--- /dev/null
+/*****************************************************************************
+ * #ident "Id: main.c,v 3.27 2002-01-06 16:23:01+02 rl Exp "
+ * kaleido
+ *
+ * Kaleidoscopic construction of uniform polyhedra
+ * Copyright (c) 1991-2002 Dr. Zvi Har'El <rl@math.technion.ac.il>
+ *
+ * Redistribution and use in source and binary forms, with or without
+ * modification, are permitted provided that the following conditions
+ * are met:
+ *
+ * 1. Redistributions of source code must retain the above copyright
+ * notice, this list of conditions and the following disclaimer.
+ *
+ * 2. Redistributions in binary form must reproduce the above copyright
+ * notice, this list of conditions and the following disclaimer in
+ * the documentation and/or other materials provided with the
+ * distribution.
+ *
+ * 3. The end-user documentation included with the redistribution,
+ * if any, must include the following acknowledgment:
+ * "This product includes software developed by
+ * Dr. Zvi Har'El (http://www.math.technion.ac.il/~rl/)."
+ * Alternately, this acknowledgment may appear in the software itself,
+ * if and wherever such third-party acknowledgments normally appear.
+ *
+ * This software is provided 'as-is', without any express or implied
+ * warranty. In no event will the author be held liable for any
+ * damages arising from the use of this software.
+ *
+ * Author:
+ * Dr. Zvi Har'El,
+ * Deptartment of Mathematics,
+ * Technion, Israel Institue of Technology,
+ * Haifa 32000, Israel.
+ * E-Mail: rl@math.technion.ac.il
+ *
+ * ftp://ftp.math.technion.ac.il/kaleido/
+ * http://www.mathconsult.ch/showroom/unipoly/
+ *
+ * Adapted for xscreensaver by Jamie Zawinski <jwz@jwz.org> 25-Apr-2004
+ *
+ *****************************************************************************
+ */
+
+#include <stdio.h>
+#include <ctype.h>
+#include <string.h>
+#include <math.h>
+#include <stdlib.h>
+#include <errno.h>
+
+#include "config.h"
+#include "polyhedra.h"
+
+extern const char *progname;
+
+#ifndef MAXLONG
+#define MAXLONG 0x7FFFFFFF
+#endif
+#ifndef MAXDIGITS
+#define MAXDIGITS 10 /* (int)log10((double)MAXLONG) + 1 */
+#endif
+
+#ifndef DBL_EPSILON
+#define DBL_EPSILON 2.2204460492503131e-16
+#endif
+#define BIG_EPSILON 3e-2
+#define AZ M_PI/7 /* axis azimuth */
+#define EL M_PI/17 /* axis elevation */
+
+#define Err(x) do {\
+ fprintf (stderr, "%s: %s\n", progname, (x)); \
+ exit (1); \
+ } while(0)
+
+#define Free(lvalue) do {\
+ if (lvalue) {\
+ free((char*) lvalue);\
+ lvalue=0;\
+ }\
+ } while(0)
+
+#define Matfree(lvalue,n) do {\
+ if (lvalue) \
+ matfree((char*) lvalue, n);\
+ lvalue=0;\
+ } while(0)
+
+#define Malloc(lvalue,n,type) do {\
+ if (!(lvalue = (type*) malloc((n) * sizeof(type)))) \
+ Err("out of memory");\
+ } while(0)
+
+#define Realloc(lvalue,n,type) do {\
+ if (!(lvalue = (type*) realloc(lvalue, (n) * sizeof(type)))) \
+ Err("out of memory");\
+ } while(0)
+
+#define Calloc(lvalue,n,type) do {\
+ if (!(lvalue = (type*) calloc(n, sizeof(type))))\
+ Err("out of memory");\
+ } while(0)
+
+#define Matalloc(lvalue,n,m,type) do {\
+ if (!(lvalue = (type**) matalloc(n, (m) * sizeof(type))))\
+ Err("out of memory");\
+ } while(0)
+
+#define Sprintfrac(lvalue,x) do {\
+ if (!(lvalue=sprintfrac(x)))\
+ return 0;\
+ } while(0)
+
+#define numerator(x) (frac(x), frax.n)
+#define denominator(x) (frac(x), frax.d)
+#define compl(x) (frac(x), (double) frax.n / (frax.n-frax.d))
+
+typedef struct {
+ double x, y, z;
+} Vector;
+
+typedef struct {
+ /* NOTE: some of the int's can be replaced by short's, char's,
+ or even bit fields, at the expense of readability!!!*/
+ int index; /* index to the standard list, the array uniform[] */
+ int N; /* number of faces types (atmost 5)*/
+ int M; /* vertex valency (may be big for dihedral polyhedra) */
+ int V; /* vertex count */
+ int E; /* edge count */
+ int F; /* face count */
+ int D; /* density */
+ int chi; /* Euler characteristic */
+ int g; /* order of symmetry group */
+ int K; /* symmetry type: D=2, T=3, O=4, I=5 */
+ int hemi;/* flag hemi polyhedron */
+ int onesided;/* flag onesided polyhedron */
+ int even; /* removed face in pqr| */
+ int *Fi; /* face counts by type (array N)*/
+ int *rot; /* vertex configuration (array M of 0..N-1) */
+ int *snub; /* snub triangle configuration (array M of 0..1) */
+ int *firstrot; /* temporary for vertex generation (array V) */
+ int *anti; /* temporary for direction of ideal vertices (array E) */
+ int *ftype; /* face types (array F) */
+ int **e; /* edges (matrix 2 x E of 0..V-1)*/
+ int **dual_e; /* dual edges (matrix 2 x E of 0..F-1)*/
+ int **incid; /* vertex-face incidence (matrix M x V of 0..F-1)*/
+ int **adj; /* vertex-vertex adjacency (matrix M x V of 0..V-1)*/
+ double p[4]; /* p, q and r; |=0 */
+ double minr; /* smallest nonzero inradius */
+ double gon; /* basis type for dihedral polyhedra */
+ double *n; /* number of side of a face of each type (array N) */
+ double *m; /* number of faces at a vertex of each type (array N) */
+ double *gamma; /* fundamental angles in radians (array N) */
+ char *polyform; /* printable Wythoff symbol */
+ char *config; /* printable vertex configuration */
+ char *group; /* printable group name */
+ char *name; /* name, standard or manifuctured */
+ char *dual_name; /* dual name, standard or manifuctured */
+ char *class;
+ char *dual_class;
+ Vector *v; /* vertex coordinates (array V) */
+ Vector *f; /* face coordinates (array F)*/
+} Polyhedron;
+
+typedef struct {
+ long n,d;
+} Fraction;
+
+static Polyhedron *polyalloc(void);
+static Vector rotate(Vector vertex, Vector axis, double angle);
+
+static Vector sum3(Vector a, Vector b, Vector c);
+static Vector scale(double k, Vector a);
+static Vector sum(Vector a, Vector b);
+static Vector diff(Vector a, Vector b);
+static Vector pole (double r, Vector a, Vector b, Vector c);
+static Vector cross(Vector a, Vector b);
+static double dot(Vector a, Vector b);
+static int same(Vector a, Vector b, double epsilon);
+
+static char *sprintfrac(double x);
+
+static void frac(double x);
+static void matfree(void *mat, int rows);
+static void *matalloc(int rows, int row_size);
+
+static Fraction frax;
+
+
+static struct {
+ char *Wythoff, *name, *dual, *group, *class, *dual_class;
+ short Coxeter, Wenninger;
+} uniform[] = {
+
+ /****************************************************************************
+ * Dihedral Schwarz Triangles (D5 only)
+ ***************************************************************************/
+
+ /* (2 2 5) (D1/5) */
+ /* 1 */ {"2 5|2", "Pentagonal Prism",
+ "Pentagonal Dipyramid",
+ "Dihedral (D[1/5])",
+ "",
+ "",
+ 0, 0},
+
+ /* 2 */ {"|2 2 5", "Pentagonal Antiprism",
+ "Pentagonal Deltohedron",
+ "Dihedral (D[1/5])",
+ "",
+ "",
+ 0, 0},
+ /* (2 2 5/2) (D2/5) */
+ /* 3 */ {"2 5/2|2", "Pentagrammic Prism",
+ "Pentagrammic Dipyramid",
+ "Dihedral (D[2/5])",
+ "",
+ "",
+ 0, 0},
+
+ /* 4 */ {"|2 2 5/2", "Pentagrammic Antiprism",
+ "Pentagrammic Deltohedron",
+ "Dihedral (D[2/5])",
+ "",
+ "",
+ 0, 0},
+ /* (5/3 2 2) (D3/5) */
+
+ /* 5 */ {"|2 2 5/3", "Pentagrammic Crossed Antiprism",
+ "Pentagrammic Concave Deltohedron",
+ "Dihedral (D[3/5])",
+ "",
+ "",
+ 0, 0},
+
+ /****************************************************************************
+ * Tetrahedral
+ ***************************************************************************/
+
+ /* (2 3 3) (T1) */
+ /* 6 */ {"3|2 3", "Tetrahedron",
+ "Tetrahedron",
+ "Tetrahedral (T[1])",
