/// <summary>
/// Computes and applies a convex shape description for this WrappedShape.
/// </summary>
/// <param name="center">Computed center of the shape before recentering.</param>
public void UpdateConvexShapeInfo(out Vector3 center)
{
//Compute the volume distribution.
var samples = CommonResources.GetVectorList();
if (samples.Capacity < InertiaHelper.SampleDirections.Length)
{
samples.Capacity = InertiaHelper.SampleDirections.Length;
}
samples.Count = InertiaHelper.SampleDirections.Length;
for (int i = 0; i < InertiaHelper.SampleDirections.Length; ++i)
{
GetLocalExtremePoint(InertiaHelper.SampleDirections[i], out samples.Elements[i]);
}
var triangles = CommonResources.GetIntList();
ConvexHullHelper.GetConvexHull(samples, triangles);
float volume;
InertiaHelper.ComputeShapeDistribution(samples, triangles, out center, out volume, out volumeDistribution);
Volume = volume;
CommonResources.GiveBack(samples);
CommonResources.GiveBack(triangles);
//Now recenter the shape and compute the radii estimates.
for (int i = 0; i < shapes.Count; i++)
{
shapes.WrappedList.Elements[i].Transform.Position -= center;
}
MinimumRadius = ComputeMinimumRadius();
MaximumRadius = ComputeMaximumRadius();
}
/// <summary>
/// Computes a convex shape description for a TransformableShape and applies it.
/// </summary>
public void UpdateConvexShapeInfo()
{
//Compute the volume distribution.
var samples = CommonResources.GetVectorList();
if (samples.Capacity < InertiaHelper.SampleDirections.Length)
{
samples.Capacity = InertiaHelper.SampleDirections.Length;
}
samples.Count = InertiaHelper.SampleDirections.Length;
for (int i = 0; i < InertiaHelper.SampleDirections.Length; ++i)
{
shape.GetLocalExtremePointWithoutMargin(ref InertiaHelper.SampleDirections[i], out samples.Elements[i]);
}
var triangles = CommonResources.GetIntList();
ConvexHullHelper.GetConvexHull(samples, triangles);
Fix64 volume;
InertiaHelper.ComputeShapeDistribution(samples, triangles, out volume, out volumeDistribution);
Volume = volume;
//Estimate the minimum radius based on the surface mesh.
MinimumRadius = InertiaHelper.ComputeMinimumRadius(samples, triangles, ref Toolbox.ZeroVector) + collisionMargin;
MaximumRadius = ComputeMaximumRadius();
CommonResources.GiveBack(samples);
CommonResources.GiveBack(triangles);
}
/// <summary>
/// Identifies the points on the surface of hull.
/// </summary>
/// <param name="points">List of points in the set.</param>
/// <param name="outputSurfacePoints">Unique points on the surface of the convex hull.</param>
public static void GetConvexHull(IList <Vector3> points, IList <Vector3> outputSurfacePoints)
{
var rawPoints = CommonResources.GetVectorList();
rawPoints.AddRange(points);
GetConvexHull(rawPoints, outputSurfacePoints);
CommonResources.GiveBack(rawPoints);
}
///<summary>
/// Computes the center and volume of a convex hull defined by a pointset.
///</summary>
///<param name="vertices">Point set defining the convex hull.</param>
///<param name="volume">Volume of the convex hull.</param>
///<returns>Center of the convex hull.</returns>
public static Vector3 ComputeCenter(IList <Vector3> vertices, out float volume)
{
var localSurfaceVertices = CommonResources.GetVectorList();
var surfaceTriangles = CommonResources.GetIntList();
Vector3 toReturn = ComputeCenter(vertices, out volume, surfaceTriangles, localSurfaceVertices);
CommonResources.GiveBack(localSurfaceVertices);
CommonResources.GiveBack(surfaceTriangles);
return(toReturn);
}
///<summary>
/// Computes the volume and volume distribution of a shape based on a given center.
///</summary>
///<param name="shape">Shape to compute the volume information of.</param>
///<param name="center">Location to use as the center of the shape when computing the volume distribution.</param>
///<param name="volume">Volume of the shape.</param>
///<returns>Volume distribution of the shape.</returns>
public static Matrix3x3 ComputeVolumeDistribution(ConvexShape shape, ref Vector3 center, out float volume)
{
var pointContributions = CommonResources.GetVectorList();
GetPoints(shape, out volume, pointContributions);
Matrix3x3 volumeDistribution = ComputeVolumeDistribution(pointContributions, ref center);
CommonResources.GiveBack(pointContributions);
return(volumeDistribution);
}
///<summary>
/// Computes the center and volume of a convex shape.
