/* Determine whether a side is in check
* @param si identifies the check tester
* @param side_in_check which side?
* @return true iff side_in_check is in check according to slice si
*/
boolean exctinction_all_piece_observation_tester_is_in_check(slice_index si,
Side side_attacked)
{
boolean result = false;
square const *bnp;
TraceFunctionEntry(__func__);
TraceFunctionParam("%u",si);
TraceEnumerator(Side,side_attacked,"");
TraceFunctionParamListEnd();
for (bnp = boardnum; *bnp; ++bnp)
if (TSTFLAG(being_solved.spec[*bnp],side_attacked))
{
replace_observation_target(*bnp);
if (is_square_observed(EVALUATE(check)))
{
result = true;
break;
}
}
TraceFunctionExit(__func__);
TraceFunctionResult("%u",result);
TraceFunctionResultEnd();
return result;
}
static Boolean would_create_negatively_oriented_tetrahedra(
Tetrahedron *tet0,
FaceIndex f0)
{
Permutation gluing;
Tetrahedron *tet1;
FaceIndex f1,
side0,
side1;
gluing = tet0->gluing[f0];
tet1 = tet0->neighbor[f0];
f1 = EVALUATE(gluing, f0);
/*
* tet0 and tet1 meet at a common 2-simplex. For each edge
* of that 2-simplex, add the incident dihedral angles of
* tet0 and tet1. If any such sum is greater than pi, then
* the two_to_three() move would create a negatively oriented
* Tetrahedron on that side, and we return TRUE. Otherwise
* no negatively oriented Tetrahedra will be created, and we
* return FALSE.
*
* Choose ANGLE_EPSILON to allow the creation of Tetrahedra which
* are just barely negatively oriented, but essentially flat.
*/
for (side0 = 0; side0 < 4; side0++)
{
if (side0 == f0)
continue;
side1 = EVALUATE(gluing, side0);
if (tet0->shape[complete]->cwl[ultimate][edge3_between_faces[f0][side0]].log.imag
+ tet1->shape[complete]->cwl[ultimate][edge3_between_faces[f1][side1]].log.imag
> PI + ANGLE_EPSILON)
return TRUE;
}
return FALSE;
}
static void find_mates(
PerimeterPiece *perimeter_anchor)
{
PerimeterPiece *pp;
Tetrahedron *nbr_tet;
Permutation gluing;
VertexIndex nbr_vertex;
FaceIndex nbr_face;
/*
* First tell the tetrahedra about the PerimeterPieces.
*/
pp = perimeter_anchor;
do
{
pp->tet->extra[pp->vertex].its_perimeter_piece[pp->face] = pp;
pp = pp->next;
}
while (pp != perimeter_anchor);
/*
* Now let each PerimeterPiece figure out who its mate is.
*/
pp = perimeter_anchor;
do
{
nbr_tet = pp->tet->neighbor[pp->face];
gluing = pp->tet->gluing[pp->face];
nbr_vertex = EVALUATE(gluing, pp->vertex);
nbr_face = EVALUATE(gluing, pp->face);
pp->mate = nbr_tet->extra[nbr_vertex].its_perimeter_piece[nbr_face];
pp->gluing_parity =
(pp->orientation == pp->mate->orientation) ==
(parity[gluing] == orientation_preserving) ?
orientation_preserving :
orientation_reversing;
pp = pp->next;
}
while (pp != perimeter_anchor);
}
static Real sum_of_tilts(
Tetrahedron *tet0,
FaceIndex f0)
{
Tetrahedron *tet1;
FaceIndex f1;
tet1 = tet0->neighbor[f0];
f1 = EVALUATE(tet0->gluing[f0], f0);
return ( tet0->tilt[f0] + tet1->tilt[f1] );
}
static boolean is_mover_supported(numecoup n)
{
boolean result;
TraceFunctionEntry(__func__);
TraceFunctionParamListEnd();
siblingply(trait[nbply]);
push_observation_target(move_generation_stack[n].departure);
result = is_square_observed(EVALUATE(observer));
finply();
TraceFunctionExit(__func__);
TraceFunctionResult("%u",result);
TraceFunctionResultEnd();
return result;
}
static boolean is_target_unguarded(numecoup n)
{
boolean result;
TraceFunctionEntry(__func__);
TraceFunctionParam("%u",n);
TraceFunctionParamListEnd();
siblingply(advers(trait[nbply]));
push_observation_target(move_generation_stack[n].capture);
result = !is_square_observed(EVALUATE(observer));
finply();
TraceFunctionExit(__func__);
TraceFunctionResult("%u",result);
TraceFunctionResultEnd();
return result;
}
static boolean is_mover_supported_recursive(void)
{
boolean result;
Flags const mask = BIT(trait[nbply])|BIT(Royal);
TraceFunctionEntry(__func__);
TraceFunctionParamListEnd();
TraceSquare(move_generation_stack[CURRMOVE_OF_PLY(nbply)].capture);
TraceEOL();
if (TSTFULLFLAGMASK(being_solved.spec[move_generation_stack[CURRMOVE_OF_PLY(nbply)].capture],mask))
result = true;
else
result = is_square_observed(EVALUATE(observation));
TraceFunctionExit(__func__);
TraceFunctionResult("%u",result);
TraceFunctionResultEnd();
return result;
}
static void PushMagicViewsByOnePiece(piece_walk_type pi_magic)
{
square const *pos_viewed;
TraceFunctionEntry(__func__);
TraceWalk(pi_magic);
TraceFunctionParamListEnd();
for (pos_viewed = boardnum; *pos_viewed; pos_viewed++)
if (get_walk_of_piece_on_square(*pos_viewed)>Invalid
&& !TSTFLAGMASK(being_solved.spec[*pos_viewed],BIT(Magic)|BIT(Royal))
&& !is_piece_neutral(being_solved.spec[*pos_viewed]))
{
replace_observation_target(*pos_viewed);
observing_walk[nbply] = pi_magic;
/* ignore return value - it's ==false */
fork_is_square_observed_nested_delegate(temporary_hack_is_square_observed_specific[trait[nbply]],
EVALUATE(observation));
}
TraceFunctionExit(__func__);
TraceFunctionResultEnd();
}
static boolean is_attacked_exactly_once(square sq_departure, Side trait_ply)
{
TraceFunctionEntry(__func__);
TraceFunctionParamListEnd();
assert(!are_we_counting);
are_we_counting = true;
amu_attack_count = 0;
single_attacker_departure = initsquare;
is_square_observed_general_post_move_iterator_solve(advers(trait_ply),
sq_departure,
EVALUATE(observation));
are_we_counting = false;
TraceFunctionExit(__func__);
TraceFunctionResult("%u",amu_attack_count==1);
TraceFunctionResultEnd();
return amu_attack_count==1;
}
static Boolean is_isometry_plausible(
Tetrahedron *initial_tet0,
Tetrahedron *initial_tet1,
Permutation initial_map)
{
/*
* To check whether an Isometry taking initial_tet0 to
* initial_tet1 via initial_map is even plausible, let's
* check whether their EdgeClass orders match up.