+ "Platonic Solid",
+ "Platonic Solid",
+ 15, 1},
+
+ /* 7 */ {"2 3|3", "Truncated Tetrahedron",
+ "Triakistetrahedron",
+ "Tetrahedral (T[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 16, 6},
+ /* (3/2 3 3) (T2) */
+ /* 8 */ {"3/2 3|3", "Octahemioctahedron",
+ "Octahemioctacron",
+ "Tetrahedral (T[2])",
+ "",
+ "",
+ 37, 68},
+
+ /* (3/2 2 3) (T3) */
+ /* 9 */ {"3/2 3|2", "Tetrahemihexahedron",
+ "Tetrahemihexacron",
+ "Tetrahedral (T[3])",
+ "",
+ "",
+ 36, 67},
+
+ /****************************************************************************
+ * Octahedral
+ ***************************************************************************/
+
+ /* (2 3 4) (O1) */
+ /* 10 */ {"4|2 3", "Octahedron",
+ "Cube",
+ "Octahedral (O[1])",
+ "Platonic Solid",
+ "Platonic Solid",
+ 17, 2},
+
+ /* 11 */ {"3|2 4", "Cube",
+ "Octahedron",
+ "Octahedral (O[1])",
+ "Platonic Solid",
+ "Platonic Solid",
+ 18, 3},
+
+ /* 12 */ {"2|3 4", "Cuboctahedron",
+ "Rhombic Dodecahedron",
+ "Octahedral (O[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 19, 11},
+
+ /* 13 */ {"2 4|3", "Truncated Octahedron",
+ "Tetrakishexahedron",
+ "Octahedral (O[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 20, 7},
+
+ /* 14 */ {"2 3|4", "Truncated Cube",
+ "Triakisoctahedron",
+ "Octahedral (O[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 21, 8},
+
+ /* 15 */ {"3 4|2", "Rhombicuboctahedron",
+ "Deltoidal Icositetrahedron",
+ "Octahedral (O[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 22, 13},
+
+ /* 16 */ {"2 3 4|", "Truncated Cuboctahedron",
+ "Disdyakisdodecahedron",
+ "Octahedral (O[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 23, 15},
+
+ /* 17 */ {"|2 3 4", "Snub Cube",
+ "Pentagonal Icositetrahedron",
+ "Octahedral (O[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 24, 17},
+ /* (3/2 4 4) (O2b) */
+
+ /* 18 */ {"3/2 4|4", "Small Cubicuboctahedron",
+ "Small Hexacronic Icositetrahedron",
+ "Octahedral (O[2b])",
+ "",
+ "",
+ 38, 69},
+ /* (4/3 3 4) (O4) */
+
+ /* 19 */ {"3 4|4/3", "Great Cubicuboctahedron",
+ "Great Hexacronic Icositetrahedron",
+ "Octahedral (O[4])",
+ "",
+ "",
+ 50, 77},
+
+ /* 20 */ {"4/3 4|3", "Cubohemioctahedron",
+ "Hexahemioctacron",
+ "Octahedral (O[4])",
+ "",
+ "",
+ 51, 78},
+
+ /* 21 */ {"4/3 3 4|", "Cubitruncated Cuboctahedron",
+ "Tetradyakishexahedron",
+ "Octahedral (O[4])",
+ "",
+ "",
+ 52, 79},
+ /* (3/2 2 4) (O5) */
+
+ /* 22 */ {"3/2 4|2", "Great Rhombicuboctahedron",
+ "Great Deltoidal Icositetrahedron",
+ "Octahedral (O[5])",
+ "",
+ "",
+ 59, 85},
+
+ /* 23 */ {"3/2 2 4|", "Small Rhombihexahedron",
+ "Small Rhombihexacron",
+ "Octahedral (O[5])",
+ "",
+ "",
+ 60, 86},
+ /* (4/3 2 3) (O7) */
+
+ /* 24 */ {"2 3|4/3", "Stellated Truncated Hexahedron",
+ "Great Triakisoctahedron",
+ "Octahedral (O[7])",
+ "",
+ "",
+ 66, 92},
+
+ /* 25 */ {"4/3 2 3|", "Great Truncated Cuboctahedron",
+ "Great Disdyakisdodecahedron",
+ "Octahedral (O[7])",
+ "",
+ "",
+ 67, 93},
+ /* (4/3 3/2 2) (O11) */
+
+ /* 26 */ {"4/3 3/2 2|", "Great Rhombihexahedron",
+ "Great Rhombihexacron",
+ "Octahedral (O[11])",
+ "",
+ "",
+ 82, 103},
+
+ /****************************************************************************
+ * Icosahedral
+ ***************************************************************************/
+
+ /* (2 3 5) (I1) */
+ /* 27 */ {"5|2 3", "Icosahedron",
+ "Dodecahedron",
+ "Icosahedral (I[1])",
+ "Platonic Solid",
+ "Platonic Solid",
+ 25, 4},
+
+ /* 28 */ {"3|2 5", "Dodecahedron",
+ "Icosahedron",
+ "Icosahedral (I[1])",
+ "Platonic Solid",
+ "Platonic Solid",
+ 26, 5},
+
+ /* 29 */ {"2|3 5", "Icosidodecahedron",
+ "Rhombic Triacontahedron",
+ "Icosahedral (I[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 28, 12},
+
+ /* 30 */ {"2 5|3", "Truncated Icosahedron",
+ "Pentakisdodecahedron",
+ "Icosahedral (I[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 27, 9},
+
+ /* 31 */ {"2 3|5", "Truncated Dodecahedron",
+ "Triakisicosahedron",
+ "Icosahedral (I[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 29, 10},
+
+ /* 32 */ {"3 5|2", "Rhombicosidodecahedron",
+ "Deltoidal Hexecontahedron",
+ "Icosahedral (I[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 30, 14},
+
+ /* 33 */ {"2 3 5|", "Truncated Icosidodechedon",
+ "Disdyakistriacontahedron",
+ "Icosahedral (I[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 31, 16},
+
+ /* 34 */ {"|2 3 5", "Snub Dodecahedron",
+ "Pentagonal Hexecontahedron",
+ "Icosahedral (I[1])",
+ "Archimedian Solid",
+ "Catalan Solid",
+ 32, 18},
+ /* (5/2 3 3) (I2a) */
+
+ /* 35 */ {"3|5/2 3", "Small Ditrigonal Icosidodecahedron",
+ "Small Triambic Icosahedron",
+ "Icosahedral (I[2a])",
+ "",
+ "",
+ 39, 70},
+
+ /* 36 */ {"5/2 3|3", "Small Icosicosidodecahedron",
+ "Small Icosacronic Hexecontahedron",
+ "Icosahedral (I[2a])",
+ "",
+ "",
+ 40, 71},
+
+ /* 37 */ {"|5/2 3 3", "Small Snub Icosicosidodecahedron",
+ "Small Hexagonal Hexecontahedron",
+ "Icosahedral (I[2a])",
+ "",
+ "",
+ 41, 110},
+ /* (3/2 5 5) (I2b) */
+
+ /* 38 */ {"3/2 5|5", "Small Dodecicosidodecahedron",
+ "Small Dodecacronic Hexecontahedron",
+ "Icosahedral (I[2b])",
+ "",
+ "",
+ 42, 72},
+ /* (2 5/2 5) (I3) */
+
+ /* 39 */ {"5|2 5/2", "Small Stellated Dodecahedron",
+ "Great Dodecahedron",
+ "Icosahedral (I[3])",
+ "Truncated Kepler-Poinsot Solid",
+ "",
+ 43, 20},
+
+ /* 40 */ {"5/2|2 5", "Great Dodecahedron",
+ "Small Stellated Dodecahedron",
+ "Icosahedral (I[3])",
+ "",
+ "",
+ 44, 21},
+
+ /* 41 */ {"2|5/2 5", "Great Dodecadodecahedron",
+ "Medial Rhombic Triacontahedron",
+ "Icosahedral (I[3])",
+ "",
+ "",
+ 45, 73},
+
+ /* 42 */ {"2 5/2|5", "Truncated Great Dodecahedron",
+ "Small Stellapentakisdodecahedron",
+ "Icosahedral (I[3])",
+ "Truncated Kepler-Poinsot Solid",
+ "",
+ 47, 75},
+
+ /* 43 */ {"5/2 5|2", "Rhombidodecadodecahedron",
+ "Medial Deltoidal Hexecontahedron",
+ "Icosahedral (I[3])",
+ "",
+ "",
+ 48, 76},
+
+ /* 44 */ {"2 5/2 5|", "Small Rhombidodecahedron",
+ "Small Rhombidodecacron",
+ "Icosahedral (I[3])",
+ "",
+ "",
+ 46, 74},
+
+ /* 45 */ {"|2 5/2 5", "Snub Dodecadodecahedron",
+ "Medial Pentagonal Hexecontahedron",
+ "Icosahedral (I[3])",
+ "",
+ "",
+ 49, 111},
+ /* (5/3 3 5) (I4) */
+
+ /* 46 */ {"3|5/3 5", "Ditrigonal Dodecadodecahedron",
+ "Medial Triambic Icosahedron",
+ "Icosahedral (I[4])",
+ "",
+ "",
+ 53, 80},
+
+ /* 47 */ {"3 5|5/3", "Great Ditrigonal Dodecicosidodecahedron",
+ "Great Ditrigonal Dodecacronic Hexecontahedron",
+ "Icosahedral (I[4])",
+ "",
+ "",
+ 54, 81},
+
+ /* 48 */ {"5/3 3|5", "Small Ditrigonal Dodecicosidodecahedron",
+ "Small Ditrigonal Dodecacronic Hexecontahedron",
+ "Icosahedral (I[4])",
+ "",
+ "",
+ 55, 82},
+
+ /* 49 */ {"5/3 5|3", "Icosidodecadodecahedron",
+ "Medial Icosacronic Hexecontahedron",
+ "Icosahedral (I[4])",
+ "",
+ "",
+ 56, 83},
+
+ /* 50 */ {"5/3 3 5|", "Icositruncated Dodecadodecahedron",
+ "Tridyakisicosahedron",
+ "Icosahedral (I[4])",
+ "",
+ "",
+ 57, 84},
+
+ /* 51 */ {"|5/3 3 5", "Snub Icosidodecadodecahedron",
+ "Medial Hexagonal Hexecontahedron",
+ "Icosahedral (I[4])",
+ "",
+ "",
+ 58, 112},
+ /* (3/2 3 5) (I6b) */
+
+ /* 52 */ {"3/2|3 5", "Great Ditrigonal Icosidodecahedron",
+ "Great Triambic Icosahedron",
+ "Icosahedral (I[6b])",
+ "",
+ "",
+ 61, 87},
+
+ /* 53 */ {"3/2 5|3", "Great Icosicosidodecahedron",
+ "Great Icosacronic Hexecontahedron",
+ "Icosahedral (I[6b])",
+ "",
+ "",
+ 62, 88},
+
+ /* 54 */ {"3/2 3|5", "Small Icosihemidodecahedron",
+ "Small Icosihemidodecacron",
