public double[][] ComputeLaplacianDual(TriMesh mesh) { int fn = mesh.Faces.Count; double[][] laplacian = new double[3][]; laplacian[0] = new double[fn]; laplacian[1] = new double[fn]; laplacian[2] = new double[fn]; for (int i = 0; i < fn; i++) { int f1 = mesh.Faces[i].GetFace(0).Index; int f2 = mesh.Faces[i].GetFace(1).Index; int f3 = mesh.Faces[i].GetFace(2).Index; Vector3D u = mesh.DualGetVertexPosition(i); Vector3D v1 = mesh.DualGetVertexPosition(f1); Vector3D v2 = mesh.DualGetVertexPosition(f2); Vector3D v3 = mesh.DualGetVertexPosition(f3); Vector3D normal = ((v1 - v3).Cross(v2 - v3)).Normalize(); Matrix3D m = new Matrix3D(v1 - v3, v2 - v3, normal); Vector3D coord = m.Inverse() * (u - v3); laplacian[0][i] = normal.x * coord[2]; laplacian[1][i] = normal.y * coord[2]; laplacian[2][i] = normal.z * coord[2]; } return(laplacian); }
public SparseMatrix BuildMatrixDual(TriMesh mesh) { int vn = mesh.Vertices.Count; int fn = mesh.Faces.Count; SparseMatrix L = new SparseMatrix(fn, vn, 6); for (int i = 0; i < fn; i++) { int f1 = mesh.Faces[i].GetFace(0).Index; int f2 = mesh.Faces[i].GetFace(1).Index; int f3 = mesh.Faces[i].GetFace(2).Index; Vector3D dv = mesh.DualGetVertexPosition(i); Vector3D dv1 = mesh.DualGetVertexPosition(f1); Vector3D dv2 = mesh.DualGetVertexPosition(f2); Vector3D dv3 = mesh.DualGetVertexPosition(f3); Vector3D u = dv - dv3; Vector3D v1 = dv1 - dv3; Vector3D v2 = dv2 - dv3; Vector3D normal = (v1.Cross(v2)).Normalize(); Matrix3D M = new Matrix3D(v1, v2, normal); Vector3D coord = M.Inverse() * u; double alpha; alpha = 1.0 / 3.0; L.AddValueTo(i, mesh.Faces[i].GetVertex(0).Index, alpha); L.AddValueTo(i, mesh.Faces[i].GetVertex(1).Index, alpha); L.AddValueTo(i, mesh.Faces[i].GetVertex(2).Index, alpha); alpha = coord[0] / 3.0; L.AddValueTo(i, mesh.Faces[f1].GetVertex(0).Index, -alpha); L.AddValueTo(i, mesh.Faces[f1].GetVertex(1).Index, -alpha); L.AddValueTo(i, mesh.Faces[f1].GetVertex(2).Index, -alpha); alpha = coord[1] / 3.0; L.AddValueTo(i, mesh.Faces[f2].GetVertex(0).Index, -alpha); L.AddValueTo(i, mesh.Faces[f2].GetVertex(1).Index, -alpha); L.AddValueTo(i, mesh.Faces[f2].GetVertex(2).Index, -alpha); alpha = (1.0 - coord[0] - coord[1]) / 3.0; L.AddValueTo(i, mesh.Faces[f3].GetVertex(0).Index, -alpha); L.AddValueTo(i, mesh.Faces[f3].GetVertex(1).Index, -alpha); L.AddValueTo(i, mesh.Faces[f3].GetVertex(2).Index, -alpha); } L.SortElement(); return(L); }
public void DrawDualPoint(TriMesh mesh) { GL.PointSize(GlobalSetting.DisplaySetting.PointSize); GL.Color3(Color.Red); GL.Begin(BeginMode.Points); for (int i = 0; i < mesh.Faces.Count; i++) { Vector3D center = mesh.DualGetVertexPosition(i); GL.Vertex3(center.x, center.y, center.z); } GL.End(); GL.Flush(); }
public SparseMatrix BuildMatrixDual(TriMesh mesh) { int vn = mesh.Vertices.Count; int fn = mesh.Faces.Count; SparseMatrix L = new SparseMatrix(fn, vn, 6); for (int i = 0; i < fn; i++) { int f1 = mesh.Faces[i].GetFace(0).Index; int f2 = mesh.Faces[i].GetFace(1).Index; int f3 = mesh.Faces[i].GetFace(2).Index; Vector3D dv = mesh.DualGetVertexPosition(i); Vector3D dv1 = mesh.DualGetVertexPosition(f1); Vector3D dv2 = mesh.DualGetVertexPosition(f2); Vector3D dv3 = mesh.DualGetVertexPosition(f3); Vector3D u = dv - dv3; Vector3D v1 = dv1 - dv3; Vector3D v2 = dv2 - dv3; Vector3D normal = (v1.Cross(v2)).Normalize(); Matrix3D M = new Matrix3D(v1, v2, normal); Vector3D coord = M.Inverse() * u; double alpha; alpha = 1.0 / 3.0; L.AddValueTo(i, mesh.Faces[i].GetVertex(0).Index, alpha); L.AddValueTo(i, mesh.Faces[i].GetVertex(1).Index, alpha); L.AddValueTo(i, mesh.Faces[i].GetVertex(2).Index, alpha); alpha = coord[0] / 3.0; L.AddValueTo(i, mesh.Faces[f1].GetVertex(0).Index, -alpha); L.AddValueTo(i, mesh.Faces[f1].GetVertex(1).Index, -alpha); L.AddValueTo(i, mesh.Faces[f1].GetVertex(2).Index, -alpha); alpha = coord[1] / 3.0; L.AddValueTo(i, mesh.Faces[f2].GetVertex(0).Index, -alpha); L.AddValueTo(i, mesh.Faces[f2].GetVertex(1).Index, -alpha); L.AddValueTo(i, mesh.Faces[f2].GetVertex(2).Index, -alpha); alpha = (1.0 - coord[0] - coord[1]) / 3.0; L.AddValueTo(i, mesh.Faces[f3].GetVertex(0).Index, -alpha); L.AddValueTo(i, mesh.Faces[f3].GetVertex(1).Index, -alpha); L.AddValueTo(i, mesh.Faces[f3].GetVertex(2).Index, -alpha); } L.SortElement(); return L; }
public double[][] ComputeLaplacianDual(TriMesh mesh) { int fn = mesh.Faces.Count; double[][] laplacian = new double[3][]; laplacian[0] = new double[fn]; laplacian[1] = new double[fn]; laplacian[2] = new double[fn]; for (int i = 0; i < fn; i++) { int f1 = mesh.Faces[i].GetFace(0).Index; int f2 = mesh.Faces[i].GetFace(1).Index; int f3 = mesh.Faces[i].GetFace(2).Index; Vector3D u = mesh.DualGetVertexPosition(i); Vector3D v1 = mesh.DualGetVertexPosition(f1); Vector3D v2 = mesh.DualGetVertexPosition(f2); Vector3D v3 = mesh.DualGetVertexPosition(f3); Vector3D normal = ((v1 - v3).Cross(v2 - v3)).Normalize(); Matrix3D m = new Matrix3D(v1 - v3, v2 - v3, normal); Vector3D coord = m.Inverse() * (u - v3); laplacian[0][i] = normal.x * coord[2]; laplacian[1][i] = normal.y * coord[2]; laplacian[2][i] = normal.z * coord[2]; } return laplacian; }