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;
}
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();
}