+ "Icosahedral (I[6b])",
+ "",
+ "",
+ 63, 89},
+
+ /* 55 */ {"3/2 3 5|", "Small Dodecicosahedron",
+ "Small Dodecicosacron",
+ "Icosahedral (I[6b])",
+ "",
+ "",
+ 64, 90},
+ /* (5/4 5 5) (I6c) */
+
+ /* 56 */ {"5/4 5|5", "Small Dodecahemidodecahedron",
+ "Small Dodecahemidodecacron",
+ "Icosahedral (I[6c])",
+ "",
+ "",
+ 65, 91},
+ /* (2 5/2 3) (I7) */
+
+ /* 57 */ {"3|2 5/2", "Great Stellated Dodecahedron",
+ "Great Icosahedron",
+ "Icosahedral (I[7])",
+ "",
+ "",
+ 68, 22},
+
+ /* 58 */ {"5/2|2 3", "Great Icosahedron",
+ "Great Stellated Dodecahedron",
+ "Icosahedral (I[7])",
+ "",
+ "",
+ 69, 41},
+
+ /* 59 */ {"2|5/2 3", "Great Icosidodecahedron",
+ "Great Rhombic Triacontahedron",
+ "Icosahedral (I[7])",
+ "Truncated Kepler-Poinsot Solid",
+ "",
+ 70, 94},
+
+ /* 60 */ {"2 5/2|3", "Great Truncated Icosahedron",
+ "Great Stellapentakisdodecahedron",
+ "Icosahedral (I[7])",
+ "Truncated Kepler-Poinsot Solid",
+ "",
+ 71, 95},
+
+ /* 61 */ {"2 5/2 3|", "Rhombicosahedron",
+ "Rhombicosacron",
+ "Icosahedral (I[7])",
+ "",
+ "",
+ 72, 96},
+
+ /* 62 */ {"|2 5/2 3", "Great Snub Icosidodecahedron",
+ "Great Pentagonal Hexecontahedron",
+ "Icosahedral (I[7])",
+ "",
+ "",
+ 73, 113},
+ /* (5/3 2 5) (I9) */
+
+ /* 63 */ {"2 5|5/3", "Small Stellated Truncated Dodecahedron",
+ "Great Pentakisdodekahedron",
+ "Icosahedral (I[9])",
+ "",
+ "",
+ 74, 97},
+
+ /* 64 */ {"5/3 2 5|", "Truncated Dodecadodecahedron",
+ "Medial Disdyakistriacontahedron",
+ "Icosahedral (I[9])",
+ "",
+ "",
+ 75, 98},
+
+ /* 65 */ {"|5/3 2 5", "Inverted Snub Dodecadodecahedron",
+ "Medial Inverted Pentagonal Hexecontahedron",
+ "Icosahedral (I[9])",
+ "",
+ "",
+ 76, 114},
+ /* (5/3 5/2 3) (I10a) */
+
+ /* 66 */ {"5/2 3|5/3", "Great Dodecicosidodecahedron",
+ "Great Dodecacronic Hexecontahedron",
+ "Icosahedral (I[10a])",
+ "",
+ "",
+ 77, 99},
+
+ /* 67 */ {"5/3 5/2|3", "Small Dodecahemicosahedron",
+ "Small Dodecahemicosacron",
+ "Icosahedral (I[10a])",
+ "",
+ "",
+ 78, 100},
+
+ /* 68 */ {"5/3 5/2 3|", "Great Dodecicosahedron",
+ "Great Dodecicosacron",
+ "Icosahedral (I[10a])",
+ "",
+ "",
+ 79, 101},
+
+ /* 69 */ {"|5/3 5/2 3", "Great Snub Dodecicosidodecahedron",
+ "Great Hexagonal Hexecontahedron",
+ "Icosahedral (I[10a])",
+ "",
+ "",
+ 80, 115},
+ /* (5/4 3 5) (I10b) */
+
+ /* 70 */ {"5/4 5|3", "Great Dodecahemicosahedron",
+ "Great Dodecahemicosacron",
+ "Icosahedral (I[10b])",
+ "",
+ "",
+ 81, 102},
+ /* (5/3 2 3) (I13) */
+
+ /* 71 */ {"2 3|5/3", "Great Stellated Truncated Dodecahedron",
+ "Great Triakisicosahedron",
+ "Icosahedral (I[13])",
+ "",
+ "",
+ 83, 104},
+
+ /* 72 */ {"5/3 3|2", "Great Rhombicosidodecahedron",
+ "Great Deltoidal Hexecontahedron",
+ "Icosahedral (I[13])",
+ "",
+ "",
+ 84, 105},
+
+ /* 73 */ {"5/3 2 3|", "Great Truncated Icosidodecahedron",
+ "Great Disdyakistriacontahedron",
+ "Icosahedral (I[13])",
+ "",
+ "",
+ 87, 108},
+
+ /* 74 */ {"|5/3 2 3", "Great Inverted Snub Icosidodecahedron",
+ "Great Inverted Pentagonal Hexecontahedron",
+ "Icosahedral (I[13])",
+ "",
+ "",
+ 88, 116},
+ /* (5/3 5/3 5/2) (I18a) */
+
+ /* 75 */ {"5/3 5/2|5/3", "Great Dodecahemidodecahedron",
+ "Great Dodecahemidodecacron",
+ "Icosahedral (I[18a])",
+ "",
+ "",
+ 86, 107},
+ /* (3/2 5/3 3) (I18b) */
+
+ /* 76 */ {"3/2 3|5/3", "Great Icosihemidodecahedron",
+ "Great Icosihemidodecacron",
+ "Icosahedral (I[18b])",
+ "",
+ "",
+ 85, 106},
+ /* (3/2 3/2 5/3) (I22) */
+
+ /* 77 */ {"|3/2 3/2 5/2","Small Retrosnub Icosicosidodecahedron",
+ "Small Hexagrammic Hexecontahedron",
+ "Icosahedral (I[22])",
+ "",
+ "",
+ 91, 118},
+ /* (3/2 5/3 2) (I23) */
+
+ /* 78 */ {"3/2 5/3 2|", "Great Rhombidodecahedron",
+ "Great Rhombidodecacron",
+ "Icosahedral (I[23])",
+ "",
+ "",
+ 89, 109},
+
+ /* 79 */ {"|3/2 5/3 2", "Great Retrosnub Icosidodecahedron",
+ "Great Pentagrammic Hexecontahedron",
+ "Icosahedral (I[23])",
+ "",
+ "",
+ 90, 117},
+
+ /****************************************************************************
+ * Last But Not Least
+ ***************************************************************************/
+
+ /* 80 */ {"3/2 5/3 3 5/2", "Great Dirhombicosidodecahedron",
+ "Great Dirhombicosidodecacron",
+ "Non-Wythoffian",
+ "",
+ "",
+ 92, 119}
+};
+
+static int last_uniform = sizeof (uniform) / sizeof (uniform[0]);
+
+
+
+static int unpacksym(char *sym, Polyhedron *P);
+static int moebius(Polyhedron *P);
+static int decompose(Polyhedron *P);
+static int guessname(Polyhedron *P);
+static int newton(Polyhedron *P, int need_approx);
+static int exceptions(Polyhedron *P);
+static int count(Polyhedron *P);
+static int configuration(Polyhedron *P);
+static int vertices(Polyhedron *P);
+static int faces(Polyhedron *P);
+static int edgelist(Polyhedron *P);
+
+static Polyhedron *
+kaleido(char *sym, int need_coordinates, int need_edgelist, int need_approx,
+ int just_list)
+{
+ Polyhedron *P;
+ /*
+ * Allocate a Polyhedron structure P.
+ */
+ if (!(P = polyalloc()))
+ return 0;
+ /*
+ * Unpack input symbol into P.
+ */
+ if (!unpacksym(sym, P))
+ return 0;
+ /*
+ * Find Mebius triangle, its density and Euler characteristic.
+ */
+ if (!moebius(P))
+ return 0;
+ /*
+ * Decompose Schwarz triangle.
+ */
+ if (!decompose(P))
+ return 0;
+ /*
+ * Find the names of the polyhedron and its dual.
+ */
+ if (!guessname(P))
+ return 0;
+ if (just_list)
+ return P;
+ /*
+ * Solve Fundamental triangles, optionally printing approximations.
+ */
+ if (!newton(P,need_approx))
+ return 0;
+ /*
+ * Deal with exceptional polyhedra.
+ */
+ if (!exceptions(P))
+ return 0;
+ /*
+ * Count edges and faces, update density and characteristic if needed.
+ */
+ if (!count(P))
+ return 0;
+ /*
+ * Generate printable vertex configuration.
+ */
+ if (!configuration(P))
+ return 0;
+ /*
+ * Compute coordinates.
+ */
+ if (!need_coordinates && !need_edgelist)
+ return P;
+ if (!vertices(P))
+ return 0;
+ if (!faces (P))
+ return 0;
+ /*
+ * Compute edgelist.
+ */
+ if (!need_edgelist)
+ return P;
+ if (!edgelist(P))
+ return 0;
+ return P;
+}
+
+/*
+ * Allocate a blank Polyhedron structure and initialize some of its nonblank
+ * fields.
+ *
+ * Array and matrix field are allocated when needed.
+ */
+static Polyhedron *
+polyalloc()
+{
+ Polyhedron *P;
+ Calloc(P, 1, Polyhedron);
+ P->index = -1;
+ P->even = -1;
+ P->K = 2;
+ return P;
+}
+
+/*
+ * Free the struture allocated by polyalloc(), as well as all the array and
+ * matrix fields.
+ */
+static void
+polyfree(Polyhedron *P)
+{
+ Free(P->Fi);
+ Free(P->n);
+ Free(P->m);
+ Free(P->gamma);
+ Free(P->rot);
+ Free(P->snub);
+ Free(P->firstrot);
+ Free(P->anti);
+ Free(P->ftype);
+ Free(P->polyform);
+ Free(P->config);
+ if (P->index < 0) {
+ Free(P->name);
+ Free(P->dual_name);
+ }
+ Free(P->v);
+ Free(P->f);
+ Matfree(P->e, 2);
+ Matfree(P->dual_e, 2);
+ Matfree(P->incid, P->M);
+ Matfree(P->adj, P->M);
+ free(P);
+}
+
+static void *
+matalloc(int rows, int row_size)
+{
+ void **mat;
+ int i = 0;
+ if (!(mat = malloc(rows * sizeof (void *))))
+ return 0;
+ while ((mat[i] = malloc(row_size)) && ++i < rows)
+ ;
+ if (i == rows)
+ return (void *)mat;
+ while (--i >= 0)
+ free(mat[i]);
+ free(mat);
+ return 0;
+}
+
+static void
+matfree(void *mat, int rows)
+{
+ while (--rows >= 0)
+ free(((void **)mat)[rows]);
+ free(mat);
+}
+
+/*
+ * compute the mathematical modulus function.
+ */
+static int
+mod (int i, int j)
+{
+ return (i%=j)>=0?i:j<0?i-j:i+j;
+}
+
+
+/*
+ * Find the numerator and the denominator using the Euclidean algorithm.