*/
int i,
j;
for (i = 0; i < 4; i++)
for (j = i + 1; j < 4; j++)
{
if (initial_tet0->edge_class[edge_between_vertices[i][j]]->order
!= initial_tet1->edge_class[edge_between_vertices[EVALUATE(initial_map, i)]
[EVALUATE(initial_map, j)]]->order)
return FALSE;
if (initial_tet0->edge_class[edge_between_vertices[i][j]]->is_singular
!= initial_tet1->edge_class[edge_between_vertices[EVALUATE(initial_map, i)]
[EVALUATE(initial_map, j)]]->is_singular)
return FALSE;
if (initial_tet0->edge_class[edge_between_vertices[i][j]]->is_singular &&
initial_tet0->edge_class[edge_between_vertices[i][j]]->singular_order !=
initial_tet1->edge_class[edge_between_vertices[EVALUATE(initial_map, i)]
[EVALUATE(initial_map, j)]]->singular_order)
return FALSE;
}
return TRUE;
}
static FuncResult attempt_isometry(
Triangulation *manifold0,
Tetrahedron *initial_tet0,
Tetrahedron *initial_tet1,
Permutation initial_map,
int *singular_map )
{
Tetrahedron *tet0,
*tet1,
*nbr0,
*nbr1,
**queue;
EdgeClass *edge0,
*edge1;
int first,
last,
i,
j;
FaceIndex face0,
face1;
Permutation gluing0,
gluing1,
nbr0_map;
/*
* initial_tet1 and initial_map are arbitrary, so
* the vast majority of calls to attempt_isometry()
* will fail. Therefore it's worth including a quick
* plausibility check at the beginning, to make the
* algorithm run faster.
*/
if (is_isometry_plausible(initial_tet0, initial_tet1, initial_map) == FALSE)
return func_failed;
/*
* Initialize all the image fields of manifold0
* to NULL to show they haven't been set.
*/
for ( tet0 = manifold0->tet_list_begin.next;
tet0 != &manifold0->tet_list_end;
tet0 = tet0->next)
tet0->image = NULL;
/*
* Allocate space for a queue which is large enough
* to hold pointers to all the Tetrahedra in manifold0.
*/
queue = NEW_ARRAY(manifold0->num_tetrahedra, Tetrahedron *);
/*
* At all times, the Tetrahedra on the queue will be those which
*
* (1) have set their image and map fields, but
*
* (2) have not checked their neighbors.
*/
/*
* Set the image and map fields for initial_tet0.
*/
initial_tet0->image = initial_tet1;
initial_tet0->map = initial_map;
/*
* Put initial_tet0 on the queue.
*/
first = 0;
last = 0;
queue[first] = initial_tet0;
/*
* While there are Tetrahedra on the queue . . .
*/
while (last >= first)
{
/*
* Pull the first Tetrahedron off the queue and call it tet0.
*/
tet0 = queue[first++];
/*
* tet0 maps to some Tetrahedron tet1 in manifold1.
*/
tet1 = tet0->image;
/* we will keep track on how the singular edges in manifold0 map into manifold1 */
for(i=0;i<4;i++)
for(j=i+1;j<4;j++)
{
edge0 = tet0->edge_class[edge_between_vertices[i][j]];
edge1 = tet1->edge_class[edge_between_vertices[EVALUATE(tet0->map, i)]
[EVALUATE(tet0->map, j)]];
if (edge0->order != edge1->order )
{
my_free(queue);
return func_failed;
}
if (edge0->is_singular != edge1->is_singular )
{
my_free(queue);
return func_failed;
}
if (edge0->is_singular && edge0->singular_order != edge1->singular_order )
{
my_free(queue);
return func_failed;
}
if (singular_map != NULL && edge0->is_singular )
singular_map[edge0->singular_index] = edge1->singular_index;
}
/*
* For each face of tet0 . . .
*/
for (face0 = 0; face0 < 4; face0++)
{
/*
* Let nbr0 be the Tetrahedron which meets tet0 at face0.
*/
nbr0 = tet0->neighbor[face0];
/*
* tet0->map takes face0 of tet0 to face1 of tet1.
*/
face1 = EVALUATE(tet0->map, face0);
/*
* Let nbr1 be the Tetrahedron which meets tet1 at face1.
*/
nbr1 = tet1->neighbor[face1];
/*
* Let gluing0 be the gluing which identifies face0 of
* tet0 to nbr0, and similarly for gluing1.
*/
gluing0 = tet0->gluing[face0];
gluing1 = tet1->gluing[face1];
/*
* gluing0
* tet0 ------> nbr0
* | |
* tet0->map | | nbr0->map
* | |
* V gluing1 V
* tet1 ------> nbr1
*
* We want to ensure that tet1 and nbr1 enjoy the same
* relationship to each other in manifold1 that tet0 and
* nbr0 do in manifold0. The conditions
*
* nbr0->image == nbr1
* and
* nbr0->map == gluing1 o tet0->map o gluing0^-1
*
* are necessary and sufficient to insure that we have a
* combinatorial equivalence between the Triangulations.
* (The proof relies on the fact that we've already checked
* (near the beginning of compute_cusped_isometries() above)
* that the Triangulations have the same number of Tetrahedra;
* otherwise one Triangulation could be a (possibly branched)
* covering of the other.)
*/
/*
* Compute the required value for nbr0->map.
*/
nbr0_map = compose_permutations(
compose_permutations(
gluing1,
tet0->map
),
inverse_permutation[gluing0]
);
/*
* If nbr0->image and nbr0->map have already been set,
* check that they satisfy the above conditions.
*/
if (nbr0->image != NULL)
{
if (nbr0->image != nbr1 || nbr0->map != nbr0_map)
{
/*
* This isn't an isometry.
*/
my_free(queue);
return func_failed;
}
}
/*
* else . . .
* nbr0->image and nbr0->map haven't been set.
* Set them, and put nbr0 on the queue.
*/
else
{
if (!is_isometry_plausible(nbr0,nbr1,nbr0_map))
{
my_free(queue);
return func_failed;
}
nbr0->image = nbr1;
nbr0->map = nbr0_map;
queue[++last] = nbr0;
}
}
}
/*
* A quick error check.
* Is it plausible that each Tetrahedron
* has been on the queue exactly once?
*/
if (first != manifold0->num_tetrahedra
|| last != manifold0->num_tetrahedra - 1)
uFatalError("attempt_isometry", "isometry");
/*
* Free the queue, and report success.
*/
my_free(queue);
return func_OK;
}
int gss(double a, double b, double *_min, double *_fmin,
gss_evaluate_t proc_evaluate, gss_progress_t proc_progress,
void* instance, const gss_parameter_t *_param) {
double c, d, min = NAN;
double fa, fb, fc, fd, fmin = INFINITY;
int k = 0;
int retval;
unsigned short int successful = 1;
gss_parameter_t param = _param ? (*_param) : _defparam;
gss_i_warning_flag = 0;
if (a > b) {
c = a; a = b; b = c;
}
c = a + RESPHI*(b-a);
EVALUATE(a, fa);
EVALUATE(b, fb);
EVALUATE(c, fc);
if (fc >= fa || fc >= fb) {
if (param.on_error == GSS_ERROR_STOP) {
return PLFIT_FAILURE;
} else {
gss_i_warning_flag = 1;
}
}
while (fabs(a-b) > param.epsilon) {
k++;
d = c + RESPHI*(b-c);
EVALUATE(d, fd);
if (fd >= fa || fd >= fb) {
if (param.on_error == GSS_ERROR_STOP) {
successful = 0;
break;
} else {
gss_i_warning_flag = 1;
}
}
if (fc <= fd) {
b = a; a = d;
} else {
a = c; c = d; fc = fd;
}
}
if (successful) {
c = (a+b) / 2.0;
k++;
EVALUATE(c, fc);
TERMINATE;
}
return successful ? PLFIT_SUCCESS : PLFIT_FAILURE;
}
static void renumber_neighbors_and_gluings(
Tetrahedron *tet)
{
Tetrahedron *temp_neighbor;
Permutation temp_gluing;
int i,
j,
d[4],
temp_digit;
Tetrahedron *nbr_tet;
/*
* Renumbering the neighbors is easy: we simply swap
* neighbor[2] and neighbor[3].
