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/*
* tables.c
*
* This file provides tables used in working with triangulations.
* They are based on the numbering conventions for tetrahedra
* described in triangulation.h.
*
* The tables are
*
* EdgeIndex edge3[6];
* EdgeIndex edge_between_faces[4][4];
* EdgeIndex edge3_between_faces[4][4];
* EdgeIndex edge_between_vertices[4][4];
* EdgeIndex edge3_between_vertices[4][4];
* FaceIndex one_face_at_edge[6];
* FaceIndex other_face_at_edge[6];
* VertexIndex one_vertex_at_edge[6];
* VertexIndex other_vertex_at_edge[6];
* FaceIndex remaining_face[4][4];
* FaceIndex face_between_edges[6][6];
* Permutation inverse_permutation[256];
* signed char parity[256];
* FaceIndex vt_side[4][3];
* Permutation permutation_by_index[24];
*
* Their use is described in detail below.
*
* The value 9 is used as a filler for undefined table entries.
*/
#include "kernel.h"
/*
* edge3[i] is the index of the complex edge parameter associated with
* the edge of EdgeIndex i. Opposite edges have equal complex edge
* parameters, which are stored only under the lesser EdgeIndex; thus
* even though the numbering of the edges runs from 0 to 5, the
* numbering of the edge parameters run only from 0 to 2.
*/
const EdgeIndex edge3[6] = {0, 1, 2, 2, 1, 0};
/*
* edge_between_faces[i][j] is the index of the edge lying between
* faces i and j.
*/
const EdgeIndex edge_between_faces[4][4] = {{9, 0, 1, 2},
{0, 9, 3, 4},
{1, 3, 9, 5},
{2, 4, 5, 9}};
/*
* edge3_between_faces[i][j] = edge3[ edge_between_faces[i][j] ].
* This table is useful when looking up complex edge parameters.
* Cf. edge3[] above.
*/
const EdgeIndex edge3_between_faces[4][4] = {{9, 0, 1, 2},
{0, 9, 2, 1},
{1, 2, 9, 0},
{2, 1, 0, 9}};
/*
* edge_between_vertices[i][j] is the index of the edge lying between
* vertices i and j.
*/
const EdgeIndex edge_between_vertices[4][4] = {{9, 5, 4, 3},
{5, 9, 2, 1},
{4, 2, 9, 0},
{3, 1, 0, 9}};
/*
* edge3_between_vertices[i][j] = edge3[ edge_between_vertices[i][j] ].
* This table is useful when looking up complex edge parameters.
* Cf. edge3[] above.
* Note that edge3_between_vertices[][] and edge3_between_faces[][]
* are identical.
*/
const EdgeIndex edge3_between_vertices[4][4] = {{9, 0, 1, 2},
{0, 9, 2, 1},
{1, 2, 9, 0},
{2, 1, 0, 9}};
/*
* one_face_at_edge[i] and other_face_at_edge[i] gives the indices of
* the two faces incident to edge i.
*/
const FaceIndex one_face_at_edge[6] = {0, 0, 0, 1, 1, 2};
const FaceIndex other_face_at_edge[6] = {1, 2, 3, 2, 3, 3};
/*
* one_vertex_at_edge[i] and other_vertex_at_edge[i] give the indices of
* the two vertices incident to edge i.
*/
const FaceIndex one_vertex_at_edge[6] = {2, 1, 1, 0, 0, 0};
const FaceIndex other_vertex_at_edge[6] = {3, 3, 2, 3, 2, 1};
/*
* Given two faces i and j, remaining_face[i][j] tells you the index
* of one of the remaining faces. For a right_handed tetrahedron
* (see kernel_typedefs.h for the definition of right_handed) the
* faces i, j, and remaining_face[i][j] are arranged in a counterclockwise
* order around their common ideal vertex. Thus, for two faces i and j,
* remaining_face[i][j] gives one of the remaining faces and
* remaining_face[j][i] gives the other.
*/
const FaceIndex remaining_face[4][4] = {{9, 3, 1, 2},
{2, 9, 3, 0},
{3, 0, 9, 1},
{1, 2, 0, 9}};
/*
* face_between_edges[i][j] is the index of the face lying between
* (nonopposite) edges i and j.
