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/*
* tidy_peripheral_curves.c
*
*
* This file provides the function
*
* void tidy_peripheral_curves(Triangulation *manifold);
*
* which is used within the kernel to clean up a set of peripheral
* curves.
*
* Functions which alter triangulations maintain a set of peripheral
* curves which is technically correct, but suffers two faults.
* A minor fault is that the peripheral curves wind around a lot,
* and therefore create unnecessarily complicated cusp equations.
* The more serious fault is that the curves may evolve trivial loops;
* that is, a single meridian or longitude will have several components,
* one of which is the correct curve while the others are homotopically
* trivial loops. Such trivial loops introduce erroneous multiples
* of 2pi into the computed holonomies, and thereby foul up the
* computation of hyperbolic structures.
*
* The function tidy_peripheral_curves()
*
* (1) makes a copy of the existing peripheral curves,
* (2) calls peripheral_curves() to create a nice set of
* peripheral curves, and
* (3) expresses the original curves as linear combinations
* of the nice curves.
*
* The result is an "efficient" set of curves, with no trivial
* loops.
*/
#include "kernel.h"
/*
* scratch_curves[0] will store the original peripheral curves.
* scratch_curves[1] will store the nice peripheral curves.
*/
#define original_curves 0
#define nice_curves 1
static void compute_new_curves(Triangulation *manifold);
void tidy_peripheral_curves(
Triangulation *manifold)
{
/*
* Copy the original peripheral curves to the
* scratch_curve[original_curves] fields of the Tetrahedra.
*/
copy_curves_to_scratch(manifold, original_curves, TRUE);
/*
* Compute a nice set of peripheral curves.
*/
peripheral_curves(manifold);
/*
* Copy the nice peripheral curves to the
* scratch_curve[nice_curves] fields of the Tetrahedra.
*/
copy_curves_to_scratch(manifold, nice_curves, FALSE);
/*
* Compute the intersection numbers of the original curves
* with the nice curves.
*/
compute_intersection_numbers(manifold);
/*
* Compute the new curves as linear combinations of the
* nice curves.
*/
compute_new_curves(manifold);
}
static void compute_new_curves(
Triangulation *manifold)
{
Tetrahedron *tet;
int h,
i,
j,
k;
for (tet = manifold->tet_list_begin.next;
tet != &manifold->tet_list_end;
tet = tet->next)
for (h = 0; h < 2; h++) /* which curve */
for (i = 0; i < 2; i++) /* which sheet */
for (j = 0; j < 4; j++) /* which vertex */
for (k = 0; k < 4; k++) /* which side of that vertex */
tet->curve[h][i][j][k] =
(j == k) ?
0 :
- tet->cusp[j]->intersection_number[h][L]
* tet->scratch_curve[nice_curves][M][i][j][k]
+ tet->cusp[j]->intersection_number[h][M]
* tet->scratch_curve[nice_curves][L][i][j][k];
}
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