+ */
+static void
+frac(double x)
+{
+ static Fraction zero = {0,1}, inf = {1,0};
+ Fraction r0, r;
+ long f;
+ double s = x;
+ r = zero;
+ frax = inf;
+ for (;;) {
+ if (fabs(s) > (double) MAXLONG)
+ return;
+ f = (long) floor (s);
+ r0 = r;
+ r = frax;
+ frax.n = frax.n * f + r0.n;
+ frax.d = frax.d * f + r0.d;
+ if (x == (double)frax.n/(double)frax.d)
+ return;
+ s = 1 / (s - f);
+ }
+}
+
+
+/*
+ * Unpack input symbol: Wythoff symbol or an index to uniform[]. The symbol is
+ * a # followed by a number, or a three fractions and a bar in some order. We
+ * allow no bars only if it result from the input symbol #80.
+ */
+static int
+unpacksym(char *sym, Polyhedron *P)
+{
+ int i = 0, n, d, bars = 0;
+ char c;
+ while ((c = *sym++) && isspace(c))
+ ;
+ if (!c) Err("no data");
+ if (c == '#') {
+ while ((c = *sym++) && isspace(c))
+ ;
+ if (!c)
+ Err("no digit after #");
+ if (!isdigit(c))
+ Err("not a digit");
+ n = c - '0';
+ while ((c = *sym++) && isdigit(c))
+ n = n * 10 + c - '0';
+ if (!n)
+ Err("zero index");
+ if (n > last_uniform)
+ Err("index too big");
+ sym--;
+ while ((c = *sym++) && isspace(c))
+ ;
+ if (c)
+ Err("data exceeded");
+ sym = uniform[P->index = n - 1].Wythoff;
+ } else
+ sym--;
+
+ for (;;) {
+ while ((c = *sym++) && isspace(c))
+ ;
+ if (!c) {
+ if (i == 4 && (bars || P->index == last_uniform - 1))
+ return 1;
+ if (!bars)
+ Err("no bars");
+ Err("not enough fractions");
+ }
+ if (i == 4)
+ Err("data exceeded");
+ if (c == '|'){
+ if (++bars > 1)
+ Err("too many bars");
+ P->p[i++] = 0;
+ continue;
+ }
+ if (!isdigit(c))
+ Err("not a digit");
+ n = c - '0';
+ while ((c = *sym++) && isdigit(c))
+ n = n * 10 + c - '0';
+ if (c && isspace (c))
+ while ((c = *sym++) && isspace(c))
+ ;
+ if (c != '/') {
+ sym--;
+ if ((P->p[i++] = n) <= 1)
+ Err("fraction<=1");
+ continue;
+ }
+ while ((c = *sym++) && isspace(c))
+ ;
+ if (!c || !isdigit(c))
+ return 0;
+ d = c - '0';
+ while ((c = *sym++) && isdigit(c))
+ d = d * 10 + c - '0';
+ if (!d)
+ Err("zero denominator");
+ sym--;
+ if ((P->p[i++] = (double) n / d) <= 1)
+ Err("fraction<=1");
+ }
+}
+
+/*
+ * Using Wythoff symbol (p|qr, pq|r, pqr| or |pqr), find the Moebius triangle
+ * (2 3 K) (or (2 2 n)) of the Schwarz triangle (pqr), the order g of its
+ * symmetry group, its Euler characteristic chi, and its covering density D.
+ * g is the number of copies of (2 3 K) covering the sphere, i.e.,
+ *
+ * g * pi * (1/2 + 1/3 + 1/K - 1) = 4 * pi
+ *
+ * D is the number of times g copies of (pqr) cover the sphere, i.e.
+ *
+ * D * 4 * pi = g * pi * (1/p + 1/q + 1/r - 1)
+ *
+ * chi is V - E + F, where F = g is the number of triangles, E = 3*g/2 is the
+ * number of triangle edges, and V = Vp+ Vq+ Vr, with Vp = g/(2*np) being the
+ * number of vertices with angle pi/p (np is the numerator of p).
+ */
+static int
+moebius(Polyhedron *P)
+{
+ int twos = 0, j, len = 1;
+ /*
+ * Arrange Wythoff symbol in a presentable form. In the same time check the
+ * restrictions on the three fractions: They all have to be greater then one,
+ * and the numerators 4 or 5 cannot occur together. We count the ocurrences
+ * of 2 in `two', and save the largest numerator in `P->K', since they
+ * reflect on the symmetry group.
+ */
+ P->K = 2;
+ if (P->index == last_uniform - 1) {
+ Malloc(P->polyform, ++len, char);
+ strcpy(P->polyform, "|");
+ } else
+ Calloc(P->polyform, len, char);
+ for (j = 0; j < 4; j++) {
+ if (P->p[j]) {
+ char *s;
+ Sprintfrac(s, P->p[j]);
+ if (j && P->p[j-1]) {
+ Realloc(P->polyform, len += strlen (s) + 1, char);
+ strcat(P->polyform, " ");
+ } else
+ Realloc (P->polyform, len += strlen (s), char);
+ strcat(P->polyform, s);
+ free(s);
+ if (P->p[j] != 2) {
+ int k;
+ if ((k = numerator (P->p[j])) > P->K) {
+ if (P->K == 4)
+ break;
+ P->K = k;
+ } else if (k < P->K && k == 4)
+ break;
+ } else
+ twos++;
+ } else {
+ Realloc(P->polyform, ++len, char);
+ strcat(P->polyform, "|");
+ }
+ }
+ /*
+ * Find the symmetry group P->K (where 2, 3, 4, 5 represent the dihedral,
+ * tetrahedral, octahedral and icosahedral groups, respectively), and its
+ * order P->g.
+ */
+ if (twos >= 2) {/* dihedral */
+ P->g = 4 * P->K;
+ P->K = 2;
+ } else {
+ if (P->K > 5)
+ Err("numerator too large");
+ P->g = 24 * P->K / (6 - P->K);
+ }
+ /*
+ * Compute the nominal density P->D and Euler characteristic P->chi.
+ * In few exceptional cases, these values will be modified later.
+ */
+ if (P->index != last_uniform - 1) {
+ int i;
+ P->D = P->chi = - P->g;
+ for (j = 0; j < 4; j++) if (P->p[j]) {
+ P->chi += i = P->g / numerator(P->p[j]);
+ P->D += i * denominator(P->p[j]);
+ }
+ P->chi /= 2;
+ P->D /= 4;
+ if (P->D <= 0)
+ Err("nonpositive density");
+ }
+ return 1;
+}
+
+/*
+ * Decompose Schwarz triangle into N right triangles and compute the vertex
+ * count V and the vertex valency M. V is computed from the number g of
+ * Schwarz triangles in the cover, divided by the number of triangles which
+ * share a vertex. It is halved for one-sided polyhedra, because the
+ * kaleidoscopic construction really produces a double orientable covering of
+ * such polyhedra. All q' q|r are of the "hemi" type, i.e. have equatorial {2r}
+ * faces, and therefore are (except 3/2 3|3 and the dihedra 2 2|r) one-sided. A
+ * well known example is 3/2 3|4, the "one-sided heptahedron". Also, all p q r|
+ * with one even denominator have a crossed parallelogram as a vertex figure,
+ * and thus are one-sided as well.
+ */
+static int
+decompose(Polyhedron *P)
+{
+ int j, J, *s, *t;
+ if (!P->p[1]) { /* p|q r */
+ P->N = 2;
+ P->M = 2 * numerator(P->p[0]);
+ P->V = P->g / P->M;
+ Malloc(P->n, P->N, double);
+ Malloc(P->m, P->N, double);
+ Malloc(P->rot, P->M, int);
+ s = P->rot;
+ for (j = 0; j < 2; j++) {
+ P->n[j] = P->p[j+2];
+ P->m[j] = P->p[0];
+ }
+ for (j = P->M / 2; j--;) {
+ *s++ = 0;
+ *s++ = 1;
+ }
+ } else if (!P->p[2]) { /* p q|r */
+ P->N = 3;
+ P->M = 4;
+ P->V = P->g / 2;
+ Malloc(P->n, P->N, double);
+ Malloc(P->m, P->N, double);
+ Malloc(P->rot, P->M, int);
+ s = P->rot;
+ P->n[0] = 2 * P->p[3];
+ P->m[0] = 2;
+ for (j = 1; j < 3; j++) {
+ P->n[j] = P->p[j-1];
+ P->m[j] = 1;
+ *s++ = 0;
+ *s++ = j;
+ }
+ if (fabs(P->p[0] - compl (P->p[1])) < DBL_EPSILON) {/* p = q' */
+ /* P->p[0]==compl(P->p[1]) should work. However, MSDOS
+ * yeilds a 7e-17 difference! Reported by Jim Buddenhagen
+ * <jb1556@daditz.sbc.com> */
+ P->hemi = 1;
+ P->D = 0;
+ if (P->p[0] != 2 && !(P->p[3] == 3 && (P->p[0] == 3 ||
+ P->p[1] == 3))) {
+ P->onesided = 1;
+ P->V /= 2;
+ P->chi /= 2;
+ }
+ }
+ } else if (!P->p[3]) { /* p q r| */
+ P->M = P->N = 3;
+ P->V = P->g;
+ Malloc(P->n, P->N, double);
+ Malloc(P->m, P->N, double);
+ Malloc(P->rot, P->M, int);
+ s = P->rot;
+ for (j = 0; j < 3; j++) {
+ if (!(denominator(P->p[j]) % 2)) {
+ /* what happens if there is more then one even denominator? */
+ if (P->p[(j+1)%3] != P->p[(j+2)%3]) { /* needs postprocessing */
+ P->even = j;/* memorize the removed face */
+ P->chi -= P->g / numerator(P->p[j]) / 2;
+ P->onesided = 1;
+ P->D = 0;
+ } else {/* for p = q we get a double 2 2r|p */
+ /* noted by Roman Maeder <maeder@inf.ethz.ch> for 4 4 3/2| */
+ /* Euler characteristic is still wrong */
+ P->D /= 2;
+ }
+ P->V /= 2;
+ }
+ P->n[j] = 2 * P->p[j];
+ P->m[j] = 1;
+ *s++ = j;
+ }
+ } else { /* |p q r - snub polyhedron */
+ P->N = 4;
+ P->M = 6;
+ P->V = P->g / 2;/* Only "white" triangles carry a vertex */
+ Malloc(P->n, P->N, double);
+ Malloc(P->m, P->N, double);
+ Malloc(P->rot, P->M, int);
+ Malloc(P->snub, P->M, int);
+ s = P->rot;
+ t = P->snub;
+ P->m[0] = P->n[0] = 3;
+ for (j = 1; j < 4; j++) {
+ P->n[j] = P->p[j];
+ P->m[j] = 1;
+ *s++ = 0;
+ *s++ = j;
+ *t++ = 1;
+ *t++ = 0;
+ }
+ }
+ /*
+ * Sort the fundamental triangles (using bubble sort) according to decreasing
+ * n[i], while pushing the trivial triangles (n[i] = 2) to the end.
