public GetTriangle ( int triangleIndex, Vector3 &v1, Vector3 &v2, Vector3 &v3 ) : void | ||
triangleIndex | int | First index of a triangle's vertices in the index buffer. |
v1 | Vector3 | First vertex of the triangle. |
v2 | Vector3 | Second vertex of the triangle. |
v3 | Vector3 | Third vertex of the triangle. |
Résultat | void |
void ComputeShapeInformation(TransformableMeshData data, out ShapeDistributionInformation shapeInformation) { var indices = Resources.GetIntList(); surfaceVertices.Clear(); Toolbox.GetConvexHull(data.vertices, indices, surfaceVertices); for (int i = 0; i < surfaceVertices.count; i++) { AffineTransform.Transform(ref surfaceVertices.Elements[i], ref data.worldTransform, out surfaceVertices.Elements[i]); } shapeInformation.Center = new Vector3(); if (solidity == MobileMeshSolidity.Solid) { //The following inertia tensor calculation assumes a closed mesh. shapeInformation.Volume = 0; for (int i = 0; i < data.indices.Length; i += 3) { Vector3 v2, v3, v4; data.GetTriangle(i, out v2, out v3, out v4); //Determinant is 6 * volume. It's signed, though; this is because the mesh isn't necessarily convex nor centered on the origin. float tetrahedronVolume = v2.X * (v3.Y * v4.Z - v3.Z * v4.Y) - v3.X * (v2.Y * v4.Z - v2.Z * v4.Y) + v4.X * (v2.Y * v3.Z - v2.Z * v3.Y); shapeInformation.Volume += tetrahedronVolume; shapeInformation.Center += tetrahedronVolume * (v2 + v3 + v4); } shapeInformation.Center /= shapeInformation.Volume * 4; shapeInformation.Volume /= 6; shapeInformation.Volume = Math.Abs(shapeInformation.Volume); data.worldTransform.Translation -= shapeInformation.Center; //Source: Explicit Exact Formulas for the 3-D Tetrahedron Inertia Tensor in Terms of its Vertex Coordinates //http://www.scipub.org/fulltext/jms2/jms2118-11.pdf //x1, x2, x3, x4 are origin, triangle1, triangle2, triangle3 //Looking to find inertia tensor matrix of the form // [ a -b' -c' ] // [ -b' b -a' ] // [ -c' -a' c ] float a = 0, b = 0, c = 0, ao = 0, bo = 0, co = 0; float totalWeight = 0; for (int i = 0; i < data.indices.Length; i += 3) { Vector3 v2, v3, v4; data.GetTriangle(i, out v2, out v3, out v4); //Determinant is 6 * volume. It's signed, though; this is because the mesh isn't necessarily convex nor centered on the origin. float tetrahedronVolume = v2.X * (v3.Y * v4.Z - v3.Z * v4.Y) - v3.X * (v2.Y * v4.Z - v2.Z * v4.Y) + v4.X * (v2.Y * v3.Z - v2.Z * v3.Y); totalWeight += tetrahedronVolume; a += tetrahedronVolume * (v2.Y * v2.Y + v2.Y * v3.Y + v3.Y * v3.Y + v2.Y * v4.Y + v3.Y * v4.Y + v4.Y * v4.Y + v2.Z * v2.Z + v2.Z * v3.Z + v3.Z * v3.Z + v2.Z * v4.Z + v3.Z * v4.Z + v4.Z * v4.Z); b += tetrahedronVolume * (v2.X * v2.X + v2.X * v3.X + v3.X * v3.X + v2.X * v4.X + v3.X * v4.X + v4.X * v4.X + v2.Z * v2.Z + v2.Z * v3.Z + v3.Z * v3.Z + v2.Z * v4.Z + v3.Z * v4.Z + v4.Z * v4.Z); c += tetrahedronVolume * (v2.X * v2.X + v2.X * v3.X + v3.X * v3.X + v2.X * v4.X + v3.X * v4.X + v4.X * v4.X + v2.Y * v2.Y + v2.Y * v3.Y + v3.Y * v3.Y + v2.Y * v4.Y + v3.Y * v4.Y + v4.Y * v4.Y); ao += tetrahedronVolume * (2 * v2.Y * v2.Z + v3.Y * v2.Z + v4.Y * v2.Z + v2.Y * v3.Z + 2 * v3.Y * v3.Z + v4.Y * v3.Z + v2.Y * v4.Z + v3.Y * v4.Z + 2 * v4.Y * v4.Z); bo += tetrahedronVolume * (2 * v2.X * v2.Z + v3.X * v2.Z + v4.X * v2.Z + v2.X * v3.Z + 2 * v3.X * v3.Z + v4.X * v3.Z + v2.X * v4.Z + v3.X * v4.Z + 2 * v4.X * v4.Z); co += tetrahedronVolume * (2 * v2.X * v2.Y + v3.X * v2.Y + v4.X * v2.Y + v2.X * v3.Y + 2 * v3.X * v3.Y + v4.X * v3.Y + v2.X * v4.Y + v3.X * v4.Y + 2 * v4.X * v4.Y); } float density = 1 / totalWeight; float diagonalFactor = density / 10; float offFactor = -density / 20; a *= diagonalFactor; b *= diagonalFactor; c *= diagonalFactor; ao *= offFactor; bo *= offFactor; co *= offFactor; shapeInformation.VolumeDistribution = new Matrix3X3(a, bo, co, bo, b, ao, co, ao, c); } else { shapeInformation.Center = new Vector3(); float totalWeight = 0; for (int i = 0; i < data.indices.Length; i += 3) { //Configure the inertia tensor to be local. 