static FuncResult validate_hyperbolic_structure(
Triangulation *manifold)
{
int i;
/*
* First make sure some sort of solution is in place.
*/
if (manifold->solution_type[complete] == not_attempted)
find_complete_hyperbolic_structure(manifold);
/*
* If the solution is something other than geometric_solution
* or nongeometric_solution, we're out of luck.
*/
if (manifold->solution_type[complete] != geometric_solution
&& manifold->solution_type[complete] != nongeometric_solution)
return func_failed;
/*
* Overwrite the filled structure with the complete structure
* to keep the low-level retriangulation routines happy.
* (See the technical note at the top of this file for a
* more complete explanation.)
*/
copy_solution(manifold, complete, filled);
/*
* If all Tetrahedra are positively oriented, we're golden.
*/
if (manifold->solution_type[complete] == geometric_solution)
return func_OK;
/*
* Try to find a geometric_solution by randomizing the Triangulation.
* If we can't find one within MAX_RETRIANGULATIONS randomizations,
* give up and return func_failed.
*/
for (i = 0; i < MAX_RETRIANGULATIONS; i++)
{
randomize_triangulation(manifold);
if (manifold->solution_type[complete] == geometric_solution)
return func_OK;
}
/*
* Before we go, we'd better restore the filled solution.
*/
polish_hyperbolic_structures(manifold);
return func_failed;
}
static Triangulation *try_Dirichlet_to_triangulation(
WEPolyhedron *polyhedron)
{
/*
* Implement Plan A as described above.
*/
Triangulation *triangulation;
WEEdge *edge,
*nbr_edge,
*mate_edge;
WEEdgeEnd end;
WEEdgeSide side;
Tetrahedron *new_tet;
FaceIndex f;
/*
* Don't attempt to triangulate an orbifold.
*/
if (singular_set_is_empty(polyhedron) == FALSE)
return NULL;
/*
* Set up the Triangulation.
*/
triangulation = NEW_STRUCT(Triangulation);
initialize_triangulation(triangulation);
/*
* Allocate and copy the name.
*/
triangulation->name = NEW_ARRAY(strlen(DEFAULT_NAME) + 1, char);
strcpy(triangulation->name, DEFAULT_NAME);
/*
* Allocate the Tetrahedra.
*/
triangulation->num_tetrahedra = 4 * polyhedron->num_edges;
for (edge = polyhedron->edge_list_begin.next;
edge != &polyhedron->edge_list_end;
edge = edge->next)
for (end = 0; end < 2; end++) /* = tail, tip */
for (side = 0; side < 2; side++) /* = left, right */
{
new_tet = NEW_STRUCT(Tetrahedron);
initialize_tetrahedron(new_tet);
INSERT_BEFORE(new_tet, &triangulation->tet_list_end);
edge->tet[end][side] = new_tet;
}
/*
* Initialize neighbors.
*/
for (edge = polyhedron->edge_list_begin.next;
edge != &polyhedron->edge_list_end;
edge = edge->next)
for (end = 0; end < 2; end++) /* = tail, tip */
for (side = 0; side < 2; side++) /* = left, right */
{
/*
* Neighbor[0] is associated to this same WEEdge.
* It lies on the same side (left or right), but
* at the opposite end (tail or tip).
*/
edge->tet[end][side]->neighbor[0] = edge->tet[!end][side];
/*
* Neighbor[1] lies on the same face of the Dirichlet
* domain, but at the "next side" of that face.
*/
nbr_edge = edge->e[end][side];
if (nbr_edge->v[!end] == edge->v[end])
/* edge and nbr_edge point in the same direction */
edge->tet[end][side]->neighbor[1] = nbr_edge->tet[!end][side];
else if (nbr_edge->v[end] == edge->v[end])
/* edge and nbr_edge point in opposite directions */
edge->tet[end][side]->neighbor[1] = nbr_edge->tet[end][!side];
else
uFatalError("Dirichlet_to_triangulation", "Dirichlet_conversion");
/*
* Neighbor[2] is associated to this same WEEdge.
* It lies at the same end (tail or tip), but
* on the opposite side (left or right).
*/
edge->tet[end][side]->neighbor[2] = edge->tet[end][!side];
/*
* Neighbor[3] lies on this face's "mate" elsewhere
* on the Dirichlet domain.
*/
mate_edge = edge->neighbor[side];
edge->tet[end][side]->neighbor[3] = mate_edge->tet
[edge->preserves_direction[side] ? end : !end ]
[edge->preserves_sides[side] ? side : !side];
}
/*
* Initialize all gluings to the identity.
*/
for (edge = polyhedron->edge_list_begin.next;
edge != &polyhedron->edge_list_end;
edge = edge->next)
for (end = 0; end < 2; end++) /* = tail, tip */
for (side = 0; side < 2; side++) /* = left, right */
for (f = 0; f < 4; f++)
edge->tet[end][side]->gluing[f] = IDENTITY_PERMUTATION;
/*
* Set up the EdgeClasses.
*/
create_edge_classes(triangulation);
orient_edge_classes(triangulation);
/*
* Attempt to orient the manifold.
*/
orient(triangulation);
/*
* Set up the Cusps, including "fake cusps" for the finite vertices.
* Then locate and remove the fake cusps. If the manifold is closed,
* drill out an arbitrary curve to express it as a Dehn filling.
* Finally, determine the topology of each cusp (torus or Klein bottle)
* and count them.
*/
create_cusps(triangulation);
mark_fake_cusps(triangulation);
peripheral_curves(triangulation);
remove_finite_vertices(triangulation);
count_cusps(triangulation);
/*
* Try to compute a hyperbolic structure, first for the unfilled
* manifold, and then for the closed manifold if appropriate.
*/
find_complete_hyperbolic_structure(triangulation);
do_Dehn_filling(triangulation);
/*
* If the manifold is hyperbolic, install a shortest basis on each cusp.
*/
if ( triangulation->solution_type[complete] == geometric_solution
|| triangulation->solution_type[complete] == nongeometric_solution)
install_shortest_bases(triangulation);
/*
* All done!
*/
return triangulation;
}