+ */
+ J = P->N - 1;
+ while (J) {
+ int last;
+ last = J;
+ J = 0;
+ for (j = 0; j < last; j++) {
+ if ((P->n[j] < P->n[j+1] || P->n[j] == 2) && P->n[j+1] != 2) {
+ int i;
+ double temp;
+ temp = P->n[j];
+ P->n[j] = P->n[j+1];
+ P->n[j+1] = temp;
+ temp = P->m[j];
+ P->m[j] = P->m[j+1];
+ P->m[j+1] = temp;
+ for (i = 0; i < P->M; i++) {
+ if (P->rot[i] == j)
+ P->rot[i] = j+1;
+ else if (P->rot[i] == j+1)
+ P->rot[i] = j;
+ }
+ if (P->even != -1) {
+ if (P->even == j)
+ P->even = j+1;
+ else if (P->even == j+1)
+ P->even = j;
+ }
+ J = j;
+ }
+ }
+ }
+ /*
+ * Get rid of repeated triangles.
+ */
+ for (J = 0; J < P->N && P->n[J] != 2;J++) {
+ int k, i;
+ for (j = J+1; j < P->N && P->n[j]==P->n[J]; j++)
+ P->m[J] += P->m[j];
+ k = j - J - 1;
+ if (k) {
+ for (i = j; i < P->N; i++) {
+ P->n[i - k] = P->n[i];
+ P->m[i - k] = P->m[i];
+ }
+ P->N -= k;
+ for (i = 0; i < P->M; i++) {
+ if (P->rot[i] >= j)
+ P->rot[i] -= k;
+ else if (P->rot[i] > J)
+ P->rot[i] = J;
+ }
+ if (P->even >= j)
+ P->even -= k;
+ }
+ }
+ /*
+ * Get rid of trivial triangles.
+ */
+ if (!J)
+ J = 1; /* hosohedron */
+ if (J < P->N) {
+ int i;
+ P->N = J;
+ for (i = 0; i < P->M; i++) {
+ if (P->rot[i] >= P->N) {
+ for (j = i + 1; j < P->M; j++) {
+ P->rot[j-1] = P->rot[j];
+ if (P->snub)
+ P->snub[j-1] = P->snub[j];
+ }
+ P->M--;
+ }
+ }
+ }
+ /*
+ * Truncate arrays
+ */
+ Realloc(P->n, P->N, double);
+ Realloc(P->m, P->N, double);
+ Realloc(P->rot, P->M, int);
+ if (P->snub)
+ Realloc(P->snub, P->M, int);
+ return 1;
+}
+
+
+static int dihedral(Polyhedron *P, char *name, char *dual_name);
+
+
+/*
+ * Get the polyhedron name, using standard list or guesswork. Ideally, we
+ * should try to locate the Wythoff symbol in the standard list (unless, of
+ * course, it is dihedral), after doing few normalizations, such as sorting
+ * angles and splitting isoceles triangles.
+ */
+static int
+guessname(Polyhedron *P)
+{
+ if (P->index != -1) {/* tabulated */
+ P->name = uniform[P->index].name;
+ P->dual_name = uniform[P->index].dual;
+ P->group = uniform[P->index].group;
+ P->class = uniform[P->index].class;
+ P->dual_class = uniform[P->index].dual_class;
+ return 1;
+ } else if (P->K == 2) {/* dihedral nontabulated */
+ if (!P->p[0]) {
+ if (P->N == 1) {
+ Malloc(P->name, sizeof ("Octahedron"), char);
+ Malloc(P->dual_name, sizeof ("Cube"), char);
+ strcpy(P->name, "Octahedron");
+ strcpy(P->dual_name, "Cube");
+ return 1;
+ }
+ P->gon = P->n[0] == 3 ? P->n[1] : P->n[0];
+ if (P->gon >= 2)
+ return dihedral(P, "Antiprism", "Deltohedron");
+ else
+ return dihedral(P, "Crossed Antiprism", "Concave Deltohedron");
+ } else if (!P->p[3] ||
+ (!P->p[2] &&
+ P->p[3] == 2)) {
+ if (P->N == 1) {
+ Malloc(P->name, sizeof("Cube"), char);
+ Malloc(P->dual_name, sizeof("Octahedron"), char);
+ strcpy(P->name, "Cube");
+ strcpy(P->dual_name, "Octahedron");
+ return 1;
+ }
+ P->gon = P->n[0] == 4 ? P->n[1] : P->n[0];
+ return dihedral(P, "Prism", "Dipyramid");
+ } else if (!P->p[1] && P->p[0] != 2) {
+ P->gon = P->m[0];
+ return dihedral(P, "Hosohedron", "Dihedron");
+ } else {
+ P->gon = P->n[0];
+ return dihedral(P, "Dihedron", "Hosohedron");
+ }
+ } else {/* other nontabulated */
+ static char *pre[] = {"Tetr", "Oct", "Icos"};
+ Malloc(P->name, 50, char);
+ Malloc(P->dual_name, 50, char);
+ sprintf(P->name, "%sahedral ", pre[P->K - 3]);
+ if (P->onesided)
+ strcat (P->name, "One-Sided ");
+ else if (P->D == 1)
+ strcat(P->name, "Convex ");
+ else
+ strcat(P->name, "Nonconvex ");
+ strcpy(P->dual_name, P->name);
+ strcat(P->name, "Isogonal Polyhedron");
+ strcat(P->dual_name, "Isohedral Polyhedron");
+ Realloc(P->name, strlen (P->name) + 1, char);
+ Realloc(P->dual_name, strlen (P->dual_name) + 1, char);
+ return 1;
+ }
+}
+
+static int
+dihedral(Polyhedron *P, char *name, char *dual_name)
+{
+ char *s;
+ int i;
+ Sprintfrac(s, P->gon < 2 ? compl (P->gon) : P->gon);
+ i = strlen(s) + sizeof ("-gonal ");
+ Malloc(P->name, i + strlen (name), char);
+ Malloc(P->dual_name, i + strlen (dual_name), char);
+ sprintf(P->name, "%s-gonal %s", s, name);
+ sprintf(P->dual_name, "%s-gonal %s", s, dual_name);
+ free(s);
+ return 1;
+}
+
+/*
+ * Solve the fundamental right spherical triangles.
+ * If need_approx is set, print iterations on standard error.
+ */
+static int
+newton(Polyhedron *P, int need_approx)
+{
+ /*
+ * First, we find initial approximations.
+ */
+ int j;
+ double cosa;
+ Malloc(P->gamma, P->N, double);
+ if (P->N == 1) {
+ P->gamma[0] = M_PI / P->m[0];
+ return 1;
+ }
+ for (j = 0; j < P->N; j++)
+ P->gamma[j] = M_PI / 2 - M_PI / P->n[j];
+ errno = 0; /* may be non-zero from some reason */
+ /*
+ * Next, iteratively find closer approximations for gamma[0] and compute
+ * other gamma[j]'s from Napier's equations.
+ */
+ if (need_approx)
+ fprintf(stderr, "Solving %s\n", P->polyform);
+ for (;;) {
+ double delta = M_PI, sigma = 0;
+ for (j = 0; j < P->N; j++) {
+ if (need_approx)
+ fprintf(stderr, "%-20.15f", P->gamma[j]);
+ delta -= P->m[j] * P->gamma[j];
+ }
+ if (need_approx)
+ printf("(%g)\n", delta);
+ if (fabs(delta) < 11 * DBL_EPSILON)
+ return 1;
+ /* On a RS/6000, fabs(delta)/DBL_EPSILON may occilate between 8 and
+ * 10. Reported by David W. Sanderson <dws@ssec.wisc.edu> */
+ for (j = 0; j < P->N; j++)
+ sigma += P->m[j] * tan(P->gamma[j]);
+ P->gamma[0] += delta * tan(P->gamma[0]) / sigma;
+ if (P->gamma[0] < 0 || P->gamma[0] > M_PI)
+ Err("gamma out of bounds");
+ cosa = cos(M_PI / P->n[0]) / sin(P->gamma[0]);
+ for (j = 1; j < P->N; j++)
+ P->gamma[j] = asin(cos(M_PI / P->n[j]) / cosa);
+ if (errno)
+ Err(strerror(errno));
+ }
+}
+
+/*
+ * Postprocess pqr| where r has an even denominator (cf. Coxeter &al. Sec.9).
+ * Remove the {2r} and add a retrograde {2p} and retrograde {2q}.
+ */
+static int
+exceptions(Polyhedron *P)
+{
+ int j;
+ if (P->even != -1) {
+ P->M = P->N = 4;
+ Realloc(P->n, P->N, double);
+ Realloc(P->m, P->N, double);
+ Realloc(P->gamma, P->N, double);
+ Realloc(P->rot, P->M, int);
+ for (j = P->even + 1; j < 3; j++) {
+ P->n[j-1] = P->n[j];
+ P->gamma[j-1] = P->gamma[j];
+ }
+ P->n[2] = compl(P->n[1]);
+ P->gamma[2] = - P->gamma[1];
+ P->n[3] = compl(P->n[0]);
+ P->m[3] = 1;
+ P->gamma[3] = - P->gamma[0];
+ P->rot[0] = 0;
+ P->rot[1] = 1;
+ P->rot[2] = 3;
+ P->rot[3] = 2;
+ }
+
+ /*
+ * Postprocess the last polyhedron |3/2 5/3 3 5/2 by taking a |5/3 3 5/2,
+ * replacing the three snub triangles by four equatorial squares and adding
+ * the missing {3/2} (retrograde triangle, cf. Coxeter &al. Sec. 11).
