void InitQuadrics()
{
Matrix <double>[] faceQuadrics = new Matrix <double> [heMesh.Faces.Length];
// Compute quadrics for each face
for (int i = 0; i < faceQuadrics.Length; i++)
{
Face f = heMesh.Faces[i];
if (f.IsBoundary)
{
continue;
}
Vector3 normal = f.Normal;
Vector3 point = f.anyHalfEdge.tailVertex.position;
float d = -Vector3.Dot(normal, point);
DenseVector v = DenseVector.OfArray(new double[] { normal.x, normal.y, normal.z, d });
faceQuadrics[i] = v.OuterProduct(v);
}
// Compute quadrics for each vertex by adding face quadrics
vertQuadrics = new ErrorQuadric[heMesh.Vertices.Length];
for (int i = 0; i < vertQuadrics.Length; i++)
{
vertQuadrics[i] = new ErrorQuadric();
Vertex v = heMesh.Vertices[i];
HalfEdge he = v.anyHalfEdge;
HalfEdge start = he;
do
{
Face f = he.face;
if (!f.IsBoundary)
{
vertQuadrics[i].AddQuadric(faceQuadrics[f.Index]);
}
he = he.flip.next;
}while (he != start);
}
edgeCosts = new float[heMesh.Edges.Length];
// Compute initial error values for each edge
for (int i = 0; i < heMesh.Edges.Length; i++)
{
ErrorQuadric Qsum = new ErrorQuadric();
int v1 = heMesh.Edges[i].anyHalfEdge.tailVertex.Index;
int v2 = heMesh.Edges[i].anyHalfEdge.headVertex.Index;
Qsum.AddQuadric(vertQuadrics[v1]);
Qsum.AddQuadric(vertQuadrics[v2]);
Vector3 opt = Qsum.OptimalPoint(heMesh.Vertices[v1].position, heMesh.Vertices[v2].position);
edgeCosts[i] = Qsum.ErrorAtPoint(opt);
}
}
float QuadricCostOfEdge(Edge e)
{
int v1 = e.anyHalfEdge.tailVertex.Index;
int v2 = e.anyHalfEdge.headVertex.Index;
ErrorQuadric Qsum = new ErrorQuadric();
Qsum.AddQuadric(uf.Find(v1).Quadric);
Qsum.AddQuadric(uf.Find(v2).Quadric);
Vector3 optPoint = Qsum.OptimalPoint(heMesh.Vertices[v1].position,
heMesh.Vertices[v2].position);
return(Qsum.ErrorAtPoint(optPoint));
}
public static UnionFind <VertexNode> MakeUnionFind(HalfEdgeMesh mesh)
{
UnionFind <VertexNode> uf = new UnionFind <VertexNode>(mesh.Vertices.Length);
Matrix <double>[] faceQuadrics = new Matrix <double> [mesh.Faces.Length];
for (int i = 0; i < faceQuadrics.Length; i++)
{
Face f = mesh.Faces[i];
if (f.IsBoundary)
{
continue;
}
Vector3 normal = f.Normal;
Vector3 v1 = f.anyHalfEdge.tailVertex.position;
float d = -Vector3.Dot(v1, normal);
Vector <double> v = DenseVector.OfArray(new double[] { normal.x, normal.y, normal.z, d });
faceQuadrics[i] = v.OuterProduct(v);
}
for (int i = 0; i < uf.NumNodes; i++)
{
VertexNode current = uf[i];
current.position = mesh.Vertices[i].position;
current.containingUF = uf;
ErrorQuadric vertQuadric = new ErrorQuadric();
// Iterate over all faces surrounding this vertex and sum up the face quadrics
HalfEdge start = mesh.Vertices[i].anyHalfEdge;
HalfEdge he = start;
do
{
Face f = he.face;
if (!f.IsBoundary)
{
Matrix <double> faceQuadric = faceQuadrics[he.face.Index];
vertQuadric.AddQuadric(faceQuadric);
}
he = he.flip.next;
}while (he != start);
current.quadric = vertQuadric;
current.mergedPoints = new HashSet <int>();
current.mergedPoints.Add(i);
current.Index = i;
}
return(uf);
}
public override void Merge(UnionFindNode child)
{
VertexNode childNode = child as VertexNode;
if (child.Parent != child)
{
throw new System.Exception("Merge wasn't given parent node");
}
quadric.AddQuadric(childNode.quadric);
//position = (position + childNode.position) / 2;
//position = quadric.OptimalPoint(position, childNode.position);
int n1 = mergedPoints.Count;
int n2 = childNode.mergedPoints.Count;
position = ((n1 * position) + (n2 * childNode.position)) / (n1 + n2);
currentCost = Cost(position);
mergedPoints.UnionWith(childNode.mergedPoints);
}