///</summary>
///<param name="shape">Shape to compute the center of.</param>
///<param name="volume">Volume of the shape.</param>
///<returns>Center of the shape.</returns>
public static Vector3 ComputeCenter(ConvexShape shape, out float volume)
{
var pointContributions = CommonResources.GetVectorList();
GetPoints(shape, out volume, pointContributions);
Vector3 center = AveragePoints(pointContributions);
CommonResources.GiveBack(pointContributions);
MathChecker.Validate(center);
return(center);
}
/// <summary>
/// Computes the volume distribution of the shape as well as its volume.
/// The volume distribution can be used to compute inertia tensors when
/// paired with mass and other tuning factors.
/// </summary>
/// <param name="volume">Volume of the shape.</param>
/// <returns>Volume distribution of the shape.</returns>
public override Matrix3x3 ComputeVolumeDistribution(out float volume)
{
var surfaceTriangles = CommonResources.GetIntList();
var surfaceVertices = CommonResources.GetVectorList();
ComputeCenter(out volume, surfaceTriangles, surfaceVertices);
Matrix3x3 toReturn = ComputeVolumeDistribution(volume, surfaceTriangles);
CommonResources.GiveBack(surfaceTriangles);
CommonResources.GiveBack(surfaceVertices);
return(toReturn);
}
/// <summary>
/// Removes redundant points. Two points are redundant if they occupy the same hash grid cell.
/// </summary>
/// <param name="points">List of points to prune.</param>
/// <param name="cellSize">Size of cells to determine redundancy.</param>
public static void RemoveRedundantPoints(IList <Vector3> points, double cellSize)
{
var rawPoints = CommonResources.GetVectorList();
rawPoints.AddRange(points);
RemoveRedundantPoints(rawPoints, cellSize);
points.Clear();
for (int i = 0; i < rawPoints.Count; ++i)
{
points.Add(rawPoints.Elements[i]);
}
CommonResources.GiveBack(rawPoints);
}
/// <summary>
/// Identifies the points on the surface of hull.
/// </summary>
/// <param name="points">List of points in the set.</param>
/// <param name="outputTriangleIndices">List of indices into the input point set composing the triangulated surface of the convex hull.
/// Each group of 3 indices represents a triangle on the surface of the hull.</param>
/// <param name="outputSurfacePoints">Unique points on the surface of the convex hull.</param>
public static void GetConvexHull(IList <Vector3> points, IList <int> outputTriangleIndices, IList <Vector3> outputSurfacePoints)
{
var rawPoints = CommonResources.GetVectorList();
var rawIndices = CommonResources.GetIntList();
rawPoints.AddRange(points);
GetConvexHull(rawPoints, rawIndices, outputSurfacePoints);
CommonResources.GiveBack(rawPoints);
for (int i = 0; i < rawIndices.Count; i++)
{
outputTriangleIndices.Add(rawIndices[i]);
}
CommonResources.GiveBack(rawIndices);
}
///<summary>
/// Constructs a new convex hull shape.
/// The point set will be recentered on the local origin.
///</summary>
///<param name="vertices">Point set to use to construct the convex hull.</param>
/// <param name="center">Computed center of the convex hull shape prior to recentering.</param>
///<exception cref="ArgumentException">Thrown when the point set is empty.</exception>
public ConvexHullShape(IList <Vector3> vertices, out Vector3 center)
{
if (vertices.Count == 0)
{
throw new ArgumentException("Vertices list used to create a ConvexHullShape cannot be empty.");
}
var surfaceVertices = CommonResources.GetVectorList();
center = ComputeCenter(vertices, surfaceVertices);
this.vertices = new RawList <Vector3>(surfaceVertices);
CommonResources.GiveBack(surfaceVertices);
OnShapeChanged();
}
/// <summary>
/// Computes and applies a convex shape description for this MinkowskiSumShape.
/// </summary>
/// <returns>Description required to define a convex shape.</returns>
public void UpdateConvexShapeInfo()
{
//Compute the volume distribution.