*/
temp_neighbor = tet->neighbor[2];
tet->neighbor[2] = tet->neighbor[3];
tet->neighbor[3] = temp_neighbor;
/*
* Renumbering the gluings is trickier, because three
* changes are required:
*
* Change A: Swap gluing[2] and gluing[3].
*
* Change B: Within each gluing of tet, swap the image of
* vertex 2 and the image of vertex 3, e.g. 0312 -> 3012.
*
* Change C: For each gluing of a face (typically of a Tetrahedron
* other than tet) that glues to tet, interchange
* 2 and 3, e.g. 0312 -> 0213.
*/
/*
* Change A: Swap gluing[2] and gluing[3].
*/
temp_gluing = tet->gluing[2];
tet->gluing[2] = tet->gluing[3];
tet->gluing[3] = temp_gluing;
/*
* Changes B and C are carried out for each of the four gluings of tet.
*/
for (i = 0; i < 4; i++)
{
/*
* Change B: Swap the image of vertex 2 and the image of vertex 3.
*/
/*
* Unpack the digits of the gluing.
*/
for (j = 0; j < 4; j++)
{
d[j] = tet->gluing[i] & 0x3;
tet->gluing[i] >>= 2;
}
/*
* Swap the digits in positions 2 and 3.
*/
temp_digit = d[3];
d[3] = d[2];
d[2] = temp_digit;
/*
* Repack the digits.
*/
for (j = 4; --j >= 0; )
{
tet->gluing[i] <<= 2;
tet->gluing[i] += d[j];
}
/*
* Change C: Fix up the inverse of tet->gluing[i].
*
* If tet->neighbor[i] != tet, we simply write the inverse of
* tet->gluing[i] into the appropriate gluing field of the neighbor.
*
* If tet->neighbor[i] == tet, the simple approach doesn't work
* because of the messy interaction between Changes B and C.
* Instead, we exploit the fact that tet->gluing[i] is the inverse
* of some other gluing of tet, and apply Change C directly to
* tet->gluing[i] rather than its inverse.
*/
nbr_tet = tet->neighbor[i];
if (nbr_tet != tet)
/*
* Write the inverse directly.
*/
nbr_tet->gluing[EVALUATE(tet->gluing[i],i)] = inverse_permutation[tet->gluing[i]];
else
{
/*
* Perform Change C on tet->gluing[i].
*/
/*
* Unpack the digits.
*/
for (j = 0; j < 4; j++)
{
d[j] = tet->gluing[i] & 0x3;
tet->gluing[i] >>= 2;
}
/*
* Swap 2 and 3 in the images.
*/
for (j = 0; j < 4; j++)
switch (d[j])
{
case 0:
case 1:
/* leave d[j] alone */
break;
case 2:
d[j] = 3;
break;
case 3:
d[j] = 2;
break;
}
/*
* Repack the digits.
*/
for (j = 4; --j >= 0; )
{
tet->gluing[i] <<= 2;
tet->gluing[i] += d[j];
}
}
}
}
static void visit_tetrahedra(
Triangulation *manifold,
Boolean compute_corners,
Boolean centroid_at_origin)
{
Tetrahedron **queue,
*tet;
int queue_first,
queue_last;
Tetrahedron *nbr_tet;
Permutation gluing;
FaceIndex face,
nbr_face;
int i;
VertexIndex nbr_i;
/*
* choose_generators() has already called initialize_flags().
*/
/*
* Initialize num_generators to zero.
*/
manifold->num_generators = 0;
/*
* Allocate space for a queue of pointers to the Tetrahedra.
* Each Tetrahedron will appear on the queue exactly once,
* so an array of length manifold->num_tetrahedra will be just right.
*/
queue = NEW_ARRAY(manifold->num_tetrahedra, Tetrahedron *);
/*
* Initialize the queue.
*/
queue_first = 0;
queue_last = 0;
/*
* Choose the initial Tetrahedron according to some criterion.
* If compute_corners is TRUE, position its corners.
* 2000/4/2 The choice of initial tetrahedron is independent
* of compute_corners.
*/
initial_tetrahedron(manifold, &queue[0], compute_corners, centroid_at_origin);
/*
* Mark the initial Tetrahedron as visited.
*/
queue[0]->generator_path = -1;
queue[0]->flag = right_handed;
/*
* Start processing the queue.
*/
do
{
/*
* Pull a Tetrahedron off the front of the queue.
*/
tet = queue[queue_first++];
/*
* Look at the four neighboring Tetrahedra.
*/
for (face = 0; face < 4; face++)
{
/*
* Note who the neighbor is, and which of
* its faces we're glued to.
*/
nbr_tet = tet->neighbor[face];
gluing = tet->gluing[face];
nbr_face = EVALUATE(gluing, face);
/*
* If nbr_tet hasn't been visited, set the appropriate
* generator_statuses to not_a_generator, and then put
* nbr_tet on the back of the queue.
*/
if (nbr_tet->flag == unknown_orientation)
{
tet ->generator_status[face] = not_a_generator;
nbr_tet->generator_status[nbr_face] = not_a_generator;
tet ->generator_index[face] = -1; /* garbage value */
nbr_tet->generator_index[nbr_face] = -1;
nbr_tet->generator_path = nbr_face;
nbr_tet->flag = (parity[gluing] == orientation_preserving) ?
tet->flag :
! tet->flag;
if (compute_corners)
{
for (i = 0; i < 4; i++)
{
if (i == face)
continue;
nbr_i = EVALUATE(gluing, i);
nbr_tet->corner[nbr_i] = tet->corner[i];
}
compute_fourth_corner(
nbr_tet->corner, /* array of corner coordinates */
nbr_face, /* the corner to be computed */
nbr_tet->flag, /* nbr_tet's current orientation */
nbr_tet->shape[filled]->cwl[ultimate]); /* shapes */
}
queue[++queue_last] = nbr_tet;
}
/*
* If nbr_tet has been visited, check whether a generator
* has been assigned to common face, and if not, assign one.
*/
else if (tet->generator_status[face] == unassigned_generator)
{
tet ->generator_status[face] = outbound_generator;
nbr_tet->generator_status[nbr_face] = inbound_generator;
tet ->generator_index[face] = manifold->num_generators;
nbr_tet->generator_index[nbr_face] = manifold->num_generators;
tet ->generator_parity[face] =
nbr_tet->generator_parity[nbr_face] = ((parity[gluing] == orientation_preserving)
== (tet->flag == nbr_tet->flag)) ?
orientation_preserving :
orientation_reversing;
manifold->num_generators++;
}
}
}
while (queue_first <= queue_last);
/*
* Free the memory used for the queue.
*/
my_free(queue);
/*
* An "unnecessary" (but quick) error check.
