
graphicsDevice.DepthStencilState = DepthStencilState.DepthRead;
graphicsDevice.BlendState = BlendState.AlphaBlend;
// Camera properties
var cameraNode = context.CameraNode;
Pose cameraPose = cameraNode.PoseWorld;
Matrix view = (Matrix) new Matrix44F(cameraPose.Orientation.Transposed, new Vector3F(0));
Matrix projection = cameraNode.Camera.Projection;
_effectParameterViewProjection.SetValue(view * projection);
// Update SceneNode.LastFrame for all visible nodes.
int frame = context.Frame;
cameraNode.LastFrame = frame;
for (int i = 0; i < numberOfNodes; i++)
{
var node = nodes[i] as SkyObjectNode;
if (node == null)
{
continue;
}
// SkyObjectNode is visible in current frame.
node.LastFrame = frame;
// Get billboard axes from scene node pose.
Matrix33F orientation = node.PoseWorld.Orientation;
Vector3F right = orientation.GetColumn(0);
Vector3F up = orientation.GetColumn(1);
Vector3F normal = orientation.GetColumn(2);
Vector3F forward = -normal;
_effectParameterNormal.SetValue((Vector3)(normal));
// ----- Render object texture.
var texture = node.Texture;
if (texture != null)
{
_effectParameterUp.SetValue((Vector3)(up));
_effectParameterRight.SetValue((Vector3)(right));
_effectParameterSunLight.SetValue((Vector3)node.SunLight);
_effectParameterAmbientLight.SetValue(new Vector4((Vector3)node.AmbientLight, node.Alpha));
_effectParameterObjectTexture.SetValue(texture.TextureAtlas);
_effectParameterLightWrapSmoothness.SetValue(new Vector2(node.LightWrap, node.LightSmoothness));
_effectParameterSunDirection.SetValue((Vector3)node.SunDirection);
float halfWidthX = (float)Math.Tan(node.AngularDiameter.X / 2);
float halfWidthY = (float)Math.Tan(node.AngularDiameter.Y / 2);
// Texture coordinates of packed texture.
Vector2F texCoordLeftTop = texture.GetTextureCoordinates(new Vector2F(0, 0), 0);
Vector2F texCoordRightBottom = texture.GetTextureCoordinates(new Vector2F(1, 1), 0);
float texCoordLeft = texCoordLeftTop.X;
float texCoordTop = texCoordLeftTop.Y;
float texCoordRight = texCoordRightBottom.X;
float texCoordBottom = texCoordRightBottom.Y;
_effectParameterTextureParameters.SetValue(new Vector4(
(texCoordLeft + texCoordRight) / 2,
(texCoordTop + texCoordBottom) / 2,
1 / ((texCoordRight - texCoordLeft) / 2), // 1 / half extent
1 / ((texCoordBottom - texCoordTop) / 2)));
_vertices[0].Position = (Vector3)(forward - right * halfWidthX - up * halfWidthY);
_vertices[0].TextureCoordinate = new Vector2(texCoordLeft, texCoordBottom);
_vertices[1].Position = (Vector3)(forward - right * halfWidthX + up * halfWidthY);
_vertices[1].TextureCoordinate = new Vector2(texCoordLeft, texCoordTop);
_vertices[2].Position = (Vector3)(forward + right * halfWidthX - up * halfWidthY);
_vertices[2].TextureCoordinate = new Vector2(texCoordRight, texCoordBottom);
_vertices[3].Position = (Vector3)(forward + right * halfWidthX + up * halfWidthY);
_vertices[3].TextureCoordinate = new Vector2(texCoordRight, texCoordTop);
if (context.IsHdrEnabled())
{
_effectPassObjectLinear.Apply();
}
else
{
_effectPassObjectGamma.Apply();
}
graphicsDevice.DrawUserPrimitives(PrimitiveType.TriangleStrip, _vertices, 0, 2);
}
// ----- Render glows.