+ */
+ if (P->index == last_uniform - 1) {
+ P->N = 5;
+ P->M = 8;
+ Realloc(P->n, P->N, double);
+ Realloc(P->m, P->N, double);
+ Realloc(P->gamma, P->N, double);
+ Realloc(P->rot, P->M, int);
+ Realloc(P->snub, P->M, int);
+ P->hemi = 1;
+ P->D = 0;
+ for (j = 3; j; j--) {
+ P->m[j] = 1;
+ P->n[j] = P->n[j-1];
+ P->gamma[j] = P->gamma[j-1];
+ }
+ P->m[0] = P->n[0] = 4;
+ P->gamma[0] = M_PI / 2;
+ P->m[4] = 1;
+ P->n[4] = compl(P->n[1]);
+ P->gamma[4] = - P->gamma[1];
+ for (j = 1; j < 6; j += 2) P->rot[j]++;
+ P->rot[6] = 0;
+ P->rot[7] = 4;
+ P->snub[6] = 1;
+ P->snub[7] = 0;
+ }
+ return 1;
+}
+
+/*
+ * Compute edge and face counts, and update D and chi. Update D in the few
+ * cases the density of the polyhedron is meaningful but different than the
+ * density of the corresponding Schwarz triangle (cf. Coxeter &al., p. 418 and
+ * p. 425).
+ * In these cases, spherical faces of one type are concave (bigger than a
+ * hemisphere), and the actual density is the number of these faces less the
+ * computed density. Note that if j != 0, the assignment gamma[j] = asin(...)
+ * implies gamma[j] cannot be obtuse. Also, compute chi for the only
+ * non-Wythoffian polyhedron.
+ */
+static int
+count(Polyhedron *P)
+{
+ int j, temp;
+ Malloc(P->Fi, P->N, int);
+ for (j = 0; j < P->N; j++) {
+ P->E += temp = P->V * numerator(P->m[j]);
+ P->F += P->Fi[j] = temp / numerator(P->n[j]);
+ }
+ P->E /= 2;
+ if (P->D && P->gamma[0] > M_PI / 2)
+ P->D = P->Fi[0] - P->D;
+ if (P->index == last_uniform - 1)
+ P->chi = P->V - P->E + P->F;
+ return 1;
+}
+
+/*
+ * Generate a printable vertex configuration symbol.
+ */
+static int
+configuration(Polyhedron *P)
+{
+ int j, len = 2;
+ for (j = 0; j < P->M; j++) {
+ char *s;
+ Sprintfrac(s, P->n[P->rot[j]]);
+ len += strlen (s) + 2;
+ if (!j) {
+ Malloc(P->config, len, char);
+/* strcpy(P->config, "(");*/
+ strcpy(P->config, "");
+ } else {
+ Realloc(P->config, len, char);
+ strcat(P->config, ", ");
+ }
+ strcat(P->config, s);
+ free(s);
+ }
+/* strcat (P->config, ")");*/
+ if ((j = denominator (P->m[0])) != 1) {
+ char s[MAXDIGITS + 2];
+ sprintf(s, "/%d", j);
+ Realloc(P->config, len + strlen (s), char);
+ strcat(P->config, s);
+ }
+ return 1;
+}
+
+/*
+ * Compute polyhedron vertices and vertex adjecency lists.
+ * The vertices adjacent to v[i] are v[adj[0][i], v[adj[1][i], ...
+ * v[adj[M-1][i], ordered counterclockwise. The algorith is a BFS on the
+ * vertices, in such a way that the vetices adjacent to a givem vertex are
+ * obtained from its BFS parent by a cyclic sequence of rotations. firstrot[i]
+ * points to the first rotaion in the sequence when applied to v[i]. Note that
+ * for non-snub polyhedra, the rotations at a child are opposite in sense when
+ * compared to the rotations at the parent. Thus, we fill adj[*][i] from the
+ * end to signify clockwise rotations. The firstrot[] array is not needed for
+ * display thus it is freed after being used for face computations below.
+ */
+static int
+vertices(Polyhedron *P)
+{
+ int i, newV = 2;
+ double cosa;
+ Malloc(P->v, P->V, Vector);
+ Matalloc(P->adj, P->M, P->V, int);
+ Malloc(P->firstrot, P->V, int); /* temporary , put in Polyhedron
+ structure so that may be freed on
+ error */
+ cosa = cos(M_PI / P->n[0]) / sin(P->gamma[0]);
+ P->v[0].x = 0;
+ P->v[0].y = 0;
+ P->v[0].z = 1;
+ P->firstrot[0] = 0;
+ P->adj[0][0] = 1;
+ P->v[1].x = 2 * cosa * sqrt(1 - cosa * cosa);
+ P->v[1].y = 0;
+ P->v[1].z = 2 * cosa * cosa - 1;
+ if (!P->snub) {
+ P->firstrot[1] = 0;
+ P->adj[0][1] = -1;/* start the other side */
+ P->adj[P->M-1][1] = 0;
+ } else {
+ P->firstrot[1] = P->snub[P->M-1] ? 0 : P->M-1 ;
+ P->adj[0][1] = 0;
+ }
+ for (i = 0; i < newV; i++) {
+ int j, k;
+ int last, one, start, limit;
+ if (P->adj[0][i] == -1) {
+ one = -1; start = P->M-2; limit = -1;
+ } else {
+ one = 1; start = 1; limit = P->M;
+ }
+ k = P->firstrot[i];
+ for (j = start; j != limit; j += one) {
+ Vector temp;
+ int J;
+ temp = rotate (P->v[P->adj[j-one][i]], P->v[i],
+ one * 2 * P->gamma[P->rot[k]]);
+ for (J=0; J<newV && !same(P->v[J],temp,BIG_EPSILON); J++)
+ ;/* noop */
+ P->adj[j][i] = J;
+ last = k;
+ if (++k == P->M)
+ k = 0;
+ if (J == newV) { /* new vertex */
+ if (newV == P->V) Err ("too many vertices");
+ P->v[newV++] = temp;
+ if (!P->snub) {
+ P->firstrot[J] = k;
+ if (one > 0) {
+ P->adj[0][J] = -1;
+ P->adj[P->M-1][J] = i;
+ } else {
+ P->adj[0][J] = i;
+ }
+ } else {
+ P->firstrot[J] = !P->snub[last] ? last :
+ !P->snub[k] ? (k+1)%P->M : k ;
+ P->adj[0][J] = i;
+ }
+ }
+ }
+ }
+ return 1;
+}
+
+/*
+ * Compute polyhedron faces (dual vertices) and incidence matrices.
+ * For orientable polyhedra, we can distinguish between the two faces meeting
+ * at a given directed edge and identify the face on the left and the face on
+ * the right, as seen from the outside. For one-sided polyhedra, the vertex
+ * figure is a papillon (in Coxeter &al. terminology, a crossed parallelogram)
+ * and the two faces meeting at an edge can be identified as the side face
+ * (n[1] or n[2]) and the diagonal face (n[0] or n[3]).
+ */
+static int
+faces(Polyhedron *P)
+{
+ int i, newF = 0;
+ Malloc (P->f, P->F, Vector);
+ Malloc (P->ftype, P->F, int);
+ Matalloc (P->incid, P->M, P->V, int);
+ P->minr = 1 / fabs (tan (M_PI / P->n[P->hemi]) * tan (P->gamma[P->hemi]));
+ for (i = P->M; --i>=0;) {
+ int j;
+ for (j = P->V; --j>=0;)
+ P->incid[i][j] = -1;
+ }
+ for (i = 0; i < P->V; i++) {
+ int j;
+ for (j = 0; j < P->M; j++) {
+ int i0, J;
+ int pap;/* papillon edge type */
+ if (P->incid[j][i] != -1)
+ continue;
+ P->incid[j][i] = newF;
+ if (newF == P->F)
+ Err("too many faces");
+ P->f[newF] = pole(P->minr, P->v[i], P->v[P->adj[j][i]],
+ P->v[P->adj[mod(j + 1, P->M)][i]]);
+ P->ftype[newF] = P->rot[mod(P->firstrot[i] + ((P->adj[0][i] <
+ P->adj[P->M - 1][i])
+ ? j
+ : -j - 2),
+ P->M)];
+ if (P->onesided)
+ pap = (P->firstrot[i] + j) % 2;
+ i0 = i;
+ J = j;
+ for (;;) {
+ int k;
+ k = i0;
+ if ((i0 = P->adj[J][k]) == i) break;
+ for (J = 0; J < P->M && P->adj[J][i0] != k; J++)
+ ;/* noop */
+ if (J == P->M)
+ Err("too many faces");
+ if (P->onesided && (J + P->firstrot[i0]) % 2 == pap) {
+ P->incid [J][i0] = newF;
+ if (++J >= P->M)
+ J = 0;
+ } else {
+ if (--J < 0)
+ J = P->M - 1;
+ P->incid [J][i0] = newF;
+ }
+ }
+ newF++;
+ }
+ }
+ Free(P->firstrot);
+ Free(P->rot);
+ Free(P->snub);
+ return 1;
+}
+
+/*
+ * Compute edge list and graph polyhedron and dual.
+ * If the polyhedron is of the "hemi" type, each edge has one finite vertex and
+ * one ideal vertex. We make sure the latter is always the out-vertex, so that
+ * the edge becomes a ray (half-line). Each ideal vertex is represented by a
+ * unit Vector, and the direction of the ray is either parallel or
+ * anti-parallel this Vector. We flag this in the array P->anti[E].