*/
if ( queue_first != manifold->num_tetrahedra
|| queue_last != manifold->num_tetrahedra - 1)
uFatalError("visit_tetrahedra", "choose_generators");
}
static void compute_singular_action(
Triangulation *manifold,
Isometry *isometry)
{
Boolean lower_index_is_at_top;
EdgeIndex index, image_index;
VertexIndex image_v1,image_v2,v1,v2;
Tetrahedron *tet, *image_tet;
EdgeClass *edge, *image_edge;
PositionedTet ptet, ptet0;
for( edge = manifold->edge_list_begin.next;
edge!=&manifold->edge_list_end;
edge = edge->next )
if (edge->is_singular)
{
if (edge->singular_index<0)
uFatalError("compute_singular_action","isometry_cusped");
tet = edge->incident_tet;
index = edge->incident_edge_index;
v1 = MIN(one_vertex_at_edge[index], other_vertex_at_edge[index]);
v2 = MAX(one_vertex_at_edge[index], other_vertex_at_edge[index]);
image_tet = tet->image;
image_v1 = EVALUATE(tet->map,v1);
image_v2 = EVALUATE(tet->map,v2);
image_index = edge_between_vertices[image_v1][image_v2];
image_edge = image_tet->edge_class[image_index];
if (image_edge->singular_index<0 || image_edge->singular_order != edge->singular_order )
uFatalError("compute_singular_action","isometry_cusped");
/* i have never kept track of a direction only the singular edges. prehaps this is something i should be doing...
* for now, here is how we'll kept track of orientation of these maps from singular edge to singular edge:
* each edge has an incident tet and an incident edge index, define an ordering on the ends of the singular
* edge by the ordering of the vertex indices of this edge.
*
* there may be some clever way of doing this with the handedness of the edge classes. i am not sure.
*/
set_left_edge( image_edge, &ptet0 );
ptet = ptet0;
lower_index_is_at_top = ( ptet.bottom_face < ptet.right_face );
isometry->singular_image[edge->singular_index] = 0;
do{
if (ptet.tet == image_tet && edge_between_faces[ptet.near_face][ptet.left_face] == image_index)
{
if (lower_index_is_at_top)
{
if (image_v1 == ptet.bottom_face)
isometry->singular_image[edge->singular_index] = image_edge->singular_index + 1;
else isometry->singular_image[edge->singular_index] = -(image_edge->singular_index + 1);
}
else
{
if (image_v1 == ptet.bottom_face)
isometry->singular_image[edge->singular_index] = -(image_edge->singular_index + 1);
else isometry->singular_image[edge->singular_index] = image_edge->singular_index + 1;
}
break;
}
veer_left( &ptet );
}while(!same_positioned_tet( &ptet0, &ptet ));
if (isometry->singular_image[edge->singular_index] == 0)
uFatalError("compute_singular_action","isometry_cusped");
}
}
static void expand_perimeter(
PerimeterPiece *perimeter_anchor)
{
int num_unchecked_pieces;
PerimeterPiece *pp,
*new_piece;
Permutation gluing;
Tetrahedron *nbr_tet;
VertexIndex nbr_vertex;
FaceIndex nbr_back_face,
nbr_left_face,
nbr_right_face;
Orientation nbr_orientation;
for (num_unchecked_pieces = 3, pp = perimeter_anchor;
num_unchecked_pieces;
pp = pp->next)
if (pp->checked == FALSE)
{
gluing = pp->tet->gluing[pp->face];
nbr_tet = pp->tet->neighbor[pp->face];
nbr_vertex = EVALUATE(gluing, pp->vertex);
if (nbr_tet->extra[nbr_vertex].visited)
{
pp->checked = TRUE;
num_unchecked_pieces--;
}
else
{
/*
* Extend the tree to the neighboring vertex.
*/
nbr_back_face = EVALUATE(gluing, pp->face);
if (parity[gluing] == orientation_preserving)
nbr_orientation = pp->orientation;
else
nbr_orientation = ! pp->orientation;
if (nbr_orientation == right_handed)
{
nbr_left_face = remaining_face[nbr_vertex][nbr_back_face];
nbr_right_face = remaining_face[nbr_back_face][nbr_vertex];
}
else
{
nbr_left_face = remaining_face[nbr_back_face][nbr_vertex];
nbr_right_face = remaining_face[nbr_vertex][nbr_back_face];
}
nbr_tet->extra[nbr_vertex].visited = TRUE;
nbr_tet->extra[nbr_vertex].parent_tet = pp->tet;
nbr_tet->extra[nbr_vertex].parent_vertex = pp->vertex;
nbr_tet->extra[nbr_vertex].this_faces_parent = nbr_back_face;
nbr_tet->extra[nbr_vertex].parent_faces_this = pp->face;
nbr_tet->extra[nbr_vertex].orientation = nbr_orientation;
/*
* Extend the perimeter across the neighboring
* vertex. The new PerimeterPiece is added on
* the right side of the old one, so that the
* pp = pp->next step in the loop moves us past
* both the old and new perimeter pieces. This
* causes the perimeter to expand uniformly in
* all directions.
*/
new_piece = NEW_STRUCT(PerimeterPiece);
new_piece->tet = nbr_tet;
new_piece->vertex = nbr_vertex;
new_piece->face = nbr_right_face;
new_piece->orientation = nbr_orientation;
new_piece->checked = FALSE;
new_piece->next = pp;
new_piece->prev = pp->prev;
pp->prev->next = new_piece;
pp->tet = nbr_tet;
pp->vertex = nbr_vertex;
pp->face = nbr_left_face;
pp->orientation = nbr_orientation;
pp->checked = FALSE; /* unchanged */
pp->next = pp->next; /* unchanged */
pp->prev = new_piece;
/*
* Increment the count of unchecked pieces.
*/
num_unchecked_pieces++;
}
}
}
static void drill_tube(
Triangulation *manifold,
Tetrahedron *tet,
EdgeIndex e,
Boolean creating_new_cusp)
{
/*
* Insert a triangular-pillow-with-tunnel (as described at the top
* of this file) so as to connect the boundary component at one
* end of the given edge to the boundary component at the other end.
* The orientation on the triangular pillow will match the
* orientation on tet, so that the orientation on the manifold
* (if there is one) will be preserved. Edge orientations are also
* respected.
*/
VertexIndex v0,
v1,
v2,
vv0,
vv1,
vv2;
FaceIndex f,
ff;
Tetrahedron *nbr_tet,
*new_tet0,
*new_tet1;
Permutation gluing;
EdgeClass *edge0,
*edge1,
*edge2,
*new_edge;
Orientation edge_orientation0,
edge_orientation1,
edge_orientation2;
PeripheralCurve c;
Orientation h;
int num_strands,
intersection_number[2],
the_gcd;
Cusp *unique_cusp;
MatrixInt22 basis_change[1];
/*
* Relative to the orientation of tet, the vertices v0, v1 and v2
* are arranged in counterclockwise order around the face f.
*/
v0 = one_vertex_at_edge[e];
v1 = other_vertex_at_edge[e];
v2 = remaining_face[v1][v0];
f = remaining_face[v0][v1];
/*
* Note the matching face and its vertices.
*/
nbr_tet = tet->neighbor[f];
gluing = tet->gluing[f];
ff = EVALUATE(gluing, f);
vv0 = EVALUATE(gluing, v0);
vv1 = EVALUATE(gluing, v1);
vv2 = EVALUATE(gluing, v2);
/*
* Note the incident EdgeClasses (which may or may not be distinct).
*/
edge0 = tet->edge_class[e];
edge1 = tet->edge_class[edge_between_vertices[v1][v2]];
edge2 = tet->edge_class[edge_between_vertices[v2][v0]];
/*
* Construct the triangular-pillow-with-tunnel, as described
* at the top of this file.
