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/*
* tet_shapes.c
*
* This file contains the following low-level functions for
* working with TetShapes.
*
* void add_edge_angles( Tetrahedron *tet0, EdgeIndex e0,
* Tetrahedron *tet1, EdgeIndex e1,
* Tetrahedron *tet2, EdgeIndex e2)
*
* Boolean angles_sum_to_zero( Tetrahedron *tet0, EdgeIndex e0,
* Tetrahedron *tet1, EdgeIndex e1);
*
* void compute_remaining_angles(Tetrahedron *tet, EdgeIndex e);
*
*
* add_edge_angles() adds the edge angles at edge e0 of tet0
* to the corresponding angles at edge e1 of tet1, and writes
* the results to edge e2 of tet2. It pays careful attention
* to the edge_orientations. Note that even though opposite
* edges of a Tetrahedron have equal angles, they needn't have
* the same edge_orientation, so you should pass an actual
* EdgeIndex in the range 0-5, not merely a quasi-equivalent
* index in the range 0-2. The edge angle of the sum will be
* in the range [(-1/2) pi, (3/2) pi], regardless of the angles
* of the summands.
*
* angles_sum_to_zero() returns TRUE iff one of the angles
* (shape[complete]->cwl[ultimate] or shape[filled]->cwl[ultimate])
* at edge e0 of tet0 cancels the corresponding angle at edge e1
* of tet1 (mod 2 pi i). Accounts for edge_orientations.
*
* compute_remaining_angles() assumes the angle at edge e is
* correct, and computes the remaining angles in terms of it.
* The EdgeIndex may be given in either the range 0-5 or the
* range 0-2. The arguments of the remaining angles will be
* in the range [(-1/2) pi, (3/2) pi].
*/
#include "kernel.h"
/*
* CANCELLATION_EPSILON says how close the logs of two complex
* numbers must be to be considered equal.
*/
#define CANCELLATION_EPSILON 1e-4
static void add_tet_shapes(
TetShape *ts0, EdgeIndex e30, Orientation eo0,
TetShape *ts1, EdgeIndex e31, Orientation eo1,
TetShape *ts2, EdgeIndex e32, Orientation eo2);
static void add_complex_with_log(
ComplexWithLog *cwl0, Orientation eo0,
ComplexWithLog *cwl1, Orientation eo1,
ComplexWithLog *cwl2, Orientation eo2);
static Boolean logs_sum_to_zero(
Complex summand0, Orientation eo0,
Complex summand1, Orientation eo1);
static void compute_cwl(ComplexWithLog cwl[3], EdgeIndex e);
static void normalize_angle(double *angle);
void add_edge_angles(
Tetrahedron *tet0, EdgeIndex e0,
Tetrahedron *tet1, EdgeIndex e1,
Tetrahedron *tet2, EdgeIndex e2)
{
int i;
for (i = 0; i < 2; i++) /* i = complete, filled */
add_tet_shapes(
tet0->shape[i], edge3[e0], tet0->edge_orientation[e0],
tet1->shape[i], edge3[e1], tet1->edge_orientation[e1],
tet2->shape[i], edge3[e2], tet2->edge_orientation[e2]);
}
static void add_tet_shapes(
TetShape *ts0, EdgeIndex e30, Orientation eo0,
TetShape *ts1, EdgeIndex e31, Orientation eo1,
TetShape *ts2, EdgeIndex e32, Orientation eo2)
{
int i;
for (i = 0; i < 2; i++) /* i = ultimate, penultimate */
add_complex_with_log(
&ts0->cwl[i][e30], eo0,
&ts1->cwl[i][e31], eo1,
&ts2->cwl[i][e32], eo2);
}
static void add_complex_with_log(
ComplexWithLog *cwl0, Orientation eo0,
ComplexWithLog *cwl1, Orientation eo1,
ComplexWithLog *cwl2, Orientation eo2)
{
/*
* First compute the sum of the logs, then recover
* the rectangular form.
*
* We do all computations relative to the Orientation
* of the EdgeClass. So if a particular edge is seen
* as left_handed by the EdgeClass, we must negate the
* real part of the log of its complex angle. (Recall
* that all all TetShapes are stored relative to the
* right_handed Orientation of the Tetrahedron.)
*/
Complex summand0,
summand1,
sum;
summand0 = cwl0->log;
if (eo0 == left_handed)
summand0.real = - summand0.real;
summand1 = cwl1->log;
if (eo1 == left_handed)
summand1.real = - summand1.real;
sum = complex_plus(summand0, summand1);
if (eo2 == left_handed)
sum.real = - sum.real;
normalize_angle(&sum.imag);
cwl2->log = sum;
cwl2->rect = complex_exp(sum);
}
Boolean angles_sum_to_zero(
Tetrahedron *tet0, EdgeIndex e0,
Tetrahedron *tet1, EdgeIndex e1)
{
int i;
for (i = 0; i < 2; i++) /* i = complete, filled */
if (logs_sum_to_zero(
tet0->shape[i]->cwl[ultimate][edge3[e0]].log,
tet0->edge_orientation[e0],
tet1->shape[i]->cwl[ultimate][edge3[e1]].log,
tet1->edge_orientation[e1]))
return TRUE;
return FALSE;
}
static Boolean logs_sum_to_zero(
Complex summand0, Orientation eo0,
Complex summand1, Orientation eo1)
{
Complex sum;
if (eo0 != eo1)
summand1.real = - summand1.real;
sum = complex_plus(summand0, summand1);
normalize_angle(&sum.imag);
return (complex_modulus(sum) < CANCELLATION_EPSILON);
}
void compute_remaining_angles(
Tetrahedron *tet,
EdgeIndex e)
{
int i,
j;
for (i = 0; i < 2; i++) /* i = complete, filled */
for (j = 0; j < 2; j++) /* j = ultimate, penultimate */
compute_cwl(tet->shape[i]->cwl[j], edge3[e]);
}
static void compute_cwl(
ComplexWithLog cwl[3],
EdgeIndex e)
{
/*
* Compute cwl[(e+1)%3] and cwl[(e+2)%3] in terms of cwl[e].
*/
int i;
for (i = 1; i < 3; i++)
{
cwl[(e+i)%3].rect = complex_div(One, complex_minus(One, cwl[(e+i-1)%3].rect));
cwl[(e+i)%3].log = complex_log(cwl[(e+i)%3].rect, PI_OVER_2);
}
}
static void normalize_angle(
double *angle)
{
/*
* Normalize the angle to lie in the range [(-1/2) pi, (3/2) pi].
*/
while (*angle > THREE_PI_OVER_2)
*angle -= TWO_PI;
while (*angle < - PI_OVER_2)
*angle += TWO_PI;
}
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