if (node.GlowColor0.LengthSquared > 0 || node.GlowColor1.LengthSquared > 0)
{
_effectParameterGlow0.SetValue(new Vector4((Vector3)node.GlowColor0, node.GlowExponent0));
_effectParameterGlow1.SetValue(new Vector4((Vector3)node.GlowColor1, node.GlowExponent1));
float halfWidth0 = (float)Math.Tan(Math.Acos(Math.Pow(node.GlowCutoffThreshold / node.GlowColor0.LargestComponent, 1 / node.GlowExponent0)));
if (!Numeric.IsPositiveFinite(halfWidth0))
{
halfWidth0 = 0;
}
float halfWidth1 = (float)Math.Tan(Math.Acos(Math.Pow(node.GlowCutoffThreshold / node.GlowColor1.LargestComponent, 1 / node.GlowExponent1)));
if (!Numeric.IsPositiveFinite(halfWidth1))
{
halfWidth1 = 0;
}
float halfWidth = Math.Max(halfWidth0, halfWidth1);
_vertices[0].Position = (Vector3)(forward - right * halfWidth - up * halfWidth);
_vertices[0].TextureCoordinate = (Vector2) new Vector2F(0, 1);
_vertices[1].Position = (Vector3)(forward - right * halfWidth + up * halfWidth);
_vertices[1].TextureCoordinate = (Vector2) new Vector2F(0, 0);
_vertices[2].Position = (Vector3)(forward + right * halfWidth - up * halfWidth);
_vertices[2].TextureCoordinate = (Vector2) new Vector2F(1, 1);
_vertices[3].Position = (Vector3)(forward + right * halfWidth + up * halfWidth);
_vertices[3].TextureCoordinate = (Vector2) new Vector2F(1, 0);
if (context.IsHdrEnabled())
{
_effectPassGlowLinear.Apply();
}
else
{
_effectPassGlowGamma.Apply();
}
graphicsDevice.DrawUserPrimitives(PrimitiveType.TriangleStrip, _vertices, 0, 2);
}
}
savedRenderState.Restore();
}
public override void Render(IList <SceneNode> nodes, RenderContext context, RenderOrder order)
{
if (nodes == null)
{
throw new ArgumentNullException("nodes");
}
if (context == null)
{
throw new ArgumentNullException("context");
}
int numberOfNodes = nodes.Count;
if (numberOfNodes == 0)
{
return;
}
Debug.Assert(context.CameraNode != null, "A camera node has to be set in the render context.");
Debug.Assert(context.Scene != null, "A scene has to be set in the render context.");
var originalRenderTarget = context.RenderTarget;
var originalViewport = context.Viewport;
var originalReferenceNode = context.ReferenceNode;
// Camera properties
var cameraNode = context.CameraNode;
var cameraPose = cameraNode.PoseWorld;
var projection = cameraNode.Camera.Projection;
if (!(projection is PerspectiveProjection))
{
throw new NotImplementedException("VSM shadow maps not yet implemented for scenes with perspective camera.");
}
float fieldOfViewY = projection.FieldOfViewY;
float aspectRatio = projection.AspectRatio;
// Update SceneNode.LastFrame for all rendered nodes.
int frame = context.Frame;
cameraNode.LastFrame = frame;
// The scene node renderer should use the light camera instead of the player camera.
context.CameraNode = _orthographicCameraNode;
// The shadow map is rendered using the technique "DirectionalVsm".
// See ShadowMap.fx in the DigitalRune source code folder.
context.Technique = "DirectionalVsm";
var graphicsService = context.GraphicsService;
var graphicsDevice = graphicsService.GraphicsDevice;
var originalBlendState = graphicsDevice.BlendState;
var originalDepthStencilState = graphicsDevice.DepthStencilState;
var originalRasterizerState = graphicsDevice.RasterizerState;
for (int i = 0; i < numberOfNodes; i++)
{
var lightNode = nodes[i] as LightNode;
if (lightNode == null)
{
continue;
}
var shadow = lightNode.Shadow as VarianceShadow;
if (shadow == null)
{
continue;
}
// LightNode is visible in current frame.
lightNode.LastFrame = frame;
// The format of the shadow map:
var format = new RenderTargetFormat(
shadow.PreferredSize,
shadow.PreferredSize,
false,
shadow.Prefer16Bit ? SurfaceFormat.HalfVector2 : SurfaceFormat.Vector2, // VSM needs two channels!
DepthFormat.Depth24);
if (shadow.ShadowMap != null && shadow.IsLocked)
{
continue;
}
if (shadow.ShadowMap == null)
{
shadow.ShadowMap = graphicsService.RenderTargetPool.Obtain2D(format);
}
graphicsDevice.DepthStencilState = DepthStencilState.Default;
graphicsDevice.BlendState = BlendState.Opaque;
// Render front and back faces for VSM due to low shadow map texel density.