*/
new_tet0 = NEW_STRUCT(Tetrahedron);
new_tet1 = NEW_STRUCT(Tetrahedron);
initialize_tetrahedron(new_tet0);
initialize_tetrahedron(new_tet1);
INSERT_BEFORE(new_tet0, &manifold->tet_list_end);
INSERT_BEFORE(new_tet1, &manifold->tet_list_end);
manifold->num_tetrahedra += 2;
new_edge = NEW_STRUCT(EdgeClass);
initialize_edge_class(new_edge);
INSERT_BEFORE(new_edge, &manifold->edge_list_end);
new_tet0->neighbor[0] = new_tet1;
new_tet0->neighbor[1] = NULL; /* assigned below */
new_tet0->neighbor[2] = NULL; /* assigned below */
new_tet0->neighbor[3] = new_tet1;
new_tet1->neighbor[0] = new_tet0;
new_tet1->neighbor[1] = new_tet1;
new_tet1->neighbor[2] = new_tet1;
new_tet1->neighbor[3] = new_tet0;
new_tet0->gluing[0] = CREATE_PERMUTATION(0, 0, 1, 2, 2, 1, 3, 3);
new_tet0->gluing[1] = 0x00; /* assigned below */
new_tet0->gluing[2] = 0x00; /* assigned below */
new_tet0->gluing[3] = CREATE_PERMUTATION(0, 1, 1, 0, 2, 2, 3, 3);
new_tet1->gluing[0] = CREATE_PERMUTATION(0, 0, 1, 2, 2, 1, 3, 3);
new_tet1->gluing[1] = CREATE_PERMUTATION(0, 0, 1, 2, 2, 1, 3, 3);
new_tet1->gluing[2] = CREATE_PERMUTATION(0, 0, 1, 2, 2, 1, 3, 3);
new_tet1->gluing[3] = CREATE_PERMUTATION(0, 1, 1, 0, 2, 2, 3, 3);
new_tet0->edge_class[0] = edge1;
new_tet0->edge_class[1] = edge1;
new_tet0->edge_class[2] = edge0;
new_tet0->edge_class[3] = edge2;
new_tet0->edge_class[4] = edge0;
new_tet0->edge_class[5] = edge0;
new_tet1->edge_class[0] = edge1;
new_tet1->edge_class[1] = edge1;
new_tet1->edge_class[2] = edge0;
new_tet1->edge_class[3] = new_edge;
new_tet1->edge_class[4] = edge0;
new_tet1->edge_class[5] = edge0;
edge0->order += 6;
edge1->order += 4;
edge2->order += 1;
new_edge->order = 1;
new_edge->incident_tet = new_tet1;
new_edge->incident_edge_index = 3;
edge_orientation0 = tet->edge_orientation[e];
edge_orientation1 = tet->edge_orientation[edge_between_vertices[v1][v2]];
edge_orientation2 = tet->edge_orientation[edge_between_vertices[v2][v0]];
new_tet0->edge_orientation[0] = edge_orientation1;
new_tet0->edge_orientation[1] = edge_orientation1;
new_tet0->edge_orientation[2] = edge_orientation0;
new_tet0->edge_orientation[3] = edge_orientation2;
new_tet0->edge_orientation[4] = edge_orientation0;
new_tet0->edge_orientation[5] = edge_orientation0;
new_tet1->edge_orientation[0] = edge_orientation1;
new_tet1->edge_orientation[1] = edge_orientation1;
new_tet1->edge_orientation[2] = edge_orientation0;
new_tet1->edge_orientation[3] = right_handed;
new_tet1->edge_orientation[4] = edge_orientation0;
new_tet1->edge_orientation[5] = edge_orientation0;
new_tet0->cusp[0] = tet->cusp[v0];
new_tet0->cusp[1] = tet->cusp[v0];
new_tet0->cusp[2] = tet->cusp[v0];
new_tet0->cusp[3] = tet->cusp[v2];
new_tet1->cusp[0] = tet->cusp[v0];
new_tet1->cusp[1] = tet->cusp[v0];
new_tet1->cusp[2] = tet->cusp[v0];
new_tet1->cusp[3] = tet->cusp[v2];
/*
* Install the triangular-pillow-with-tunnel.
*/
tet->neighbor[f] = new_tet0;
tet->gluing[f] = CREATE_PERMUTATION(f, 2, v0, 0, v1, 1, v2, 3);
new_tet0->neighbor[2] = tet;
new_tet0->gluing[2] = inverse_permutation[tet->gluing[f]];
nbr_tet->neighbor[ff] = new_tet0;
nbr_tet->gluing[ff] = CREATE_PERMUTATION(ff, 1, vv0, 0, vv1, 2, vv2, 3);
new_tet0->neighbor[1] = nbr_tet;
new_tet0->gluing[1] = inverse_permutation[nbr_tet->gluing[ff]];
/*
* Typically creating_new_cusp is FALSE, meaning that we are
* connecting a spherical boundary component to a torus or
* Klein bottle boundary component, and we simply extend the
* existing peripheral curves across the new tetrahedra.
*
* In the exceptional case that creating_new_cusp is TRUE,
* meaning that the manifold has no real cusps and we are
* connecting the "special fake cusp" to itself, we must
* install a meridian and longitude, and set up the Dehn filling.
*/
if (creating_new_cusp == FALSE)
{
/*
* Extend the peripheral curves across the boundary of the
* triangular-pillow-with-tunnel.
*
* Note: The orientations of new_tet0 and new_tet1 match that
* of tet, so the right_handed and left_handed sheets match up
* in the obvious way.
*/
for (c = 0; c < 2; c++) /* c = M, L */
for (h = 0; h < 2; h++) /* h = right_handed, left_handed */
{
num_strands = tet->curve[c][h][v0][f];
new_tet0->curve[c][h][0][2] = -num_strands;
new_tet0->curve[c][h][0][1] = +num_strands;
num_strands = tet->curve[c][h][v1][f];
new_tet0->curve[c][h][1][2] = -num_strands;
new_tet0->curve[c][h][1][0] = +num_strands;
new_tet1->curve[c][h][2][0] = -num_strands;
new_tet1->curve[c][h][2][1] = +num_strands;
new_tet1->curve[c][h][1][2] = -num_strands;
new_tet1->curve[c][h][1][0] = +num_strands;
new_tet0->curve[c][h][2][0] = -num_strands;
new_tet0->curve[c][h][2][1] = +num_strands;
num_strands = tet->curve[c][h][v2][f];
new_tet0->curve[c][h][3][2] = -num_strands;
new_tet0->curve[c][h][3][1] = +num_strands;
}
}
else /* creating_new_cusp == TRUE */
{
/*
* We have just installed a tube connecting the (unique)
* spherical "cusp" to itself, to convert it to a torus or
* Klein bottle.
*/
unique_cusp = tet->cusp[v0]->matching_cusp;
unique_cusp->is_complete = TRUE; /* to be filled below */
unique_cusp->index = 0;
unique_cusp->is_finite = FALSE;
manifold->num_cusps = 1;
/*
* Install an arbitrary meridian and longitude.
*/
peripheral_curves(manifold);
count_cusps(manifold);
/*
* Two sides of the (truncated) vertex 0 of new_tet0
* (namely the sides incident to faces 1 and 2 of new_tet0)
* define the Dehn filling curve by which we can recover
* the closed manifold. Count how many times the newly
* installed meridian and longitude cross this Dehn filling curve.
* To avoid messy questions about which sheet of the cusp's
* double cover we're on, use two (parallel) copies of the
* Dehn filling curve, one on each sheet of the cover.
* Ultimately we're looking for a linear combination of the
* meridian and longitude whose intersection number with
* the Dehn filling curve is zero, so it won't matter if
* we're off by a factor of two.
