private static Sphere GetCircumsphere(Tetrahedron tetra)
{
var p = tetra.p;
float[][] a = new float[][] {
new float[] { p[1].x - p[0].x, p[1].y - p[0].y, p[1].z - p[0].z },
new float[] { p[2].x - p[0].x, p[2].y - p[0].y, p[2].z - p[0].z },
new float[] { p[3].x - p[0].x, p[3].y - p[0].y, p[3].z - p[0].z }
};
float[] b =
{
0.5f * (p[1].x * p[1].x - p[0].x * p[0].x + p[1].y * p[1].y - p[0].y * p[0].y + p[1].z * p[1].z - p[0].z * p[0].z),
0.5f * (p[2].x * p[2].x - p[0].x * p[0].x + p[2].y * p[2].y - p[0].y * p[0].y + p[2].z * p[2].z - p[0].z * p[0].z),
0.5f * (p[3].x * p[3].x - p[0].x * p[0].x + p[3].y * p[3].y - p[0].y * p[0].y + p[3].z * p[3].z - p[0].z * p[0].z)
};
float[] x = { 0f, 0f, 0f };
var det = Gauss(a, b, ref x);
if (det == 0)
{
return(new Sphere(Vector3.zero, -1));
}
else
{
var center = new Vector3(x[0], x[1], x[2]);
return(new Sphere(center, Vector3.Distance(center, p[0])));
}
}
private static List <Triangle> GetDelaunayTriangles(List <Vector3> vertices)
{
var tetras = new HashSet <Tetrahedron>();
Tetrahedron huge = GetHugeTetrahedron(vertices);
tetras.Add(huge);
foreach (var v in vertices)
{
var counter = new Counter <Tetrahedron>();
var trash = new List <Tetrahedron>();
foreach (var t in tetras)
{
var sphere = GetCircumsphere(t);
if (Vector3.Distance(sphere.center, v) < sphere.radius)
{
counter.Add(new Tetrahedron(v, t.p[0], t.p[1], t.p[2]));
counter.Add(new Tetrahedron(v, t.p[0], t.p[2], t.p[3]));
counter.Add(new Tetrahedron(v, t.p[0], t.p[1], t.p[3]));
counter.Add(new Tetrahedron(v, t.p[1], t.p[2], t.p[3]));
trash.Add(t);
}
}
tetras.RemoveWhere(t => trash.Contains(t));
foreach (KeyValuePair <Tetrahedron, int> entry in counter)
{
if (entry.Value == 1)
{
tetras.Add(entry.Key);
}
}
}
tetras.RemoveWhere(t => huge.ShareVertex(t));
var triangles = new HashSet <Triangle>();
foreach (var t in tetras)
{
triangles.Add(new Triangle(t.p[0], t.p[1], t.p[2]));
triangles.Add(new Triangle(t.p[0], t.p[2], t.p[3]));
triangles.Add(new Triangle(t.p[0], t.p[1], t.p[3]));
triangles.Add(new Triangle(t.p[1], t.p[2], t.p[3]));
}
return(triangles.ToList());
}