/// <summary>
/// Compute the convex hull in 3-D space
/// </summary>
/// <returns>surfaces of the convex hull</returns>
public List <TriangularFace> Compute()
{
NumFace = 0;
if (NumVertex < 4)
{
return(null);
}
Prepare();
for (int i = 4; i < NumVertex; i++)
{
for (int j = 0; j < NumFace; j++)
{
if (HullFace[j].Valid && HullFace[j].VOutFace(Vertices[i]))
{
Horizon.Clear();
ComputeHorizon(HullFace[j], Vertices[i]);
SortHorizons();
TriangularFace first = null;
TriangularFace last = null;
DualSite v = Vertices[i];
for (int ii = 0; ii < Horizon.Count; ii++)
{
Edge e = Horizon[ii];
TriangularFace f = e.NeighborFace;
TriangularFace add = new TriangularFace(e.Vertex0, e.Vertex1, v);
HullFace.Add(add);
NumFace++;
f.SetNeighbor(add, e.Vertex0, e.Vertex1);
if (first == null)
{
first = add;
}
else
{
add.SetNeighbor(last, e.Vertex0, v);
}
last = add;
}
last.SetNeighbor(first, last.Edge0.Vertex1, Vertices[i]);
break;
}
}
}
List <TriangularFace> result = new List <TriangularFace>();
for (int i = 0; i < HullFace.Count; i++)
{
if (HullFace[i].Valid)
{
result.Add(HullFace[i]);
}
}
return(result);
}
/// <summary>
/// let the first three vertices noncollinear and the first four vertices noncoplanar
/// </summary>
private void Prepare()
{
Vector3D tmp_vector = new Vector3D();
for (int i = 2; i < NumVertex; i++)
{
tmp_vector = Vector3D.CrossProduct(Vertices[1].Coordinate - Vertices[0].Coordinate, Vertices[i].Coordinate - Vertices[0].Coordinate);
if (tmp_vector.LengthSquared > Eps)//三点不共线
{
if (i != 2)
{
DualSite tmp = Vertices[i];
Vertices[i] = Vertices[2];
Vertices[2] = tmp;
}
break;
}
}
for (int i = 3; i < NumVertex; i++)
{
if (Math.Abs(Vector3D.DotProduct(tmp_vector, Vertices[i].Coordinate - Vertices[0].Coordinate)) > Eps)//四点不共面
{
if (i != 3)
{
DualSite tmp = Vertices[i];
Vertices[i] = Vertices[3];
Vertices[3] = tmp;
}
break;
}
}
//为使面法向量方向指向凸包外
TriangularFace tmp_face = new TriangularFace(Vertices[0], Vertices[1], Vertices[2]);
if (tmp_face.VOutFace(Vertices[3]))
{
DualSite tmp = Vertices[2];
Vertices[2] = Vertices[3];
Vertices[3] = tmp;
}
HullFace.Add(new TriangularFace(Vertices[0], Vertices[1], Vertices[2]));
HullFace.Add(new TriangularFace(Vertices[1], Vertices[3], Vertices[2]));
HullFace.Add(new TriangularFace(Vertices[0], Vertices[2], Vertices[3]));
HullFace.Add(new TriangularFace(Vertices[0], Vertices[3], Vertices[1]));
HullFace[0].SetNeighbor(HullFace[1], Vertices[1], Vertices[2]);
HullFace[0].SetNeighbor(HullFace[2], Vertices[0], Vertices[2]);
HullFace[0].SetNeighbor(HullFace[3], Vertices[0], Vertices[1]);
HullFace[1].SetNeighbor(HullFace[2], Vertices[2], Vertices[3]);
HullFace[1].SetNeighbor(HullFace[3], Vertices[1], Vertices[3]);
HullFace[2].SetNeighbor(HullFace[3], Vertices[0], Vertices[3]);
NumFace = 4;
}