*/
for (c = 0; c < 2; c++) /* c = M, L */
{
intersection_number[c] = 0;
for (h = 0; h < 2; h++) /* h = right_handed, left_handed */
{
intersection_number[c] += new_tet0->curve[c][h][0][1];
intersection_number[c] += new_tet0->curve[c][h][0][2];
}
}
/*
* Use the intersection numbers to deduce
* the desired Dehn filling coefficients.
*/
the_gcd = gcd(intersection_number[M], intersection_number[L]);
unique_cusp->is_complete = FALSE;
unique_cusp->m = -intersection_number[L] / the_gcd;
unique_cusp->l = +intersection_number[M] / the_gcd;
/*
* Switch to a basis in which the Dehn filling curve is a meridian.
*/
unique_cusp->cusp_shape[initial] = Zero; /* force current_curve_basis() to ignore the cusp shape */
current_curve_basis(manifold, unique_cusp->index, basis_change[0]);
if (change_peripheral_curves(manifold, basis_change) != func_OK)
uFatalError("drill_tube", "finite_vertices");
}
}
static void kill_the_incident_generator(
Triangulation *manifold,
EdgeClass *edge)
{
PositionedTet ptet,
ptet0;
int dead_index;
Tetrahedron *tet,
*nbr_tet;
Permutation gluing;
FaceIndex face,
nbr_face;
/*
* The EdgeClass edge is incident to a unique generator.
* Find it.
*/
set_left_edge(edge, &ptet0);
ptet = ptet0;
while (TRUE)
{
/*
* If we've found the active generator,
* break out of the while loop. Otherwise . . .
*/
if (ptet.tet->generator_status[ptet.near_face] != not_a_generator)
break;
/*
* . . . move on to the next Tetrahedron incident to the EdgeClass.
*/
veer_left(&ptet);
/*
* If we've come all the way around the EdgeClass without
* finding a generator, something has gone terribly wrong.
*/
if (same_positioned_tet(&ptet, &ptet0))
uFatalError("kill_the_incident_generator", "choose_generators");
}
/*
* Note the index of the about to be killed generator . . .
*/
dead_index = ptet.tet->generator_index[ptet.near_face];
/*
* . . . then kill it.
*/
nbr_tet = ptet.tet->neighbor[ptet.near_face];
gluing = ptet.tet->gluing[ptet.near_face];
nbr_face = EVALUATE(gluing, ptet.near_face);
ptet.tet->generator_status[ptet.near_face] = not_a_generator;
nbr_tet ->generator_status[nbr_face] = not_a_generator;
ptet.tet->generator_index[ptet.near_face] = -1; /* garbage value */
nbr_tet ->generator_index[nbr_face] = -1;
/*
* The EdgeClass no longer represents an active relation.
*/
edge->active_relation = FALSE;
/*
* Decrement the num_incident_generators count at each of
* the incident EdgeClasses.
*/
ptet.tet->edge_class[edge_between_faces[ptet.near_face][ptet.left_face] ]->num_incident_generators--;
ptet.tet->edge_class[edge_between_faces[ptet.near_face][ptet.right_face] ]->num_incident_generators--;
ptet.tet->edge_class[edge_between_faces[ptet.near_face][ptet.bottom_face]]->num_incident_generators--;
/*
* Decrement *number_of_generators.
*/
manifold->num_generators--;
/*
* If dead_index was not the highest numbered generator, then removing
* it will have left a gap in the numbering scheme. Renumber the highest
* numbered generator to keep the numbering contiguous.
*/
if (dead_index != manifold->num_generators)
{
for (tet = manifold->tet_list_begin.next;
tet != &manifold->tet_list_end;
tet = tet->next)
for (face = 0; face < 4; face++)
if (tet->generator_index[face] == manifold->num_generators)
{
if (tet->generator_status[face] == not_a_generator)
uFatalError("kill_the_incident_generator", "choose_generators");
nbr_tet = tet->neighbor[face];
gluing = tet->gluing[face];
nbr_face = EVALUATE(gluing, face);
tet ->generator_index[face] = dead_index;
nbr_tet->generator_index[nbr_face] = dead_index;
/*
* Rather than worrying about breaking out of a
* double loop, let's just return from here.
*/
return;
}
/*
* The program should return from within the above double loop.
*/
uFatalError("kill_the_incident_generator", "choose_generators");
}
else /* dead_index == manifold->num_generators, so nothing else to do */
return;
}
static void compute_cusp_map(
Triangulation *manifold0,
Triangulation *manifold1,
Isometry *isometry)
{
Tetrahedron *tet;
VertexIndex v;
int i;
/*
* Copy the manifold1's peripheral curves into
* scratch_curves[0], and copy the images of manifold0's
* peripheral curves into scratch_curves[1].
*
* When the manifold is orientable and the Isometry is
* orientation-reversing, and sometimes when the manifold
* is nonorientable, the images of the peripheral curves
* of a torus will lie on the "wrong" sheet of the Cusp's
* orientation double cover. (See peripheral_curves.c for
* background material.) Therefore we copy the images of
* the peripheral curves of torus cusps to both sheets of
* the orientation double cover, to guarantee that the
* intersection numbers come out right.
*/
copy_curves_to_scratch(manifold1, 0, FALSE);
copy_images_to_scratch(manifold0, 1, TRUE);
/*
* Compute the intersection numbers of the images of manifold0's
* peripheral curves with manifold1's peripheral curves..
*/
compute_intersection_numbers(manifold1);
/*
* Now extract the cusp_maps from the linking numbers.
*
* There's a lot of redundancy in this loop, but a trivial
* computation so the redundancy hardly matters.
*
* Ignore negatively indexed Cusps -- they're finite vertices.
*/
for (tet = manifold0->tet_list_begin.next;
tet != &manifold0->tet_list_end;
tet = tet->next)
for (v = 0; v < 4; v++)
if (tet->cusp[v]->index >= 0)
for (i = 0; i < 2; i++) /* i = M, L */
{
isometry->cusp_map[tet->cusp[v]->index][M][i]
= + tet->image->cusp[EVALUATE(tet->map, v)]->intersection_number[L][i];
isometry->cusp_map[tet->cusp[v]->index][L][i]
= - tet->image->cusp[EVALUATE(tet->map, v)]->intersection_number[M][i];
}
}
/* DJH */
void my_drill_tube(
Triangulation *manifold,
int singular_index )
{
/*
* Insert a triangular-pillow-with-tunnel (as described at the top
* of this file) so as to connect the boundary component at one
* end of the given edge to the boundary component at the other end.
* The orientation on the triangular pillow will match the
* orientation on tet, so that the orientation on the manifold
* (if there is one) will be preserved. Edge orientations are also
* respected.
*/
EdgeIndex e;
VertexIndex v0,
v1,
v2,
vv0,
vv1,
vv2;
FaceIndex f,
ff;
Tetrahedron *nbr_tet, *tet, *tet0,
*new_tet0,
*new_tet1;
Permutation gluing;
EdgeClass *edge0,
*edge1,
*edge2, *edge,
*new_edge,
*edge3;
Orientation edge_orientation0,
edge_orientation1,
edge_orientation2;
PeripheralCurve c;
Orientation h;
int num_strands,
i,
intersection_number[2],
the_gcd;
Cusp *unique_cusp, *merged_cusp, *dead_cusp, *cusp;
MatrixInt22 *basis_change = NULL;
Boolean creating_new_cusp, same_cusp;
int *cone_points, num_cone_points, dead_index;
for( edge = manifold->edge_list_begin.next;
edge!=&manifold->edge_list_end;
edge = edge->next )
if (edge->is_singular)
if (edge->singular_index == singular_index)
break;
if (edge == &manifold->edge_list_end)
uFatalError("my_drill_tube", "finite_vertices");
tet = edge->incident_tet;
e = edge->incident_edge_index;
/*
* Relative to the orientation of tet, the vertices v0, v1 and v2
* are arranged in counterclockwise order around the face f.
