void ExtremalQuery3BSP<Real>::CreateSphericalBisectors (BasicMesh& mesh,
std::multiset<SphericalArc>& arcs)
{
// For each vertex, sort the normals into a counterclockwise spherical
// polygon when viewed from outside the sphere.
SortVertexAdjacents(mesh);
int numVertices = mesh.GetNumVertices();
const BasicMesh::Vertex* vertices = mesh.GetVertices();
std::queue<std::pair<int,int> > queue;
for (int i = 0; i < numVertices; ++i)
{
const BasicMesh::Vertex& vertex = vertices[i];
queue.push(std::make_pair(0, vertex.NumTriangles));
while (!queue.empty())
{
std::pair<int,int> arc = queue.front();
queue.pop();
int i0 = arc.first, i1 = arc.second;
int separation = i1 - i0;
if (separation > 1 && separation != vertex.NumTriangles - 1)
{
if (i1 < vertex.NumTriangles)
{
SphericalArc arc;
arc.NIndex[0] = vertex.T[i0];
arc.NIndex[1] = vertex.T[i1];
arc.Separation = separation;
arc.Normal = mFaceNormals[arc.NIndex[0]].Cross(
mFaceNormals[arc.NIndex[1]]);
arc.PosVertex = i;
arc.NegVertex = i;
arcs.insert(arc);
}
int iMid = (i0 + i1 + 1)/2;
if (iMid != i1)
{
queue.push(std::make_pair(i0, iMid));
queue.push(std::make_pair(iMid, i1));
}
}
}
}
}
void ExtremalQuery3BSP<Real>::SortVertexAdjacents (BasicMesh& mesh)
{
// The typecast is to allow modifying the vertices. As long as the
// sorting algorithm is correct, this is a safe thing to do.
int numVertices = mesh.GetNumVertices();
BasicMesh::Vertex* vertices = (BasicMesh::Vertex*)mesh.GetVertices();
const BasicMesh::Triangle* triangles = mesh.GetTriangles();
for (int i = 0; i < numVertices; ++i)
{
// This copy circumvents the constness of the mesh vertices, which
// allows the sorting of the mesh triangles shared by a mesh vertex.
BasicMesh::Vertex& vertex = vertices[i];
// This is a consequence of the mesh being a polyhedron.
assertion(vertex.NumVertices == vertex.NumTriangles,
"Unexpected condition\n");
// Once we have the first vertex to sort and an initial triangle
// sharing it, we can walk around the vertex following triangle
// adjacency links. It is safe to overwrite the vertex data.
int t = vertex.T[0];
const BasicMesh::Triangle* tri = &triangles[t];
for (int adj = 0; adj < vertex.NumVertices; ++adj)
{
int prev, curr;
for (prev = 2, curr = 0; curr < 3; prev = curr++)
{
if (tri->V[curr] == i)
{
vertex.V[adj] = tri->V[prev];
vertex.E[adj] = tri->E[prev];
vertex.T[adj] = t;
// The next triangle to visit.
t = tri->T[prev];
tri = &triangles[t];
break;
}
}
assertion(curr < 3, "Unexpected condition\n");
}
}
}