// from http://www.geometry.caltech.edu/pubs/DMSB_III.pdf
public static double VoronoiArea(NGonsCore.geometry3Sharp.mesh.DMesh3 mesh, int v_i)
{
double areaSum = 0;
Vector3D Vi = mesh.GetVertex(v_i);
foreach (int tid in mesh.VtxTrianglesItr(v_i))
{
Index3i t = mesh.GetTriangle(tid);
int ti = (t[0] == v_i) ? 0 : ((t[1] == v_i) ? 1 : 2);
Vector3D Vj = mesh.GetVertex(t[(ti + 1) % 3]);
Vector3D Vk = mesh.GetVertex(t[(ti + 2) % 3]);
if (math.MathUtil.IsObtuse(Vi, Vj, Vk))
{
Vector3D Vij = Vj - Vi;
Vector3D Vik = Vk - Vi;
Vij.Normalize(); Vik.Normalize();
double areaT = 0.5 * Vij.Cross(Vik).Length;
if (Vector3D.AngleR(Vij, Vik) > math.MathUtil.HalfPI)
{
areaSum += (areaT * 0.5); // obtuse at v_i
}
else
{
areaSum += (areaT * 0.25); // not obtuse
}
}
else
{
// voronoi area
Vector3D Vji = Vi - Vj;
double dist_ji = Vji.Normalize();
Vector3D Vki = Vi - Vk;
double dist_ki = Vki.Normalize();
Vector3D Vkj = (Vj - Vk).Normalized;
double cot_alpha_ij = math.MathUtil.VectorCot(Vki, Vkj);
double cot_alpha_ik = math.MathUtil.VectorCot(Vji, -Vkj);
areaSum += dist_ji * dist_ji * cot_alpha_ij * 0.125;
areaSum += dist_ki * dist_ki * cot_alpha_ik * 0.125;
}
}
return(areaSum);
}