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/*
* identify_solution_type.c
*
* This file provides the function
*
* void identify_solution_type(Triangulation *manifold);
*
* which identifies the type of solution contained in the
* tet->shape[filled] structures of the Tetrahedra of Triangulation *manifold,
* and writes the result to manifold->solution_type[filled]. Possible
* values are given by the SolutionType enum (see SnapPea.h).
*
* Its subroutine
*
* Boolean solution_is_degenerate(Triangulation *manifold);
*
* Is also available within the kernel, so do_Dehn_filling() can tell
* whether it is converging towards a degenerate structure.
*/
#include "kernel.h"
/*
* A solution must have volume at least VOLUME_EPSILON to count
* as a positive volume solution. Otherwise the volume will be
* considered zero or negative.
*/
#define VOLUME_EPSILON 1e-2
/*
* DEGENERACY_EPSILON defines how close a tetrahedron shape must
* be to zero to count as zero. It is given in logarithmic form.
* E.g., if DEGENERACY_EPSILON is -6, then the tetrahedron shape
* (in rectangular form) must lie within a distance exp(-6) = 0.0024...
* of the origin.
*/
#define DEGENERACY_EPSILON -6
/*
* A solution is considered flat iff it's not degenerate and the
* argument of each edge parameter is within FLAT_EPSILON of 0.0 or PI.
*/
#define FLAT_EPSILON 1e-2
static Boolean solution_is_flat(Triangulation *manifold);
static Boolean solution_is_geometric(Triangulation *manifold);
void identify_solution_type(
Triangulation *manifold)
{
if (solution_is_degenerate(manifold))
{
manifold->solution_type[filled] = degenerate_solution;
return;
}
if (solution_is_flat(manifold))
{
manifold->solution_type[filled] = flat_solution;
return;
}
if (solution_is_geometric(manifold))
{
manifold->solution_type[filled] = geometric_solution;
return;
}
if (volume(manifold, NULL) > VOLUME_EPSILON)
{
manifold->solution_type[filled] = nongeometric_solution;
return;
}
manifold->solution_type[filled] = other_solution;
}
Boolean solution_is_degenerate(
Triangulation *manifold)
{
Tetrahedron *tet;
int i;
/*
* If any complex edge parameter of any Tetrahedron is
* close to zero, return TRUE. Otherwise return FALSE.
*
* Note that it's enough to check for shapes close to
* zero: if an edge parameter is close to one or infinity,
* then some other edge parameter of the same Tetrahedron
* will be close to zero.
*/
for (tet = manifold->tet_list_begin.next;
tet != &manifold->tet_list_end;
tet = tet->next)
for (i = 0; i < 3; i++)
if (tet->shape[filled]->cwl[ultimate][i].log.real < DEGENERACY_EPSILON)
return TRUE;
return FALSE;
}
static Boolean solution_is_flat(
Triangulation *manifold)
{
Tetrahedron *tet;
int i;
double the_angle;
/*
* If any edge parameter has angle more than FLAT_EPSILON away
* from 0.0 or PI, return FALSE. Otherwise, return TRUE.
*/
for (tet = manifold->tet_list_begin.next;
tet != &manifold->tet_list_end;
tet = tet->next)
for (i = 0; i < 3; i++)
{
the_angle = tet->shape[filled]->cwl[ultimate][i].log.imag;
if (fabs(the_angle) > FLAT_EPSILON
&& fabs(the_angle - PI) > FLAT_EPSILON)
return FALSE;
}
return TRUE;
}
static Boolean solution_is_geometric(
Triangulation *manifold)
{
Tetrahedron *tet;
/*
* If any edge parameter has argument less than minus FLAT_EPSILON
* or greater than PI + FLAT_EPSILON, return FALSE.
* Otherwise, return TRUE.
*
* This allows a solution with some flat tetrahedra to count as geometric.
* However, if all the tetrahedra were flat, the SolutionType would have
* been previously identified as flat_solution, and we wouldn't have
* gotten to this function.
*/
for (tet = manifold->tet_list_begin.next;
tet != &manifold->tet_list_end;
tet = tet->next)
if (tetrahedron_is_geometric(tet) == FALSE)
return FALSE;
return TRUE;
}
Boolean tetrahedron_is_geometric(
Tetrahedron *tet)
{
int i;
double the_angle;
/*
* See comments in solution_is_geometric() above.
*/
for (i = 0; i < 3; i++)
{
the_angle = tet->shape[filled]->cwl[ultimate][i].log.imag;
if (the_angle < - FLAT_EPSILON
|| the_angle > PI + FLAT_EPSILON)
return FALSE;
}
return TRUE;
}
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