void data_to_triangulation(
TriangulationData *data,
Triangulation **manifold_ptr)
{
/*
* We assume the UI has done some basic error checking
* on the data, so we don't repeat it here.
*/
Triangulation *manifold;
Tetrahedron **tet_array;
Cusp **cusp_array;
Boolean cusps_are_given;
int i,
j,
k,
l,
m;
Boolean all_peripheral_curves_are_zero,
finite_vertices_are_present;
/*
* Initialize *manifold_ptr to NULL.
* We'll do all our work with manifold, and then copy
* manifold to *manifold_ptr at the very end.
*/
*manifold_ptr = NULL;
/*
* Allocate and initialize the Triangulation structure.
*/
manifold = NEW_STRUCT(Triangulation);
initialize_triangulation(manifold);
/*
* Allocate and copy the name.
*/
manifold->name = NEW_ARRAY(strlen(data->name) + 1, char);
strcpy(manifold->name, data->name);
/*
* Set up the global information.
*
* The hyperbolic structure is included in the file only for
* human readers; here we recompute it from scratch.
*/
manifold->num_tetrahedra = data->num_tetrahedra;
manifold->solution_type[complete] = not_attempted;
manifold->solution_type[ filled ] = not_attempted;
manifold->orientability = data->orientability;
manifold->num_or_cusps = data->num_or_cusps;
manifold->num_nonor_cusps = data->num_nonor_cusps;
manifold->num_cusps = manifold->num_or_cusps
+ manifold->num_nonor_cusps;
/*
* Allocate the Tetrahedra.
* Keep pointers to them on a temporary array, so we can
* find them by their indices.
*/
tet_array = NEW_ARRAY(manifold->num_tetrahedra, Tetrahedron *);
for (i = 0; i < manifold->num_tetrahedra; i++)
{
tet_array[i] = NEW_STRUCT(Tetrahedron);
initialize_tetrahedron(tet_array[i]);
INSERT_BEFORE(tet_array[i], &manifold->tet_list_end);
}
/*
* If num_or_cusps or num_nonor_cusps is nonzero, allocate the Cusps.
* Keep pointers to them on temporary arrays, so we can find them
* by their indices.
* Otherwise we will create arbitrary Cusps later.
*/
cusps_are_given = (data->num_or_cusps != 0) || (data->num_nonor_cusps != 0);
if (cusps_are_given == TRUE)
{
cusp_array = NEW_ARRAY(manifold->num_cusps, Cusp *);
for (i = 0; i < manifold->num_cusps; i++)
{
cusp_array[i] = NEW_STRUCT(Cusp);
initialize_cusp(cusp_array[i]);
INSERT_BEFORE(cusp_array[i], &manifold->cusp_list_end);
}
}
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;
}
