public static DenseVector VectorOfVertexPositions(HalfEdgeMesh mesh)
{
int numVertices = mesh.Vertices.Length;
DenseVector vec = DenseVector.Create(3 * numVertices, 0);
for (int i = 0; i < numVertices; i++)
{
Vector3 pos = mesh.Vertices[i].position;
int vBase = 3 * i;
vec[vBase + 0] = pos.x;
vec[vBase + 1] = pos.y;
vec[vBase + 2] = pos.z;
}
return(vec);
}
public static void MassMatrix(out SparseMatrix M, out SparseMatrix M_inverse, HalfEdgeMesh mesh)
{
int numVertices = mesh.Vertices.Length;
List <Tuple <int, int, double> > M_triples = new List <Tuple <int, int, double> >();
List <Tuple <int, int, double> > M_inv_triples = new List <Tuple <int, int, double> >();
for (int i = 0; i < numVertices; i++)
{
int vBase = 3 * i;
float area = mesh.Vertices[i].DualArea;
for (int n = 0; n < 3; n++)
{
M_triples.Add(new Tuple <int, int, double>(vBase + n, vBase + n, area));
M_inv_triples.Add(new Tuple <int, int, double>(vBase + n, vBase + n, 1f / area));
}
}
M = SparseMatrix.OfIndexed(3 * numVertices, 3 * numVertices, M_triples);
M_inverse = SparseMatrix.OfIndexed(3 * numVertices, 3 * numVertices, M_inv_triples);
}
/// <summary>
/// Returns I + hA, where A is the matrix mapping vertex positions to area normals.
/// </summary>
/// <param name="mesh"></param>
/// <param name="h"></param>
/// <returns></returns>
public static SparseMatrix AreaNormalMatrix(HalfEdgeMesh mesh, double h)
{
int numVertices = mesh.Vertices.Length;
List <Tuple <int, int, double> > triplets = new List <Tuple <int, int, double> >();
// Compute the matrix row by row
for (int i = 0; i < numVertices; i++)
{
HalfEdge startHE = mesh.Vertices[i].anyHalfEdge;
HalfEdge he = startHE;
int rowBase = 3 * i;
DenseMatrix A_ii = DenseMatrix.Create(3, 3, 0);
do
{
// This is edge e(i -> a)
HalfEdge hePrev = he;
Vector3 f_a = hePrev.headVertex.position;
// This is edge e(i -> j), which is the one we're
// actually computing the matrix element for
HalfEdge heCenter = hePrev.flip.next;
// This is edge e(i -> b)
HalfEdge heNext = heCenter.flip.next;
Vector3 f_b = heNext.headVertex.position;
int columnBase = 3 * heCenter.headVertex.Index;
Vector3 w_ij = (f_a - f_b) / 12;
DenseMatrix A_ij = -1 * CrossProductMatrix(w_ij);
triplets.Add(new Tuple <int, int, double>(rowBase + 0, columnBase + 1, A_ij[0, 1]));
triplets.Add(new Tuple <int, int, double>(rowBase + 0, columnBase + 2, A_ij[0, 2]));
triplets.Add(new Tuple <int, int, double>(rowBase + 1, columnBase + 0, A_ij[1, 0]));
triplets.Add(new Tuple <int, int, double>(rowBase + 1, columnBase + 2, A_ij[1, 2]));
triplets.Add(new Tuple <int, int, double>(rowBase + 2, columnBase + 0, A_ij[2, 0]));
triplets.Add(new Tuple <int, int, double>(rowBase + 2, columnBase + 1, A_ij[2, 1]));
A_ii += A_ij;
he = he.flip.next;
}while (he != startHE);
A_ii *= -1;
triplets.Add(new Tuple <int, int, double>(rowBase + 0, rowBase + 0, A_ii[0, 0]));
triplets.Add(new Tuple <int, int, double>(rowBase + 0, rowBase + 1, A_ii[0, 1]));
triplets.Add(new Tuple <int, int, double>(rowBase + 0, rowBase + 2, A_ii[0, 2]));
triplets.Add(new Tuple <int, int, double>(rowBase + 1, rowBase + 0, A_ii[1, 0]));
triplets.Add(new Tuple <int, int, double>(rowBase + 1, rowBase + 1, A_ii[1, 1]));
triplets.Add(new Tuple <int, int, double>(rowBase + 1, rowBase + 2, A_ii[1, 2]));
triplets.Add(new Tuple <int, int, double>(rowBase + 2, rowBase + 0, A_ii[2, 0]));
triplets.Add(new Tuple <int, int, double>(rowBase + 2, rowBase + 1, A_ii[2, 1]));
triplets.Add(new Tuple <int, int, double>(rowBase + 2, rowBase + 2, A_ii[2, 2]));
}
return(SparseMatrix.OfIndexed(3 * numVertices, 3 * numVertices, triplets));
}