*/
const FaceIndex face_between_edges[6][6] = {{9, 0, 0, 1, 1, 9},
{0, 9, 0, 2, 9, 2},
{0, 0, 9, 9, 3, 3},
{1, 2, 9, 9, 1, 2},
{1, 9, 3, 1, 9, 3},
{9, 2, 3, 2, 3, 9}};
/*
* inverse_permutation[p] is the inverse of Permutation p.
*/
const Permutation inverse_permutation[256] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x1b, 0x00, 0x00, 0x4b, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x27, 0x00, 0x00, 0x00, 0x00, 0x00, 0x63, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x87, 0x00, 0x00, 0x93, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x1e, 0x00, 0x00, 0x4e, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x2d, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x6c, 0x00, 0x00, 0x00,
0x00, 0x00, 0x8d, 0x00, 0x00, 0x00, 0x00, 0x00, 0x9c, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x36, 0x00, 0x00, 0x00, 0x00, 0x00, 0x72, 0x00, 0x00,
0x00, 0x00, 0x00, 0x39, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x78, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0xb1, 0x00, 0x00, 0xb4, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xc6, 0x00, 0x00, 0xd2, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0xc9, 0x00, 0x00, 0x00, 0x00, 0x00, 0xd8, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0xe1, 0x00, 0x00, 0xe4, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00};
/*
* parity[p] is the parity of Permutation p.
*
* 0 signifies an even permutation
* (corresponding to an orientation reversing gluing)
*
* 1 signifies an odd permutation
* (corresponding to an orientation preserving gluing)
*
* 9 signifies an invalid permutation
*
* Notes:
* (1) The typedef GluingParity relies on 0 and 1 meaning what they do.
* (2) The 0 and 1 are reversed relative to the parity[] table in the
* old version of snappea.
* (3) Use the constants in GluingParity; don't use 0 and 1 directly.
*/
const signed char parity[256] = {
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 9, 9, 1, 9,
9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9, 0, 9, 9, 1, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9,
9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 0, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 9, 1, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9, 0, 9, 9, 9, 9, 9, 1, 9, 9, 9, 9, 9, 9, 9,
9, 1, 9, 9, 0, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9};
/*
* vt_side[i][j] is the side of the cross sectional triangle at
* vertex i which lies between edges j and (j+1)%3, where
* the edge numbering is as in edge3_between_faces[][] above.
*
* An alternate interpretation is that vt_side[v][0], vt_side[v][1]
* and vt_side[v][2] are the three faces surrounding vertex v, given
* in counterclockwise order relative to the right_handed orientation
* of the Tetrahedron.
*/
const FaceIndex vt_side[4][3] = {{3, 1, 2},
{2, 0, 3},
{1, 3, 0},
{0, 2, 1}};
/*
* There are 24 possible Permutations of the set {3, 2, 1, 0}. The table
* permutation_by_index[] list them all. E.g. permutation_by_index[2] = 0xD2
* = 3102, which is the permutation taking 3210 to 3102.
*/
const Permutation permutation_by_index[24] = {
0xE4, 0xE1, 0xD2, 0xD8, 0xC9, 0xC6,
0x93, 0x9C, 0x8D, 0x87, 0xB4, 0xB1,
0x4E, 0x4B, 0x78, 0x72, 0x63, 0x6C,
0x39, 0x36, 0x27, 0x2D, 0x1E, 0x1B};
/*
* index_by_permutation[] is the inverse of permutation_by_index[].
* That is, for 0 <= i < 24, index_by_permutation[permutation_by_index[i]] = i.
*/
const char index_by_permutation[256] = {
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 23, -1, -1, 22, -1,
-1, -1, -1, -1, -1, -1, -1, 20, -1, -1, -1, -1, -1, 21, -1, -1,
-1, -1, -1, -1, -1, -1, 19, -1, -1, 18, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 13, -1, -1, 12, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, 16, -1, -1, -1, -1, -1, -1, -1, -1, 17, -1, -1, -1,
-1, -1, 15, -1, -1, -1, -1, -1, 14, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, 9, -1, -1, -1, -1, -1, 8, -1, -1,
-1, -1, -1, 6, -1, -1, -1, -1, -1, -1, -1, -1, 7, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, 11, -1, -1, 10, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1, 5, -1, -1, 4, -1, -1, -1, -1, -1, -1,
-1, -1, 2, -1, -1, -1, -1, -1, 3, -1, -1, -1, -1, -1, -1, -1,
-1, 1, -1, -1, 0, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1,
-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1};
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