public PrincipalCurvature ComputePrincipalCurvature(TriMesh.Vertex v)
{
Vector3D sum = Vector3D.Zero;
Vector3D mid = v.Traits.Position;
foreach (var hf in v.HalfEdges)
{
Vector3D buttom = hf.ToVertex.Traits.Position;
Vector3D left = hf.Opposite.Next.ToVertex.Traits.Position;
Vector3D right = hf.Next.ToVertex.Traits.Position;
double cota = (mid - left).Dot(buttom - left) / (mid - left).Cross(buttom - left).Length();
double cotb = (mid - right).Dot(buttom - right) / (mid - right).Cross(buttom - right).Length();
sum += (cota + cotb) * (this.Normal[v.Index] - this.Normal[hf.ToVertex.Index]);
}
double mixedArea = TriMeshUtil.ComputeAreaMixed(v);
Vector3D laplace = sum / mixedArea / 2d;
double square = -laplace.Dot(this.Normal[v.Index]);
double k = this.K[v.Index].Length();
double delta = -k * k + 2d * square;
if (delta < 0d)
{
delta = 0d;
}
PrincipalCurvature pc = new PrincipalCurvature();
pc.max = (k + Math.Pow(delta, 0.5)) / 2d;
pc.min = (k - Math.Pow(delta, 0.5)) / 2d;
return(pc);
}
public SparseMatrix BuildLaplaceCotArea(TriMesh mesh)
{
double[] areas = TriMeshUtil.ComputeAreaMixed(mesh);
SparseMatrix cot = BuildLaplaceCot(mesh);
int n = mesh.Vertices.Count;
for (int i = 0; i < n; i++)
{
foreach (SparseMatrix.Element e in cot.Rows[i])
{
e.value = e.value * (1 / areas[i]);
}
}
return(cot);
}
public CurvaturePG07(TriMesh mesh)
{
this.mesh = mesh;
this.K = new Vector3D[this.mesh.Vertices.Count];
this.Mean = new double[this.mesh.Vertices.Count];
this.Normal = new Vector3D[this.mesh.Vertices.Count];
this.PrincipalCurv = new PrincipalCurvature[this.mesh.Vertices.Count];
foreach (var v in this.mesh.Vertices)
{
double mixedArea = TriMeshUtil.ComputeAreaMixed(v);
this.K[v.Index] = ComputeK(v, mixedArea);
this.Mean[v.Index] = ComputeMeanCurvature(this.K[v.Index]);
this.Normal[v.Index] = ComputeNormal(this.K[v.Index]);
}
foreach (var v in this.mesh.Vertices)
{
this.PrincipalCurv[v.Index] = this.ComputePrincipalCurvature(v);
}
}