public static SparseMatrix BuildMatrixDualL(ref NonManifoldMesh mesh) { // build dual Laplacian weight matrix L int vn = mesh.VertexCount; int fn = mesh.FaceCount; SparseMatrix L = new SparseMatrix(fn, vn, 6); for (int i = 0; i < fn; i++) { int f1 = mesh.AdjFF[i][0]; int f2 = mesh.AdjFF[i][1]; int f3 = mesh.AdjFF[i][2]; Vector3D dv = mesh.GetDualPosition(i); Vector3D dv1 = mesh.GetDualPosition(f1); Vector3D dv2 = mesh.GetDualPosition(f2); Vector3D dv3 = mesh.GetDualPosition(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; for (int j = 0, k = i * 3; j < 3; j++) { L.AddValueTo(i, mesh.FaceIndex[k++], alpha); } alpha = coord[0] / 3.0; for (int j = 0, k = f1 * 3; j < 3; j++) { L.AddValueTo(i, mesh.FaceIndex[k++], -alpha); } alpha = coord[1] / 3.0; for (int j = 0, k = f2 * 3; j < 3; j++) { L.AddValueTo(i, mesh.FaceIndex[k++], -alpha); } alpha = (1.0 - coord[0] - coord[1]) / 3.0; for (int j = 0, k = f3 * 3; j < 3; j++) { L.AddValueTo(i, mesh.FaceIndex[k++], -alpha); } } L.SortElement(); return(L); }
public void DrawLapCoord(NonManifoldMesh mesh) { GL.LineWidth(2.0f); GL.Color3(1.0, 0.0, 0.0); GL.Begin(BeginMode.Lines); double[] lapCoordiante = MeshOperators.ComputeDualLap(ref mesh); for (int i = 0, j = 0; i < mesh.FaceCount; i++, j += 3) { GraphicResearchHuiZhao.Vector3D u = mesh.GetDualPosition(i); GraphicResearchHuiZhao.Vector3D lap = new GraphicResearchHuiZhao.Vector3D(lapCoordiante[j], lapCoordiante[j + 1], lapCoordiante[j + 2]); GraphicResearchHuiZhao.Vector3D v = u + 3.0 * lap; GL.Vertex3(u.x, u.y, u.z); GL.Vertex3(v.x, v.y, v.z); } GL.End(); }
public static SparseMatrix BuildMatrixDualL(ref NonManifoldMesh mesh) { // build dual Laplacian weight matrix L int vn = mesh.VertexCount; int fn = mesh.FaceCount; SparseMatrix L = new SparseMatrix(fn, vn, 6); for (int i = 0; i < fn; i++) { int f1 = mesh.AdjFF[i][0]; int f2 = mesh.AdjFF[i][1]; int f3 = mesh.AdjFF[i][2]; Vector3D dv = mesh.GetDualPosition(i); Vector3D dv1 = mesh.GetDualPosition(f1); Vector3D dv2 = mesh.GetDualPosition(f2); Vector3D dv3 = mesh.GetDualPosition(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; for (int j = 0, k = i * 3; j < 3; j++) L.AddValueTo(i, mesh.FaceIndex[k++], alpha); alpha = coord[0] / 3.0; for (int j = 0, k = f1 * 3; j < 3; j++) L.AddValueTo(i, mesh.FaceIndex[k++], -alpha); alpha = coord[1] / 3.0; for (int j = 0, k = f2 * 3; j < 3; j++) L.AddValueTo(i, mesh.FaceIndex[k++], -alpha); alpha = (1.0 - coord[0] - coord[1]) / 3.0; for (int j = 0, k = f3 * 3; j < 3; j++) L.AddValueTo(i, mesh.FaceIndex[k++], -alpha); } L.SortElement(); return L; }