/// <summary>
/// calculate tetrahedrone involved all points
/// </summary>
/// <param name="pVectorList">xyz point list</param>
/// <returns>tetrahedrone</returns>
private static Tetrahedron GetFirstTetra(List <PVector> pVectorList)
{
float xMin = pVectorList.Min(value => value.X);
float yMin = pVectorList.Min(value => value.Y);
float zMin = pVectorList.Min(value => value.Z);
float xMax = pVectorList.Max(value => value.X);
float yMax = pVectorList.Max(value => value.Y);
float zMax = pVectorList.Max(value => value.Z);
//rectangular solid size
float width = xMax - xMin;
float height = yMax - yMin;
float depth = zMax - zMin;
//center of globe
float cX = width / 2 + xMin;
float cY = height / 2 + yMin;
float cZ = depth / 2 + zMin;
PVector center = new PVector(cX, cY, cZ);
//radius
//0.1f is addition
float radius = Common.GetDist(new PVector(xMax, yMax, zMax), new PVector(xMin, yMin, zMin)) / 2 + 0.1f;
PVector p1 = new PVector(center.X, center.Y + 3.0f, center.Z);
PVector p2 = new PVector(center.X + (float)2 * (float)Math.Sqrt(2) * radius, center.Y - radius, center.Z);
PVector p3 = new PVector(-(float)Math.Sqrt(2) * radius + center.X, -radius + center.Y, (float)Math.Sqrt(6) * radius + center.Z);
PVector p4 = new PVector(-(float)Math.Sqrt(2) * radius + center.X, -radius + center.Y, -(float)Math.Sqrt(6) * radius + center.Z);
return(new Tetrahedron(p1, p2, p3, p4));
}
/// <summary>
/// calculate radius and circle of outer circle from tetrahedron points
/// ref URL　http://www.openprocessing.org/sketch/31295
/// </summary>
private void getCenterCircumcircle()
{
//translation from P1
double[,] A = new double[, ] {
{ P2.X - P1.X, P2.Y - P1.Y, P2.Z - P1.Z },
{ P3.X - P1.X, P3.Y - P1.Y, P3.Z - P1.Z },
{ P4.X - P1.X, P4.Y - P1.Y, P4.Z - P1.Z }
};
//I did not understand this mean
double[] b = new double[] {
0.5 * (P2.X * P2.X - P1.X * P1.X + P2.Y * P2.Y - P1.Y * P1.Y + P2.Z * P2.Z - P1.Z * P1.Z),
0.5 * (P3.X * P3.X - P1.X * P1.X + P3.Y * P3.Y - P1.Y * P1.Y + P3.Z * P3.Z - P1.Z * P1.Z),
0.5 * (P4.X * P4.X - P1.X * P1.X + P4.Y * P4.Y - P1.Y * P1.Y + P4.Z * P4.Z - P1.Z * P1.Z)
};
//solve
double[] x = new double[3];
if (gauss(A, b, x) == 0)
{
O = null;
R = -1;
}
else
{
O = new PVector((float)x[0], (float)x[1], (float)x[2]);
R = Common.GetDist(O, P1);
}
}
/// <summary>
/// Calculate Delaunay Triangulation
/// </summary>
/// <param name="pVectorList">AllPoints</param>
/// <returns>Tetrahedrone List</returns>
private List <Tetrahedron> GetTetraList(List <PVector> pVectorList)
{
List <Tetrahedron> tetraList = new List <Tetrahedron>();
tetraList.Add(this.FirstTetra);
List <Tetrahedron> tmpTList = new List <Tetrahedron>();
List <Tetrahedron> newTList = new List <Tetrahedron>();
List <Tetrahedron> removeTList = new List <Tetrahedron>();
foreach (var point in pVectorList)
{
tmpTList.Clear();
newTList.Clear();
removeTList.Clear();
foreach (var t in tetraList)
{
if ((t.O != null) &&
(t.R > Common.GetDist(point, t.O)))
{
tmpTList.Add(t);
}
}
foreach (var t1 in tmpTList)
{
tetraList.Remove(t1);
PVector v1 = t1.P1;
PVector v2 = t1.P2;
PVector v3 = t1.P3;
PVector v4 = t1.P4;
newTList.Add(new Tetrahedron(v1, v2, v3, point));
newTList.Add(new Tetrahedron(v1, v2, v4, point));
newTList.Add(new Tetrahedron(v1, v3, v4, point));
newTList.Add(new Tetrahedron(v2, v3, v4, point));
}
bool[] isRedundancy = new bool[newTList.Count];
for (int i = 0; i < newTList.Count - 1; i++)
{
for (int j = i + 1; j < newTList.Count; j++)
{
if (newTList[i].Equal(newTList[j]))
{
isRedundancy[i] = isRedundancy[j] = true;
}
}
}
for (int i = 0; i < newTList.Count; i++)
{
if (!isRedundancy[i])
{
tetraList.Add(newTList[i]);
}
}
}
PVector[] outer = new PVector[] { this.FirstTetra.P1, this.FirstTetra.P2, this.FirstTetra.P3, this.FirstTetra.P4 };
bool isOuter = false;
var count = 0;
for (int i = tetraList.Count - 1; i >= 0; i--)
{
isOuter = false;
foreach (var t4Point in tetraList[i].Vertices)
{
foreach (var outerPoint in outer)
{
if (t4Point.X == outerPoint.X &&
t4Point.Y == outerPoint.Y &&
t4Point.Z == outerPoint.Z)
{
isOuter = true;
}
}
}
if (isOuter)
{
tetraList.RemoveAt(i);
count++;
Console.WriteLine(count);
}
}
return(tetraList);
}