RawList <Vector3> samples = CommonResources.GetVectorList();
if (samples.Capacity < InertiaHelper.SampleDirections.Length)
{
samples.Capacity = InertiaHelper.SampleDirections.Length;
}
samples.Count = InertiaHelper.SampleDirections.Length;
for (int i = 0; i < InertiaHelper.SampleDirections.Length; ++i)
{
GetLocalExtremePoint(InertiaHelper.SampleDirections[i], out samples.Elements[i]);
}
RawList <int> triangles = CommonResources.GetIntList();
ConvexHullHelper.GetConvexHull(samples, triangles);
float volume;
Vector3 center;
InertiaHelper.ComputeShapeDistribution(samples, triangles, out center, out volume, out volumeDistribution);
Volume = volume;
//Recenter the shape.
localOffset = -center;
CommonResources.GiveBack(samples);
CommonResources.GiveBack(triangles);
//Compute the radii.
float minRadius = 0, maxRadius = 0;
for (int i = 0; i < Shapes.Count; i++)
{
minRadius += Shapes.WrappedList.Elements[i].CollisionShape.MinimumRadius;
maxRadius += Shapes.WrappedList.Elements[i].CollisionShape.MaximumRadius;
}
MinimumRadius = minRadius + collisionMargin;
MaximumRadius = maxRadius + collisionMargin;
}
///<summary>
/// Constructs a new convex hull shape.
/// The point set will be recentered on the local origin.
///</summary>
///<param name="vertices">Point set to use to construct the convex hull.</param>
/// <param name="center">Computed center of the convex hull shape prior to recentering.</param>
///<exception cref="ArgumentException">Thrown when the point set is empty.</exception>
public ConvexHullShape(IList <Vector3> vertices, out Vector3 center)
{
if (vertices.Count == 0)
{
throw new ArgumentException("Vertices list used to create a ConvexHullShape cannot be empty.");
}
var surfaceVertices = CommonResources.GetVectorList();
var hullTriangleIndices = CommonResources.GetIntList();
UpdateConvexShapeInfo(ComputeDescription(vertices, collisionMargin, out center, hullTriangleIndices, surfaceVertices));
this.vertices = surfaceVertices.ToArray();
CommonResources.GiveBack(hullTriangleIndices);
CommonResources.GiveBack(surfaceVertices);
unexpandedMaximumRadius = MaximumRadius - collisionMargin;
unexpandedMinimumRadius = MinimumRadius - collisionMargin;
}
///<summary>
/// Computes the center, volume, and surface triangles of a convex hull defined by a point set.
///</summary>
///<param name="vertices">Point set defining the convex hull.</param>
///<param name="volume">Volume of the convex hull.</param>
///<param name="outputSurfaceTriangles">Indices of surface triangles of the convex hull.</param>
///<param name="outputLocalSurfaceVertices">Local positions of vertices on the convex hull.</param>
///<returns>Center of the convex hull.</returns>
public static Vector3 ComputeCenter(IList <Vector3> vertices, out float volume, IList <int> outputSurfaceTriangles, IList <Vector3> outputLocalSurfaceVertices)
{
Vector3 centroid = Toolbox.ZeroVector;
for (int k = 0; k < vertices.Count; k++)
{
centroid += vertices[k];
}
centroid /= vertices.Count;
//Toolbox.GetConvexHull(vertices, outputSurfaceTriangles, outputLocalSurfaceVertices);
ConvexHullHelper.GetConvexHull(vertices, outputSurfaceTriangles, outputLocalSurfaceVertices);
volume = 0;
var volumes = CommonResources.GetFloatList();
var centroids = CommonResources.GetVectorList();
for (int k = 0; k < outputSurfaceTriangles.Count; k += 3)
{
volumes.Add(Vector3.Dot(
Vector3.Cross(vertices[outputSurfaceTriangles[k + 1]] - vertices[outputSurfaceTriangles[k]],
vertices[outputSurfaceTriangles[k + 2]] - vertices[outputSurfaceTriangles[k]]),
centroid - vertices[outputSurfaceTriangles[k]]));
volume += volumes[k / 3];
centroids.Add((vertices[outputSurfaceTriangles[k]] + vertices[outputSurfaceTriangles[k + 1]] + vertices[outputSurfaceTriangles[k + 2]] + centroid) / 4);
}
Vector3 center = Toolbox.ZeroVector;
for (int k = 0; k < centroids.Count; k++)
{
center += centroids[k] * (volumes[k] / volume);
}
volume /= 6;
for (int k = 0; k < outputLocalSurfaceVertices.Count; k++)
{
outputLocalSurfaceVertices[k] -= center;
}
CommonResources.GiveBack(centroids);
CommonResources.GiveBack(volumes);
return(center);
}
/// <summary>
/// Recalculates the bounding box of the fluid based on its depth, surface normal, and surface triangles.