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); float weight = cross.Length(); totalWeight += weight; shapeInformation.Center += weight * (vA + vB + vC) / 3; } shapeInformation.Center /= totalWeight; shapeInformation.Volume = 0; data.worldTransform.Translation -= shapeInformation.Center; shapeInformation.VolumeDistribution = new Matrix3X3(); for (int i = 0; i < data.indices.Length; i += 3) { //Configure the inertia tensor to be local. 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); float weight = cross.Length(); totalWeight += weight; Matrix3X3 innerProduct; Matrix3X3.CreateScale(vA.LengthSquared(), out innerProduct); Matrix3X3 outerProduct; Matrix3X3.CreateOuterProduct(ref vA, ref vA, out outerProduct); Matrix3X3 contribution; Matrix3X3.Subtract(ref innerProduct, ref outerProduct, out contribution); Matrix3X3.Multiply(ref contribution, weight, out contribution); Matrix3X3.Add(ref shapeInformation.VolumeDistribution, ref contribution, out shapeInformation.VolumeDistribution); Matrix3X3.CreateScale(vB.LengthSquared(), out innerProduct); Matrix3X3.CreateOuterProduct(ref vB, ref vB, out outerProduct); Matrix3X3.Subtract(ref innerProduct, ref outerProduct, out outerProduct); Matrix3X3.Multiply(ref contribution, weight, out contribution); Matrix3X3.Add(ref shapeInformation.VolumeDistribution, ref contribution, out shapeInformation.VolumeDistribution); Matrix3X3.CreateScale(vC.LengthSquared(), out innerProduct); Matrix3X3.CreateOuterProduct(ref vC, ref vC, out outerProduct); Matrix3X3.Subtract(ref innerProduct, ref outerProduct, out contribution); Matrix3X3.Multiply(ref contribution, weight, out contribution); Matrix3X3.Add(ref shapeInformation.VolumeDistribution, ref contribution, out shapeInformation.VolumeDistribution); } Matrix3X3.Multiply(ref shapeInformation.VolumeDistribution, 1 / (6 * totalWeight), out shapeInformation.VolumeDistribution); } ////Configure the inertia tensor to be local. //Vector3 finalOffset = shapeInformation.Center; //Matrix3X3 finalInnerProduct; //Matrix3X3.CreateScale(finalOffset.LengthSquared(), out finalInnerProduct); //Matrix3X3 finalOuterProduct; //Matrix3X3.CreateOuterProduct(ref finalOffset, ref finalOffset, out finalOuterProduct); //Matrix3X3 finalContribution; //Matrix3X3.Subtract(ref finalInnerProduct, ref finalOuterProduct, out finalContribution); //Matrix3X3.Subtract(ref shapeInformation.VolumeDistribution, ref finalContribution, out shapeInformation.VolumeDistribution); }
/// <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 > 0) return shapeInformation; throw new ArgumentException("A solid mesh must have volume."); } shapeInformation.Center = new Vector3(); shapeInformation.VolumeDistribution = new Matrix3x3(); float totalWeight = 0; 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); float weight = cross.Length(); totalWeight += weight; float perVertexWeight = weight * (1f / 3f); Vector3 tmp; vA.Add2( ref vB, ref vC, out tmp ); shapeInformation.Center.AddScaled( ref tmp, perVertexWeight, out shapeInformation.Center ); //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.Mult( 1/totalWeight, out shapeInformation.Center ); //The extra factor of 2 is used because the cross product length was twice the actual area. Matrix3x3.Multiply(ref shapeInformation.VolumeDistribution, 1 / (2 * totalWeight), out shapeInformation.VolumeDistribution); //Move the inertia tensor into position according to the center. Matrix3x3 additionalInertia; InertiaHelper.GetPointContribution(0.5f, ref Toolbox.ZeroVector, ref shapeInformation.Center, out additionalInertia); Matrix3x3.Subtract(ref shapeInformation.VolumeDistribution, ref additionalInertia, out shapeInformation.VolumeDistribution); shapeInformation.Volume = 0; return shapeInformation; }