+ */
+static int
+edgelist(Polyhedron *P)
+{
+ int i, j, *s, *t, *u;
+ Matalloc(P->e, 2, P->E, int);
+ Matalloc(P->dual_e, 2, P->E, int);
+ s = P->e[0];
+ t = P->e[1];
+ for (i = 0; i < P->V; i++)
+ for (j = 0; j < P->M; j++)
+ if (i < P->adj[j][i]) {
+ *s++ = i;
+ *t++ = P->adj[j][i];
+ }
+ s = P->dual_e[0];
+ t = P->dual_e[1];
+ if (!P->hemi)
+ P->anti = 0;
+ else
+ Malloc(P->anti, P->E, int);
+ u = P->anti;
+ for (i = 0; i < P->V; i++)
+ for (j = 0; j < P->M; j++)
+ if (i < P->adj[j][i])
+ {
+ if (!u) {
+ *s++ = P->incid[mod(j-1,P->M)][i];
+ *t++ = P->incid[j][i];
+ } else {
+ if (P->ftype[P->incid[j][i]]) {
+ *s = P->incid[j][i];
+ *t = P->incid[mod(j-1,P->M)][i];
+ } else {
+ *s = P->incid[mod(j-1,P->M)][i];
+ *t = P->incid[j][i];
+ }
+ *u++ = dot(P->f[*s++], P->f[*t++]) > 0;
+ }
+ }
+ return 1;
+}
+
+
+static char *
+sprintfrac(double x)
+{
+ char *s;
+ frac (x);
+ if (!frax.d) {
+ Malloc(s, sizeof ("infinity"), char);
+ strcpy(s, "infinity");
+ } else if (frax.d == 1) {
+ char n[MAXDIGITS + 1];
+ sprintf(n, "%ld", frax.n);
+ Malloc(s, strlen (n) + 1, char);
+ strcpy(s, n);
+ } else {
+ char n[MAXDIGITS + 1], d[MAXDIGITS + 1];
+ sprintf(n, "%ld", frax.n);
+ sprintf(d, "%ld", frax.d);
+ Malloc(s, strlen (n) + strlen (d) + 2, char);
+ sprintf(s, "%s/%s", n, d);
+ }
+ return s;
+}
+
+static double
+dot(Vector a, Vector b)
+{
+ return a.x * b.x + a.y * b.y + a.z * b.z;
+}
+
+static Vector
+scale(double k, Vector a)
+{
+ a.x *= k;
+ a.y *= k;
+ a.z *= k;
+ return a;
+}
+
+static Vector
+diff(Vector a, Vector b)
+{
+ a.x -= b.x;
+ a.y -= b.y;
+ a.z -= b.z;
+ return a;
+}
+
+static Vector
+cross(Vector a, Vector b)
+{
+ Vector p;
+ p.x = a.y * b.z - a.z * b.y;
+ p.y = a.z * b.x - a.x * b.z;
+ p.z = a.x * b.y - a.y * b.x;
+ return p;
+}
+
+static Vector
+sum(Vector a, Vector b)
+{
+ a.x += b.x;
+ a.y += b.y;
+ a.z += b.z;
+ return a;
+}
+
+static Vector
+sum3(Vector a, Vector b, Vector c)
+{
+ a.x += b.x + c.x;
+ a.y += b.y + c.y;
+ a.z += b.z + c.z;
+ return a;
+}
+
+static Vector
+rotate(Vector vertex, Vector axis, double angle)
+{
+ Vector p;
+ p = scale(dot (axis, vertex), axis);
+ return sum3(p, scale(cos(angle), diff(vertex, p)),
+ scale(sin(angle), cross(axis, vertex)));
+}
+
+Vector x, y, z;
+
+/*
+ * rotate the standard frame
+ */
+static void
+rotframe(double azimuth, double elevation, double angle)
+{
+ static Vector X = {1,0,0}, Y = {0,1,0}, Z = {0,0,1};
+ Vector axis;
+
+ axis = rotate(rotate (X, Y, elevation), Z, azimuth);
+ x = rotate(X, axis, angle);
+ y = rotate(Y, axis, angle);
+ z = rotate(Z, axis, angle);
+}
+
+/*
+ * rotate an array of n Vectors
+ */
+static void
+rotarray(Vector *new, Vector *old, int n)
+{
+ while (n--) {
+ *new++ = sum3(scale(old->x, x), scale(old->y, y), scale(old->z, z));
+ old++;
+ }
+}
+
+static int
+same(Vector a, Vector b, double epsilon)
+{
+ return fabs(a.x - b.x) < epsilon && fabs(a.y - b.y) < epsilon
+ && fabs(a.z - b.z) < epsilon;
+}
+
+/*
+ * Compute the polar reciprocal of the plane containing a, b and c:
+ *
+ * If this plane does not contain the origin, return p such that
+ * dot(p,a) = dot(p,b) = dot(p,b) = r.
+ *
+ * Otherwise, return p such that
+ * dot(p,a) = dot(p,b) = dot(p,c) = 0
+ * and
+ * dot(p,p) = 1.
+ */
+static Vector
+pole(double r, Vector a, Vector b, Vector c)
+{
+ Vector p;
+ double k;
+ p = cross(diff(b, a), diff(c, a));
+ k = dot(p, a);
+ if (fabs(k) < 1e-6)
+ return scale(1 / sqrt(dot(p, p)), p);
+ else
+ return scale(r/ k , p);
+}
+
+\f
+/* output */
+
+
+
+
+static void rotframe(double azimuth, double elevation, double angle);
+static void rotarray(Vector *new, Vector *old, int n);
+static int mod (int i, int j);
+
+
+static void
+push_point (polyhedron *p, Vector v)
+{
+ p->points[p->npoints].x = v.x;
+ p->points[p->npoints].y = v.y;
+ p->points[p->npoints].z = v.z;
+ p->npoints++;
+}
+
+static void
+push_face3 (polyhedron *p, int x, int y, int z)
+{
+ p->faces[p->nfaces].npoints = 3;
+ Malloc (p->faces[p->nfaces].points, 3, int);
+ p->faces[p->nfaces].points[0] = x;
+ p->faces[p->nfaces].points[1] = y;
+ p->faces[p->nfaces].points[2] = z;
+ p->nfaces++;
+}
+
+static void
+push_face4 (polyhedron *p, int x, int y, int z, int w)
+{
+ p->faces[p->nfaces].npoints = 4;
+ Malloc (p->faces[p->nfaces].points, 4, int);
+ p->faces[p->nfaces].points[0] = x;
+ p->faces[p->nfaces].points[1] = y;
+ p->faces[p->nfaces].points[2] = z;
+ p->faces[p->nfaces].points[3] = w;
+ p->nfaces++;
+}
+
+
+
+
+static polyhedron *
+construct_polyhedron (Polyhedron *P, Vector *v, int V, Vector *f, int F,
+ char *name, char *dual, char *class, char *star,
+ double azimuth, double elevation, double freeze)
+{
+ int i, j, k, l, ll, ii, *hit, facelets;
+
+ polyhedron *result;
+ Vector *temp;
+
+ Malloc (result, 1, polyhedron);
+ memset (result, 0, sizeof(*result));
+
+ /*
+ * Rotate polyhedron
+ */
+ rotframe(azimuth, elevation, freeze);
+ Malloc(temp, V, Vector);
+ rotarray(temp, v, V);
+ v = temp;
+ Malloc(temp, F, Vector);
+ rotarray(temp, f, F);
+ f = temp;
+
+ result->number = P->index + 1;
+ result->name = strdup (name);
+ result->dual = strdup (dual);
+ result->wythoff = strdup (P->polyform);
+ result->config = strdup (P->config);
+ result->group = strdup (P->group);
+ result->class = strdup (class);
+
+ /*
+ * Vertex list
+ */
+ Malloc (result->points, V + F * 13, point);
+ result->npoints = 0;
+
+ result->nedges = P->E;
+ result->logical_faces = F;
+ result->logical_vertices = V;
+ result->density = P->D;
+ result->chi = P->chi;
+
+ for (i = 0; i < V; i++)
+ push_point (result, v[i]);
+
+ /*
+ * Auxiliary vertices (needed because current VRML browsers cannot handle
+ * non-simple polygons, i.e., ploygons with self intersections): Each
+ * non-simple face is assigned an auxiliary vertex. By connecting it to the
+ * rest of the vertices the face is triangulated. The circum-center is used
+ * for the regular star faces of uniform polyhedra. The in-center is used for
+ * the pentagram (#79) and hexagram (#77) of the high-density snub duals, and
+ * for the pentagrams (#40, #58) and hexagram (#52) of the stellated duals
+ * with configuration (....)/2. Finally, the self-intersection of the crossed
+ * parallelogram is used for duals with form p q r| with an even denominator.
+ *
+ * This method do not work for the hemi-duals, whose faces are not
+ * star-shaped and have two self-intersections each.
+ *
+ * Thus, for each face we need six auxiliary vertices: The self intersections
+ * and the terminal points of the truncations of the infinite edges. The
+ * ideal vertices are listed, but are not used by the face-list.
+ *
+ * Note that the face of the last dual (#80) is octagonal, and constists of
+ * two quadrilaterals of the infinite type.
+ */
+
+ if (*star && P->even != -1)
+ Malloc(hit, F, int);
+ for (i = 0; i < F; i++)
+ if ((!*star &&
+ (frac(P->n[P->ftype[i]]), frax.d != 1 && frax.d != frax.n - 1)) ||
+ (*star &&
+ P->K == 5 &&
+ (P->D > 30 ||
+ denominator (P->m[0]) != 1))) {
+ /* find the center of the face */
+ double h;
+ if (!*star && P->hemi && !P->ftype[i])
+ h = 0;
+ else
+ h = P->minr / dot(f[i],f[i]);
+ push_point(result, scale (h, f[i]));
+
+ } else if (*star && P->even != -1) {
+ /* find the self-intersection of a crossed parallelogram.
+ * hit is set if v0v1 intersects v2v3*/
+ Vector v0, v1, v2, v3, c0, c1, p;
+ double d0, d1;
+ v0 = v[P->incid[0][i]];
+ v1 = v[P->incid[1][i]];
+ v2 = v[P->incid[2][i]];
+ v3 = v[P->incid[3][i]];
+ d0 = sqrt(dot(diff(v0, v2), diff(v0, v2)));
+ d1 = sqrt(dot (diff(v1, v3), diff(v1, v3)));
+ c0 = scale(d1, sum(v0, v2));
+ c1 = scale(d0, sum(v1, v3));
+ p = scale(0.5 / (d0 + d1), sum(c0, c1));
+ push_point (result, p);
+ p = cross(diff(p, v2), diff(p, v3));
+ hit[i] = (dot(p, p) < 1e-6);
+ } else if (*star && P->hemi && P->index != last_uniform - 1) {
+ /* find the terminal points of the truncation and the
+ * self-intersections.
+ * v23 v0 v21
+ * | \ / \ / |
+ * | v0123 v0321 |
+ * | / \ / \ |
+ * v01 v2 v03
+ */
+ Vector v0, v1, v2, v3, v01, v03, v21, v23, v0123, v0321 ;
+ Vector u;
+ double t = 1.5;/* truncation adjustment factor */
+ j = !P->ftype[P->incid[0][i]];
+ v0 = v[P->incid[j][i]];/* real vertex */
+ v1 = v[P->incid[j+1][i]];/* ideal vertex (unit vector) */
+ v2 = v[P->incid[j+2][i]];/* real */
+ v3 = v[P->incid[(j+3)%4][i]];/* ideal */
+ /* compute intersections
+ * this uses the following linear algebra:
+ * v0123 = v0 + a v1 = v2 + b v3
+ * v0 x v3 + a (v1 x v3) = v2 x v3
+ * a (v1 x v3) = (v2 - v0) x v3
+ * a (v1 x v3) . (v1 x v3) = (v2 - v0) x v3 . (v1 x v3)
+ */
+ u = cross(v1, v3);
+ v0123 = sum(v0, scale(dot(cross(diff(v2, v0), v3), u) / dot(u,u),
+ v1));
+ v0321 = sum(v0, scale(dot(cross(diff(v0, v2), v1), u) / dot(u,u),
+ v3));
+ /* compute truncations */
+ v01 = sum(v0 , scale(t, diff(v0123, v0)));
+ v23 = sum(v2 , scale(t, diff(v0123, v2)));
+ v03 = sum(v0 , scale(t, diff(v0321, v0)));
+ v21 = sum(v2 , scale(t, diff(v0321, v2)));
+
+ push_point(result, v01);
+ push_point(result, v23);
+ push_point(result, v0123);
+ push_point(result, v03);
+ push_point(result, v21);
+ push_point(result, v0321);
+
+ } else if (*star && P->index == last_uniform - 1) {
+ /* find the terminal points of the truncation and the
+ * self-intersections.