// (VSM is usually used for distant geometry.)
graphicsDevice.RasterizerState = RasterizerState.CullNone;
graphicsDevice.SetRenderTarget(shadow.ShadowMap);
context.RenderTarget = shadow.ShadowMap;
context.Viewport = graphicsDevice.Viewport;
graphicsDevice.Clear(Color.White);
// Compute an orthographic camera for the light.
// If Shadow.TargetArea is null, the shadow map should cover the area in front of the player camera.
// If Shadow.TargetArea is set, the shadow map should cover this static area.
if (shadow.TargetArea == null)
{
// near/far of this shadowed area.
float near = projection.Near;
float far = shadow.MaxDistance;
// Abort if near-far distances are invalid.
if (Numeric.IsGreaterOrEqual(near, far))
{
continue;
}
// Create a view volume for frustum part that is covered by the shadow map.
_cameraVolume.SetFieldOfView(fieldOfViewY, aspectRatio, near, far);
// Find the bounding sphere of the frustum part.
Vector3F center;
float radius;
GetBoundingSphere(_cameraVolume, out center, out radius);
// Convert center to light space.
Pose lightPose = lightNode.PoseWorld;
center = cameraPose.ToWorldPosition(center);
center = lightPose.ToLocalPosition(center);
// Snap center to texel positions to avoid shadow swimming.
SnapPositionToTexels(ref center, 2 * radius, shadow.ShadowMap.Height);
// Convert center back to world space.
center = lightPose.ToWorldPosition(center);
Matrix33F orientation = lightPose.Orientation;
Vector3F backward = orientation.GetColumn(2);
var orthographicProjection = (OrthographicProjection)_orthographicCameraNode.Camera.Projection;
// Create a tight orthographic frustum around the target bounding sphere.
orthographicProjection.SetOffCenter(-radius, radius, -radius, radius, 0, 2 * radius);
Vector3F cameraPosition = center + radius * backward;
Pose frustumPose = new Pose(cameraPosition, orientation);
Pose view = frustumPose.Inverse;
shadow.ViewProjection = (Matrix)view * orthographicProjection;
// For rendering the shadow map, move near plane back by MinLightDistance
// to catch occluders in front of the camera frustum.
orthographicProjection.Near = -shadow.MinLightDistance;
_orthographicCameraNode.PoseWorld = frustumPose;
}
else
{
// Get bounding sphere of static target area.
Aabb targetAabb = shadow.TargetArea.Value;
Vector3F center = targetAabb.Center;
float radius = (targetAabb.Maximum - center).Length;
// Convert center to light space.
Matrix33F orientation = lightNode.PoseWorld.Orientation;
Vector3F backward = orientation.GetColumn(2);
var orthographicProjection = (OrthographicProjection)_orthographicCameraNode.Camera.Projection;
// Create a tight orthographic frustum around the target bounding sphere.
orthographicProjection.SetOffCenter(-radius, radius, -radius, radius, 0, 2 * radius);
Vector3F cameraPosition = center + radius * backward;
Pose frustumPose = new Pose(cameraPosition, orientation);
Pose view = frustumPose.Inverse;
shadow.ViewProjection = (Matrix)view * orthographicProjection;
// For rendering the shadow map, move near plane back by MinLightDistance
// to catch occluders in front of the camera frustum.
orthographicProjection.Near = -shadow.MinLightDistance;
_orthographicCameraNode.PoseWorld = frustumPose;
}
context.ReferenceNode = lightNode;
context.Object = shadow;
// Render objects into shadow map.
bool shadowMapContainsSomething = RenderCallback(context);
if (shadowMapContainsSomething)
{
// Blur shadow map.
if (shadow.Filter != null && shadow.Filter.Scale > 0)
{
context.SourceTexture = shadow.ShadowMap;
shadow.Filter.Process(context);
context.SourceTexture = null;
}
}
else
{
// Shadow map is empty. Recycle it.
graphicsService.RenderTargetPool.Recycle(shadow.ShadowMap);
shadow.ShadowMap = null;
}
}
graphicsDevice.SetRenderTarget(null);
graphicsDevice.BlendState = originalBlendState;
graphicsDevice.DepthStencilState = originalDepthStencilState;
graphicsDevice.RasterizerState = originalRasterizerState;
context.CameraNode = cameraNode;
context.Technique = null;
context.RenderTarget = originalRenderTarget;
context.Viewport = originalViewport;
context.ReferenceNode = originalReferenceNode;
context.Object = null;
}
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);
}