*/
v0 = one_vertex_at_edge[e];
v1 = other_vertex_at_edge[e];
if ( tet->cusp[v0] == tet->cusp[v1]
&& tet->cusp[v1]->num_cone_points ==2 /* if it's a $\S^2(n,n) orbifold then we are creating a torus cusp */
&& tet->cusp[v1]->euler_characteristic==2)
creating_new_cusp = TRUE;
else creating_new_cusp = FALSE;
v2 = remaining_face[v1][v0];
f = remaining_face[v0][v1];
/*
* Note the matching face and its vertices.
*/
nbr_tet = tet->neighbor[f];
gluing = tet->gluing[f];
ff = EVALUATE(gluing, f);
vv0 = EVALUATE(gluing, v0);
vv1 = EVALUATE(gluing, v1);
vv2 = EVALUATE(gluing, v2);
/*
* Note the incident EdgeClasses (which may or may not be distinct).
*/
edge0 = tet->edge_class[e];
edge1 = tet->edge_class[edge_between_vertices[v1][v2]];
edge2 = tet->edge_class[edge_between_vertices[v2][v0]];
/*
* Construct the triangular-pillow-with-tunnel, as described
* at the top of this file.
*/
new_tet0 = NEW_STRUCT(Tetrahedron);
new_tet1 = NEW_STRUCT(Tetrahedron);
initialize_tetrahedron(new_tet0);
initialize_tetrahedron(new_tet1);
INSERT_BEFORE(new_tet0, &manifold->tet_list_end);
INSERT_BEFORE(new_tet1, &manifold->tet_list_end);
manifold->num_tetrahedra += 2;
new_edge = NEW_STRUCT(EdgeClass);
initialize_edge_class(new_edge);
INSERT_BEFORE(new_edge, &manifold->edge_list_end);
new_tet0->neighbor[0] = new_tet1;
new_tet0->neighbor[1] = NULL; /* assigned below */
new_tet0->neighbor[2] = NULL; /* assigned below */
new_tet0->neighbor[3] = new_tet1;
new_tet1->neighbor[0] = new_tet0;
new_tet1->neighbor[1] = new_tet1;
new_tet1->neighbor[2] = new_tet1;
new_tet1->neighbor[3] = new_tet0;
new_tet0->gluing[0] = CREATE_PERMUTATION(0, 0, 1, 2, 2, 1, 3, 3);
new_tet0->gluing[1] = 0x00; /* assigned below */
new_tet0->gluing[2] = 0x00; /* assigned below */
new_tet0->gluing[3] = CREATE_PERMUTATION(0, 1, 1, 0, 2, 2, 3, 3);
new_tet1->gluing[0] = CREATE_PERMUTATION(0, 0, 1, 2, 2, 1, 3, 3);
new_tet1->gluing[1] = CREATE_PERMUTATION(0, 0, 1, 2, 2, 1, 3, 3);
new_tet1->gluing[2] = CREATE_PERMUTATION(0, 0, 1, 2, 2, 1, 3, 3);
new_tet1->gluing[3] = CREATE_PERMUTATION(0, 1, 1, 0, 2, 2, 3, 3);
new_tet0->edge_class[0] = edge1;
new_tet0->edge_class[1] = edge1;
new_tet0->edge_class[2] = edge0;
new_tet0->edge_class[3] = edge2;
new_tet0->edge_class[4] = edge0;
new_tet0->edge_class[5] = edge0;
new_tet1->edge_class[0] = edge1;
new_tet1->edge_class[1] = edge1;
new_tet1->edge_class[2] = edge0;
new_tet1->edge_class[3] = new_edge;
new_tet1->edge_class[4] = edge0;
new_tet1->edge_class[5] = edge0;
edge0->order += 6;
edge1->order += 4;
edge2->order += 1;
new_edge->order = 1;
new_edge->incident_tet = new_tet1;
new_edge->incident_edge_index = 3;
edge_orientation0 = tet->edge_orientation[e];
edge_orientation1 = tet->edge_orientation[edge_between_vertices[v1][v2]];
edge_orientation2 = tet->edge_orientation[edge_between_vertices[v2][v0]];
new_tet0->edge_orientation[0] = edge_orientation1;
new_tet0->edge_orientation[1] = edge_orientation1;
new_tet0->edge_orientation[2] = edge_orientation0;
new_tet0->edge_orientation[3] = edge_orientation2;
new_tet0->edge_orientation[4] = edge_orientation0;
new_tet0->edge_orientation[5] = edge_orientation0;
new_tet1->edge_orientation[0] = edge_orientation1;
new_tet1->edge_orientation[1] = edge_orientation1;
new_tet1->edge_orientation[2] = edge_orientation0;
new_tet1->edge_orientation[3] = right_handed;
new_tet1->edge_orientation[4] = edge_orientation0;
new_tet1->edge_orientation[5] = edge_orientation0;
new_tet0->cusp[0] = tet->cusp[v0];
new_tet0->cusp[1] = tet->cusp[v0];
new_tet0->cusp[2] = tet->cusp[v0];
new_tet0->cusp[3] = tet->cusp[v2];
new_tet1->cusp[0] = tet->cusp[v0];
new_tet1->cusp[1] = tet->cusp[v0];
new_tet1->cusp[2] = tet->cusp[v0];
new_tet1->cusp[3] = tet->cusp[v2];
/*
* Install the triangular-pillow-with-tunnel.
*/
tet->neighbor[f] = new_tet0;
tet->gluing[f] = CREATE_PERMUTATION(f, 2, v0, 0, v1, 1, v2, 3);
new_tet0->neighbor[2] = tet;
new_tet0->gluing[2] = inverse_permutation[tet->gluing[f]];
nbr_tet->neighbor[ff] = new_tet0;
nbr_tet->gluing[ff] = CREATE_PERMUTATION(ff, 1, vv0, 0, vv1, 2, vv2, 3);
new_tet0->neighbor[1] = nbr_tet;
new_tet0->gluing[1] = inverse_permutation[nbr_tet->gluing[ff]];
for(c=0;c<2;c++)
for(h=0;h<2;h++)
{
new_tet0->curve[c][h][3][2] = -nbr_tet->curve[c][h][v2][f];
new_tet0->curve[c][h][3][1] = -nbr_tet->curve[c][h][vv2][ff];
}
/*
* Typically creating_new_cusp is FALSE, meaning that we are
* connecting a spherical boundary component to a torus or
* Klein bottle boundary component, and we simply extend the
* existing peripheral curves across the new tetrahedra.
*
* In the exceptional case that creating_new_cusp is TRUE,
* meaning that the manifold has no real cusps and we are
* connecting the "special fake cusp" to itself, we must
* install a meridian and longitude, and set up the Dehn filling.
