public static void SetUpVertexNormal(TriMesh mesh, EnumNormal type)
{
Vector3D[] normal = TriMeshUtil.ComputeNormalVertex(mesh, type);
for (int i = 0; i < mesh.Vertices.Count; i++)
{
mesh.Vertices[i].Traits.Normal = normal[i];
}
}
public void MappingGauss(TriMesh mesh)
{
for (int i = 0; i < mesh.Vertices.Count; i++)
{
Vector3D[] normals = TriMeshUtil.ComputeNormalVertex(mesh, EnumNormal.SphereInscribed);
mesh.Vertices[i].Traits.Position = normals[i];
}
TriMeshUtil.SetUpNormalVertex(mesh);
}
public static PrincipalCurvature[] ComputePrincipleCurvatures(TriMesh mesh, double[] CornerArea, double[] PointArea)
{
Vector3D[] vertexNormal = TriMeshUtil.ComputeNormalVertex(mesh);
// Add dynamic trait for principle curvature computation
double[] curv = new double[mesh.Vertices.Count];
PrincipalCurvature[] pc = new PrincipalCurvature[mesh.Vertices.Count];
// Initialize a coordinate system for each vertex
foreach (TriMesh.Vertex v in mesh.Vertices)
{
pc[v.Index] = new PrincipalCurvature();
// Vector that points from this vertex to an adjacent one
pc[v.Index].maxDir = (v.HalfEdge.ToVertex.Traits.Position - v.Traits.Position).Cross(vertexNormal[v.Index]).Normalize();
// Get a vector orthogonal to this vector and the vertex normal
pc[v.Index].minDir = vertexNormal[v.Index].Cross(pc[v.Index].maxDir);
}
TriMesh.HalfEdge[] fh = new TriMesh.HalfEdge[3];
TriMesh.Vertex[] fv = new TriMesh.Vertex[3];
Vector3D[] e = new Vector3D[3];
Vector3D t, b, dn, faceNormal;
// Compute curvature for each face
foreach (TriMesh.Face f in mesh.Faces)
{
// Get halfedges for this face
fh[0] = f.HalfEdge;
fh[1] = fh[0].Next;
fh[2] = fh[1].Next;
// Get vertices for this face
fv[0] = fh[0].ToVertex;
fv[1] = fh[1].ToVertex;
fv[2] = fh[2].ToVertex;
// Edge vectors
e[0] = fv[2].Traits.Position - fv[1].Traits.Position;
e[1] = fv[0].Traits.Position - fv[2].Traits.Position;
e[2] = fv[1].Traits.Position - fv[0].Traits.Position;
t = e[0];
t.Normalize();
faceNormal = e[0].Cross(e[1]);
faceNormal.Normalize();
b = faceNormal.Cross(t);
b.Normalize();
// Estimate curvature by variation of normals along edges
double[] m = new double[3];
double[,] w = new double[3, 3];
for (int i = 0; i < 3; ++i)
{
double u = e[i].Dot(t);
double v = e[i].Dot(b);
w[0, 0] += u * u;
w[0, 1] += u * v;
w[2, 2] += v * v;
dn = vertexNormal[fv[(i + 2) % 3].Index] - vertexNormal[fv[(i + 1) % 3].Index];
double dnu = dn.Dot(t);
double dnv = dn.Dot(b);
m[0] += dnu * u;
m[1] += dnu * v + dnv * u;
m[2] += dnv * v;
}
w[1, 1] = w[0, 0] + w[2, 2];
w[1, 2] = w[0, 1];
// Least squares solution
double[] diag = new double[3];
if (Transform.LdlTransposeDecomp(w, diag))
{
Transform.LdlTransposeSolveInPlace(w, diag, m);
// Adjust curvature for vertices of this face
for (int i = 0; i < 3; ++i)
{
UV tb = new UV {
U = t, V = b
};
KUV mk = new KUV {
U = m[0], UV = m[1], V = m[2]
};
UV dst = new UV {
U = pc[fv[i].Index].maxDir, V = pc[fv[i].Index].minDir
};
KUV c = Transform.ProjectCurvature(tb, mk, dst);
double weight = CornerArea[fh[i].Index] / PointArea[fv[i].Index];
pc[fv[i].Index].max += weight * c.U;
curv[fv[i].Index] += weight * c.UV;
pc[fv[i].Index].min += weight * c.V;
}
}
}
// Compute curvature for each vertex
foreach (TriMesh.Vertex v in mesh.Vertices)
{
UV src = new UV {
U = pc[v.Index].maxDir, V = pc[v.Index].minDir
};
KUV srcK = new KUV {
U = pc[v.Index].max, UV = curv[v.Index], V = pc[v.Index].min
};
pc[v.Index] = Transform.DiagonalizeCurvature(src, srcK, vertexNormal[v.Index]);
}
return(pc);
}
