public void DrawSupertetrahedron()
{
Bounds meshBounds = _mesh.bounds;
_superTetra = Tetra.ComputeCircumTetraOfSphere(meshBounds.center, meshBounds.extents.magnitude);
_superTetra.Show(Color.red, 1000);
}
public TriangleFace(Vertex p1, Vertex p2, Vertex p3, Tetra tetra)
{
P1 = p1;
P2 = p2;
P3 = p3;
RightTetra = tetra;
LeftTetra = null;
}
public TriangleFace(Tetra tetra, Tetra otherTetra)
{
tetra.GetCommonVerticesWith(otherTetra, out Vertex p1, out Vertex p2, out Vertex p3);
P1 = p1;
P2 = p2;
P3 = p3;
LeftTetra = tetra;
RightTetra = otherTetra;
}
public bool HasACommonVertexWith(Tetra otherTetra)
{
HashSet <Vertex> tetraVertices = new HashSet <Vertex>()
{
P1, P2, P3, P4
};
HashSet <Vertex> otherTetraVertices = new HashSet <Vertex>()
{
otherTetra.P1, otherTetra.P2, otherTetra.P3, otherTetra.P4
};
tetraVertices.IntersectWith(otherTetraVertices);
return(tetraVertices.Count >= 1);
}
public void Init()
{
Mesh mesh = _meshFilter.sharedMesh;
_vector3vertices = mesh.vertices;
_numberOfVertices = _vector3vertices.Length;
FillVeticesArray();
_normals = mesh.normals;
_triangles = mesh.triangles;
_numberOfTriangles = _triangles.Length;
Bounds meshBounds = mesh.bounds;
_superTetra = Tetra.ComputeCircumTetraOfSphere(meshBounds.center, meshBounds.extents.magnitude);
}
public bool IsNeighborOf(Tetra otherTetra)
{
HashSet <Vertex> tetraVertices = new HashSet <Vertex>()
{
P1, P2, P3, P4
};
HashSet <Vertex> otherTetraVertices = new HashSet <Vertex>()
{
otherTetra.P1, otherTetra.P2, otherTetra.P3, otherTetra.P4
};
tetraVertices.IntersectWith(otherTetraVertices);
// Two tetrahedrons are neighbors if and only if they share 3 vertices;
return(tetraVertices.Count == 3);
}
public void RegisterNeighbor(Tetra tetra)
{
if (LeftTetra == null)
{
LeftTetra = tetra;
}
else if (RightTetra == null)
{
RightTetra = tetra;
}
else
{
throw new System.Exception("Trying to register a neighboring tetrahedron to a triangle that already has two neighbors.");
}
}
public Tetra GetOtherTetraThan(Tetra tetra)
{
if (tetra.Equals(RightTetra))
{
return(LeftTetra);
}
else if (tetra.Equals(LeftTetra))
{
return(RightTetra);
}
else
{
tetra.Show(Color.red, 100);
Show(Color.cyan, 100);
throw new System.Exception("The given tetrahedron is not one of the neighbors of the triangle face");
}
}
private HashSet <TriangleFace> GetPolygonalHoleFromBadTetras(HashSet <Tetra> badTetras)
{
HashSet <TriangleFace> polyHole = new HashSet <TriangleFace>();
foreach (Tetra badTetra in badTetras)
{
foreach (TriangleFace face in badTetra.Faces)
{
Tetra otherTetraOfFace = face.GetOtherTetraThan(badTetra);
if (!badTetras.Contains(otherTetraOfFace))
{
TriangleFace newFace = new TriangleFace(face.P1, face.P2, face.P3, otherTetraOfFace);
polyHole.Add(newFace);
}
}
}
return(polyHole);
}
public override bool Equals(object obj)
{
Tetra tetra = obj as Tetra;
if (tetra == null)
{
return(false);
}
Vertex[] tetraVertices = new Vertex[4];
tetraVertices[0] = tetra.P1;
tetraVertices[1] = tetra.P2;
tetraVertices[2] = tetra.P3;
tetraVertices[3] = tetra.P4;
return(tetra != null &&
tetraVertices.Contains(P1) &&
tetraVertices.Contains(P2) &&
tetraVertices.Contains(P3) &&
tetraVertices.Contains(P4));
}
public void ComputeDelaunayTriangulation()
{
HashSet <Tetra> triangulation = new HashSet <Tetra> {
_superTetra
};
foreach (Vertex vertex in _vertices)
{
HashSet <Tetra> badTetras = GetBadTetrasInCurrentTriangulation(triangulation, vertex);
HashSet <TriangleFace> polyHole = GetPolygonalHoleFromBadTetras(badTetras);
RemoveBadTetras(triangulation, badTetras);
HashSet <Tetra> tetrasToAdd = GetNewTetrasFromPolygonalHole(vertex, polyHole);
AddNewTetrasToTriangulation(triangulation, tetrasToAdd);
_triangulation = triangulation;
}
RemoveTetrasFromSuperTetra(triangulation);
_triangulation = triangulation;
Tetra.Show(triangulation, Color.green, 1000);
}
public void GetCommonVerticesWith(Tetra otherTetra, out Vertex p1, out Vertex p2, out Vertex p3)
{
if (IsNeighborOf(otherTetra))
{
HashSet <Vertex> tetraVertices = new HashSet <Vertex>()
{
P1, P2, P3, P4
};
HashSet <Vertex> otherTetraVertices = new HashSet <Vertex>()
{
otherTetra.P1, otherTetra.P2, otherTetra.P3, otherTetra.P4
};
tetraVertices.IntersectWith(otherTetraVertices);
List <Vertex> commonVertices = new List <Vertex>(tetraVertices);
p1 = commonVertices[0];
p2 = commonVertices[1];
p3 = commonVertices[2];
}
else
{
throw new Exception("The two tetrahedrons are not neighbors");
}
}
private HashSet <Tetra> GetNewTetrasFromPolygonalHole(Vertex vertex, HashSet <TriangleFace> polyHole)
{
HashSet <Tetra> tetrasToAdd = new HashSet <Tetra>();
foreach (TriangleFace face in polyHole)
{
Tetra newTetra = new Tetra(face, vertex);
tetrasToAdd.Add(newTetra);
}
foreach (Tetra tetra in tetrasToAdd)
{
foreach (Tetra otherTetra in tetrasToAdd)
{
if (tetra.IsNeighborOf(otherTetra))
{
TriangleFace face = new TriangleFace(tetra, otherTetra);
tetra.AddNeighbor(face);
}
}
}
return(tetrasToAdd);
}