*/
if (creating_new_cusp == FALSE)
{
if (tet->cusp[v0]->index<tet->cusp[v1]->index)
{
merged_cusp = tet->cusp[v0];
dead_cusp = tet->cusp[v1];
}
else
{
merged_cusp = tet->cusp[v1];
dead_cusp = tet->cusp[v0];
}
if (merged_cusp==dead_cusp)
same_cusp = TRUE;
else same_cusp = FALSE;
if (same_cusp)
merged_cusp->euler_characteristic = merged_cusp->euler_characteristic - 2;
else if (merged_cusp->euler_characteristic==2 || dead_cusp->euler_characteristic==2)
merged_cusp->euler_characteristic = merged_cusp->euler_characteristic
+dead_cusp->euler_characteristic - 2;
else merged_cusp->euler_characteristic = merged_cusp->euler_characteristic
+dead_cusp->euler_characteristic;
merged_cusp->topology = unknown_topology;
if (same_cusp)
num_cone_points = merged_cusp->num_cone_points - 2;
else num_cone_points = merged_cusp->num_cone_points + dead_cusp->num_cone_points -2;
cone_points = NEW_ARRAY( num_cone_points, int );
num_cone_points = 0;
for(i=0;i<merged_cusp->num_cone_points;i++)
if (merged_cusp->cone_points[i]!=edge->singular_index)
cone_points[num_cone_points++] = merged_cusp->cone_points[i];
my_free(merged_cusp->cone_points);
if (!same_cusp)
{
dead_index = dead_cusp->index;
/* fix cusp fields */
for( tet0 = manifold->tet_list_begin.next;
tet0!=&manifold->tet_list_end;
tet0 = tet0->next )
for( i = 0; i < 4; i++ )
if (tet0->cusp[i] == dead_cusp)
tet0->cusp[i] = merged_cusp;
for(i=0;i<dead_cusp->num_cone_points;i++)
if (dead_cusp->cone_points[i]!=edge->singular_index)
cone_points[num_cone_points++] = dead_cusp->cone_points[i];
my_free(dead_cusp->cone_points);
REMOVE_NODE(dead_cusp);
my_free(dead_cusp);
}
/* install new cone points */
merged_cusp->cone_points = cone_points;
merged_cusp->num_cone_points = num_cone_points;
for( cusp = manifold->cusp_list_begin.next;
cusp!=&manifold->cusp_list_end;
cusp = cusp->next )
{
for (i=0;i < cusp->num_cone_points;i++)
if (cusp->cone_points[i] > edge->singular_index)
cusp->cone_points[i] = cusp->cone_points[i] - 1;
if (!same_cusp && cusp->index > dead_index)
cusp->index--;
}
for( edge3 = manifold->edge_list_begin.next;
edge3!=&manifold->edge_list_end;
edge3 = edge3->next )
if (edge3->is_singular && edge3->singular_index > edge->singular_index)
edge3->singular_index--;
edge->singular_index = -1;
edge->is_singular = FALSE;
edge->singular_order = 1;
manifold->num_singular_arcs--;
if (!same_cusp)
{
manifold->num_cusps--;
manifold->num_or_cusps--;
}
}
else /* creating_new_cusp == TRUE */
{
static void copy_images_to_scratch(
Triangulation *manifold0,
int which_set,
Boolean double_copy_on_tori)
{
Tetrahedron *tet;
int i,
j,
jj,
k,
kk,
l,
ll;
/*
* This function is modelled on copy_curves_to_scratch()
* in intersection_numbers.c.
*/
/*
* Note that even though we are passed manifold0 as an
* explicit function parameter, we are ultimately writing
* the image curves in manifold1.
*/
for (tet = manifold0->tet_list_begin.next;
tet != &manifold0->tet_list_end;
tet = tet->next)
for (i = 0; i < 2; i++)
for (k = 0; k < 4; k++)
{
kk = EVALUATE(tet->map, k);
for (l = 0; l < 4; l++)
{
ll = EVALUATE(tet->map, l);
if (tet->cusp[k]->topology == torus_cusp
&& double_copy_on_tori == TRUE)
tet->image->scratch_curve[which_set][i][right_handed][kk][ll] =
tet->image->scratch_curve[which_set][i][ left_handed][kk][ll] =
tet->curve[i][right_handed][k][l]
+ tet->curve[i][ left_handed][k][l];
else
/*
* tet->cusp[k]->topology == Klein_cusp
* || double_copy_on_tori == FALSE
*/
for (j = 0; j < 2; j++)
{
/*
* parities can be tricky.
*
* When discussing gluings from a face of one Tetrahedron
* to a face of another, an even parity corresponds to an
* orientation-reversing gluing.
*
* When discussing a map from one Tetrahedron onto
* another, an even parity is an orientation-preserving
* map.
*/
/*
* If tet->map has even parity (i.e. if it's an
* orientation-preserving map) it will send the
* right-handed vertex cross section to a right-
* handed image.
*
* If tet->map has odd parity (i.e. if it's an
* orientation-reversing map) it will send the
* right-handed vertex cross section to a left-
* handed image.
*/
jj = (parity[tet->map] == 0) ? j : !j;
tet->image->scratch_curve[which_set][i][jj][kk][ll]
= tet->curve[i][j][k][l];
}
}
}
}
void create_one_cusp(
Triangulation *manifold,
Tetrahedron *tet,
Boolean is_finite,
VertexIndex v,
int cusp_index)
{
Cusp *cusp;
IdealVertex *queue;
int queue_first,
queue_last;
Tetrahedron *tet1,
*nbr;
VertexIndex v1,
nbr_v;
FaceIndex f;
/*
* Create the cusp, add it to the list, and set
* the is_finite and index fields.
*/
cusp = NEW_STRUCT(Cusp);
initialize_cusp(cusp);
INSERT_BEFORE(cusp, &manifold->cusp_list_end);
cusp->is_finite = is_finite;
cusp->index = cusp_index;
/*
* We don't set the topology, is_complete, m, l, holonomy,
* cusp_shape or shape_precision fields.
*
* For "real" cusps the calling routine may
*
* (1) call peripheral_curves() to set the cusp->topology,
*
* (2) keep the default values of cusp->is_complete,
* cusp->m and cusp->l as set by initialize_cusp(), and
*
* (3) let the holonomy and cusp_shape be computed automatically
* when hyperbolic structure is computed.
*
* Alternatively, the calling routine may set these fields in other
* ways, as it sees fit.
*
* If we were called by create_fake_cusps(), then the above fields
* are all irrelevant and ignored.
*/
/*
* Set the tet->cusp field at all vertices incident to the new cusp.
*/
/*
* Allocate space for a queue of pointers to the IdealVertices.
* Each IdealVertex will appear on the queue at most once, so an
* array of length 4 * manifold->num_tetrahedra will suffice.
*/
queue = NEW_ARRAY(4 * manifold->num_tetrahedra, IdealVertex);
/*
* Set the cusp of the given IdealVertex...
*/
tet->cusp[v] = cusp;
/*
* ...and put it on the queue.
*/
queue_first = 0;
queue_last = 0;
queue[0].tet = tet;
queue[0].v = v;
/*
* Start processing the queue.
*/
do
{
/*
* Pull an IdealVertex off the front of the queue.
*/
tet1 = queue[queue_first].tet;
v1 = queue[queue_first].v;
queue_first++;
/*
* Look at the three neighboring IdealVertices.
*/
for (f = 0; f < 4; f++)
{
if (f == v1)
continue;
nbr = tet1->neighbor[f];
nbr_v = EVALUATE(tet1->gluing[f], v1);
/*
* If the neighbor's cusp hasn't been set...
*/
if (nbr->cusp[nbr_v] == NULL)
{
/*
* ...set it...
*/
nbr->cusp[nbr_v] = cusp;
/*
* ...and add it to the end of the queue.
*/
++queue_last;
queue[queue_last].tet = nbr;
queue[queue_last].v = nbr_v;
}
}
}
while (queue_first <= queue_last);
/*
* Free the memory used for the queue.
*/
my_free(queue);
}