/// </summary>
public void RecalculateBoundingBox()
{
var points = CommonResources.GetVectorList();
foreach (var tri in SurfaceTriangles)
{
points.Add(tri[0]);
points.Add(tri[1]);
points.Add(tri[2]);
points.Add(tri[0] - upVector * MaxDepth);
points.Add(tri[1] - upVector * MaxDepth);
points.Add(tri[2] - upVector * MaxDepth);
}
boundingBox = BoundingBox.CreateFromPoints(points);
CommonResources.GiveBack(points);
//Compute the transforms used to pull objects into fluid local space.
Quaternion.GetQuaternionBetweenNormalizedVectors(ref Toolbox.UpVector, ref upVector, out surfaceTransform.Orientation);
Matrix3f.FromQuaternion(ref surfaceTransform.Orientation, out toSurfaceRotationMatrix);
surfaceTransform.Position = surfaceTriangles[0][0];
}
/// <summary>
/// Recenters the triangle data and computes the volume distribution.
/// </summary>
/// <param name="data">Mesh data to analyze.</param>
/// <returns>Computed center, volume, and volume distribution.</returns>
private ShapeDistributionInformation ComputeVolumeDistribution(TransformableMeshData data)
{
//Compute the surface vertices of the shape.
ShapeDistributionInformation shapeInformation;
if (solidity == MobileMeshSolidity.Solid)
{
//The following inertia tensor calculation assumes a closed mesh.
var transformedVertices = CommonResources.GetVectorList();
if (transformedVertices.Capacity < data.vertices.Length)
{
transformedVertices.Capacity = data.vertices.Length;
}
transformedVertices.Count = data.vertices.Length;
for (int i = 0; i < data.vertices.Length; ++i)
{
data.GetVertexPosition(i, out transformedVertices.Elements[i]);
}
InertiaHelper.ComputeShapeDistribution(transformedVertices, data.indices, out shapeInformation.Center, out shapeInformation.Volume, out shapeInformation.VolumeDistribution);
CommonResources.GiveBack(transformedVertices);
if (shapeInformation.Volume > F64.C0)
{
return(shapeInformation);
}
throw new ArgumentException("A solid mesh must have volume.");
}
shapeInformation.Center = new Vector3();
shapeInformation.VolumeDistribution = new Matrix3x3();
Fix64 totalWeight = F64.C0;
for (int i = 0; i < data.indices.Length; i += 3)
{
//Compute the center contribution.
Vector3 vA, vB, vC;
data.GetTriangle(i, out vA, out vB, out vC);
Vector3 vAvB;
Vector3 vAvC;
Vector3.Subtract(ref vB, ref vA, out vAvB);
Vector3.Subtract(ref vC, ref vA, out vAvC);
Vector3 cross;
Vector3.Cross(ref vAvB, ref vAvC, out cross);
Fix64 weight = cross.Length();
totalWeight += weight;
Fix64 perVertexWeight = weight * F64.OneThird;
shapeInformation.Center += perVertexWeight * (vA + vB + vC);
//Compute the inertia contribution of this triangle.
//Approximate it using pointmasses positioned at the triangle vertices.
//(There exists a direct solution, but this approximation will do plenty fine.)
Matrix3x3 aContribution, bContribution, cContribution;
InertiaHelper.GetPointContribution(perVertexWeight, ref Toolbox.ZeroVector, ref vA, out aContribution);
InertiaHelper.GetPointContribution(perVertexWeight, ref Toolbox.ZeroVector, ref vB, out bContribution);
InertiaHelper.GetPointContribution(perVertexWeight, ref Toolbox.ZeroVector, ref vC, out cContribution);
Matrix3x3.Add(ref aContribution, ref shapeInformation.VolumeDistribution, out shapeInformation.VolumeDistribution);
Matrix3x3.Add(ref bContribution, ref shapeInformation.VolumeDistribution, out shapeInformation.VolumeDistribution);
Matrix3x3.Add(ref cContribution, ref shapeInformation.VolumeDistribution, out shapeInformation.VolumeDistribution);
}
shapeInformation.Center /= totalWeight;
//The extra factor of 2 is used because the cross product length was twice the actual area.
Matrix3x3.Multiply(ref shapeInformation.VolumeDistribution, F64.C1 / (F64.C2 * totalWeight), out shapeInformation.VolumeDistribution);
//Move the inertia tensor into position according to the center.
Matrix3x3 additionalInertia;
InertiaHelper.GetPointContribution(F64.C0p5, ref Toolbox.ZeroVector, ref shapeInformation.Center, out additionalInertia);
Matrix3x3.Subtract(ref shapeInformation.VolumeDistribution, ref additionalInertia, out shapeInformation.VolumeDistribution);
shapeInformation.Volume = F64.C0;
return(shapeInformation);
}
