void ExtremalQuery3BSP<Real>::CreateSphericalArcs (BasicMesh& mesh,
        std::multiset<SphericalArc>& arcs)
{
    int numEdges = mesh.GetNumEdges();
    const BasicMesh::Edge* edges = mesh.GetEdges();
    const BasicMesh::Triangle* triangles = mesh.GetTriangles();

    const int prev[3] = { 2, 0, 1 };
    const int next[3] = { 1, 2, 0 };

    for (int i = 0; i < numEdges; ++i)
    {
        const BasicMesh::Edge& edge = edges[i];

        SphericalArc arc;
        arc.NIndex[0] = edge.T[0];
        arc.NIndex[1] = edge.T[1];
        arc.Separation = 1;

        arc.Normal = mFaceNormals[arc.NIndex[0]].Cross(
                         mFaceNormals[arc.NIndex[1]]);

        const BasicMesh::Triangle& adj = triangles[edge.T[0]];
        int j;
        for (j = 0; j < 3; ++j)
        {
            if (adj.V[j] != edge.V[0]
                    &&  adj.V[j] != edge.V[1])
            {
                arc.PosVertex = adj.V[prev[j]];
                arc.NegVertex = adj.V[next[j]];
                break;
            }
        }
        assertion(j < 3, "Unexpected condition\n");

        arcs.insert(arc);
    }

    CreateSphericalBisectors(mesh, arcs);
}