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/*
* canonize_result.c
*
* The function
*
* Boolean is_canonical_triangulation(Triangulation *manifold);
*
* accepts a Triangulation which it assumes to be a subdivision of a canonical
* cell decomposition (as produced by proto_canonize(), for example), and
* says whether it is indeed the canonical cell decomposition itself.
* In other words, is_canonical_triangulation() will return TRUE
* when the canonical cell decomposition is a triangulation, and FALSE when
* it is not.
*
* is_canonical_triangulation() assumes all Tetrahedra in the Triangulation
* have valid "tilt" fields, as will be the case following a call to
* proto_canonize().
*/
#include "kernel.h"
#include "canonize.h"
Boolean is_canonical_triangulation(
Triangulation *manifold)
{
Tetrahedron *tet,
*nbr_tet;
FaceIndex f,
nbr_f;
double sum_of_tilts;
Boolean result;
/*
* We'll assume the canonical cell decomposition is a triangulation
* unless we discover otherwise.
*/
result = TRUE;
for (tet = manifold->tet_list_begin.next;
tet != &manifold->tet_list_end;
tet = tet->next)
for (f = 0; f < 4; f++)
{
nbr_tet = tet->neighbor[f];
nbr_f = EVALUATE(tet->gluing[f], f);
sum_of_tilts = tet->tilt[f] + nbr_tet->tilt[nbr_f];
/*
* The sum of the tilts should never be positive, because
* this would mean that we didn't have a subdivision of the
* canonical cell decomposition after all.
*/
if (sum_of_tilts > CONCAVITY_EPSILON)
uFatalError("is_canonical_triangulation", "canonize_result");
/*
* If the sum of the tilts is zero, then the canonical cell
* decomposition contains cell other than tetrahedra.
*/
if (sum_of_tilts > -CONCAVITY_EPSILON)
result = FALSE;
/*
* Otherwise we're OK.
*/
}
return result;
}
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