+ * v23 v0 v21
+ * | \ / \ / |
+ * | v0123 v0721 |
+ * | / \ / \ |
+ * v01 v2 v07
+ *
+ * v65 v4 v67
+ * | \ / \ / |
+ * | v4365 v4567 |
+ * | / \ / \ |
+ * v43 v6 v45
+ */
+ Vector v0, v1, v2, v3, v4, v5, v6, v7, v01, v07, v21, v23;
+ Vector v43, v45, v65, v67, v0123, v0721, v4365, v4567;
+ double t = 1.5;/* truncation adjustment factor */
+ Vector u;
+ for (j = 0; j < 8; j++)
+ if (P->ftype[P->incid[j][i]] == 3)
+ break;
+ v0 = v[P->incid[j][i]];/* real {5/3} */
+ v1 = v[P->incid[(j+1)%8][i]];/* ideal */
+ v2 = v[P->incid[(j+2)%8][i]];/* real {3} */
+ v3 = v[P->incid[(j+3)%8][i]];/* ideal */
+ v4 = v[P->incid[(j+4)%8][i]];/* real {5/2} */
+ v5 = v[P->incid[(j+5)%8][i]];/* ideal */
+ v6 = v[P->incid[(j+6)%8][i]];/* real {3/2} */
+ v7 = v[P->incid[(j+7)%8][i]];/* ideal */
+ /* compute intersections */
+ u = cross(v1, v3);
+ v0123 = sum(v0, scale(dot(cross(diff(v2, v0), v3), u) / dot(u,u),
+ v1));
+ u = cross(v7, v1);
+ v0721 = sum(v0, scale(dot(cross(diff(v2, v0), v1), u) / dot(u,u),
+ v7));
+ u = cross(v5, v7);
+ v4567 = sum(v4, scale(dot(cross(diff(v6, v4), v7), u) / dot(u,u),
+ v5));
+ u = cross(v3, v5);
+ v4365 = sum(v4, scale(dot(cross(diff(v6, v4), v5), u) / dot(u,u),
+ v3));
+ /* compute truncations */
+ v01 = sum(v0 , scale(t, diff(v0123, v0)));
+ v23 = sum(v2 , scale(t, diff(v0123, v2)));
+ v07 = sum(v0 , scale(t, diff(v0721, v0)));
+ v21 = sum(v2 , scale(t, diff(v0721, v2)));
+ v45 = sum(v4 , scale(t, diff(v4567, v4)));
+ v67 = sum(v6 , scale(t, diff(v4567, v6)));
+ v43 = sum(v4 , scale(t, diff(v4365, v4)));
+ v65 = sum(v6 , scale(t, diff(v4365, v6)));
+
+ push_point(result, v01);
+ push_point(result, v23);
+ push_point(result, v0123);
+ push_point(result, v07);
+ push_point(result, v21);
+ push_point(result, v0721);
+ push_point(result, v45);
+ push_point(result, v67);
+ push_point(result, v4567);
+ push_point(result, v43);
+ push_point(result, v65);
+ push_point(result, v4365);
+ }
+
+ /*
+ * Face list:
+ * Each face is printed in a separate line, by listing the indices of its
+ * vertices. In the non-simple case, the polygon is represented by the
+ * triangulation, each triangle consists of two polyhedron vertices and one
+ * auxiliary vertex.
+ */
+ Malloc (result->faces, F * 10, face);
+ result->nfaces = 0;
+
+ ii = V;
+ facelets = 0;
+ for (i = 0; i < F; i++) {
+ if (*star) {
+ if (P->K == 5 &&
+ (P->D > 30 ||
+ denominator (P->m[0]) != 1)) {
+ for (j = 0; j < P->M - 1; j++) {
+ push_face3 (result, P->incid[j][i], P->incid[j+1][i], ii);
+ facelets++;
+ }
+
+ push_face3 (result, P->incid[j][i], P->incid[0][i], ii++);
+ facelets++;
+
+ } else if (P->even != -1) {
+ if (hit[i]) {
+ push_face3 (result, P->incid[3][i], P->incid[0][i], ii);
+ push_face3 (result, P->incid[1][i], P->incid[2][i], ii);
+ } else {
+ push_face3 (result, P->incid[0][i], P->incid[1][i], ii);
+ push_face3 (result, P->incid[2][i], P->incid[3][i], ii);
+ }
+ ii++;
+ facelets += 2;
+
+ } else if (P->hemi && P->index != last_uniform - 1) {
+ j = !P->ftype[P->incid[0][i]];
+
+ push_face3 (result, ii, ii + 1, ii + 2);
+ push_face4 (result, P->incid[j][i], ii + 2, P->incid[j+2][i], ii + 5);
+ push_face3 (result, ii + 3, ii + 4, ii + 5);
+ ii += 6;
+ facelets += 3;
+ } else if (P->index == last_uniform - 1) {
+ for (j = 0; j < 8; j++)
+ if (P->ftype[P->incid[j][i]] == 3)
+ break;
+ push_face3 (result, ii, ii + 1, ii + 2);
+ push_face4 (result,
+ P->incid[j][i], ii + 2, P->incid[(j+2)%8][i], ii + 5);
+ push_face3 (result, ii + 3, ii + 4, ii + 5);
+
+ push_face3 (result, ii + 6, ii + 7, ii + 8);
+ push_face4 (result,
+ P->incid[(j+4)%8][i], ii + 8, P->incid[(j+6)%8][i],
+ ii + 11);
+ push_face3 (result, ii + 9, ii + 10, ii + 11);
+ ii += 12;
+ facelets += 6;
+ } else {
+
+ result->faces[result->nfaces].npoints = P->M;
+ Malloc (result->faces[result->nfaces].points, P->M, int);
+ for (j = 0; j < P->M; j++)
+ result->faces[result->nfaces].points[j] = P->incid[j][i];
+ result->nfaces++;
+ facelets++;
+ }
+ } else {
+ int split = (frac(P->n[P->ftype[i]]),
+ frax.d != 1 && frax.d != frax.n - 1);
+ for (j = 0; j < V; j++) {
+ for (k = 0; k < P->M; k++)
+ if (P->incid[k][j] == i)
+ break;
+ if (k != P->M)
+ break;
+ }
+ if (split) {
+ ll = j;
+ for (l = P->adj[k][j]; l != j; l = P->adj[k][l]) {
+ for (k = 0; k < P->M; k++)
+ if (P->incid[k][l] == i)
+ break;
+ if (P->adj[k][l] == ll)
+ k = mod(k + 1 , P->M);
+ push_face3 (result, ll, l, ii);
+ facelets++;
+ ll = l;
+ }
+ push_face3 (result, ll, j, ii++);
+ facelets++;
+
+ } else {
+
+ int *pp;
+ int pi = 0;
+ Malloc (pp, 100, int);
+
+ pp[pi++] = j;
+ ll = j;
+ for (l = P->adj[k][j]; l != j; l = P->adj[k][l]) {
+ for (k = 0; k < P->M; k++)
+ if (P->incid[k][l] == i)
+ break;
+ if (P->adj[k][l] == ll)
+ k = mod(k + 1 , P->M);
+ pp[pi++] = l;
+ ll = l;
+ }
+ result->faces[result->nfaces].npoints = pi;
+ result->faces[result->nfaces].points = pp;
+ result->nfaces++;
+ facelets++;
+ }
+ }
+ }
+
+ /*
+ * Face color indices - for polyhedra with multiple face types
+ * For non-simple faces, the index is repeated as many times as needed by the
+ * triangulation.
+ */
+ {
+ int ff = 0;
+ if (!*star && P->N != 1) {
+ for (i = 0; i < F; i++)
+ if (frac(P->n[P->ftype[i]]), frax.d == 1 || frax.d == frax.n - 1)
+ result->faces[ff++].color = P->ftype[i];
+ else
+ for (j = 0; j < frax.n; j++)
+ result->faces[ff++].color = P->ftype[i];
+ } else {
+ for (i = 0; i < facelets; i++)
+ result->faces[ff++].color = 0;
+ }
+ }
+
+ if (*star && P->even != -1)
+ free(hit);
+ free(v);
+ free(f);
+
+ return result;
+}
+
+
+\f
+/* External interface (jwz)
+ */
+
+void
+free_polyhedron (polyhedron *p)
+{
+ if (!p) return;
+ Free (p->wythoff);
+ Free (p->name);
+ Free (p->group);
+ Free (p->class);
+ if (p->faces)
+ {
+ int i;
+ for (i = 0; i < p->nfaces; i++)
+ Free (p->faces[i].points);
+ Free (p->faces);
+ }
+ Free (p);
+}
+
+
+int
+construct_polyhedra (polyhedron ***polyhedra_ret)
+{
+ double freeze = 0;
+ double azimuth = AZ;
+ double elevation = EL;
+ int index = 0;
+
+ int count = 0;
+ polyhedron **result;
+ Malloc (result, last_uniform * 2 + 1, polyhedron*);
+
+ while (index < last_uniform) {
+ static char sym[4];
+ Polyhedron *P;
+
+ sprintf(sym, "#%d", index + 1);
+ if (!(P = kaleido(sym, 1, 0, 0, 0))) {
+ Err (strerror(errno));
+ }
+
+ result[count++] = construct_polyhedron (P, P->v, P->V, P->f, P->F,
+ P->name, P->dual_name,
+ P->class, "",
+ azimuth, elevation, freeze);
+
+ result[count++] = construct_polyhedron (P, P->f, P->F, P->v, P->V,
+ P->dual_name, P->name,
+ P->dual_class, "*",
+ azimuth, elevation, freeze);
+ polyfree(P);
+ index++;
+ }
+
+ *polyhedra_ret = result;
+ return count;
+}
projects / xscreensaver / blobdiff