generate beautiful pictures of the complex Anosov set
This commit is contained in:
Florian Stecker
parent
729d1a10b7
commit
429f0890d6
242
complex_anosov.c
242
complex_anosov.c
@ -8,35 +8,39 @@
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#include <stdlib.h>
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#include <math.h>
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#include <string.h>
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#include <time.h>
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#define LOOP(i,n) for(int i = 0; i < (n); i++)
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#define SWAP(t,x,y) do { t _tmp = (x); (x) = (y); (y) = _tmp; } while (0);
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//#define INFO(msg, ...) fprintf(stderr, "[%10.3f] " msg, runtime(), ##__VA_ARGS__)
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#define INFO(msg, ...)
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/*
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Elements up to length 0: 1
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Elements up to length 1: 4
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Elements up to length 2: 10
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Elements up to length 3: 22
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Elements up to length 4: 46
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Elements up to length 5: 91
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Elements up to length 6: 175
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Elements up to length 7: 334
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Elements up to length 8: 634
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Elements up to length 9: 1198
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Elements up to length 10: 2260
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Elements up to length 11: 4261
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Elements up to length 12: 8029
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Elements up to length 13: 15124
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Elements up to length 14: 28486
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Elements up to length 15: 53650
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Elements up to length 16: 101038
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Elements up to length 17: 190279
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Elements up to length 18: 358339
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Elements up to length 19: 674830
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Elements up to length 20: 1270846
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Elements up to length 21: 2393266
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Elements up to length 22: 4507012
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Elements up to length 23: 8487625
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Number of elements
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up to length 0: 1
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up to length 1: 4
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up to length 2: 10
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up to length 3: 22
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up to length 4: 46
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up to length 5: 91
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up to length 6: 175
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up to length 7: 334
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up to length 8: 634
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up to length 9: 1198
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up to length 10: 2260
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up to length 11: 4261
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up to length 12: 8029
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up to length 13: 15124
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up to length 14: 28486
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up to length 15: 53650
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up to length 16: 101038
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up to length 17: 190279
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up to length 18: 358339
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up to length 19: 674830
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up to length 20: 1270846
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up to length 21: 2393266
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up to length 22: 4507012
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up to length 23: 8487625
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*/
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static double gaussian_sqrt5_real(NUMBER x)
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@ -82,9 +86,56 @@ static double gaussian_sqrt5_imag(NUMBER x)
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return result;
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}
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static int read_idlist(const char *filename, int *list)
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{
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FILE *f = fopen(filename, "r");
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if(f == NULL) {
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fprintf(stderr, "Could not open %s\n", filename);
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exit(1);
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}
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char *line = NULL;
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size_t len = 0;
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ssize_t read;
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int n = 0;
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while ((read = getline(&line, &len, f)) != -1)
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list[n++] = atoi(line);
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if (line)
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free(line);
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fclose(f);
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return n;
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}
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static int compare_int(const void *a, const void *b)
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{
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const int *aa = a;
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const int *bb = b;
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return (*aa > *bb) - (*aa < *bb);
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}
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static double runtime()
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{
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static struct timespec starttime;
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static int started = 0;
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if(!started) {
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clock_gettime(CLOCK_MONOTONIC, &starttime);
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started = 1;
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}
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struct timespec curtime;
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double diff;
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clock_gettime(CLOCK_MONOTONIC, &curtime);
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return (curtime.tv_sec - starttime.tv_sec) + (curtime.tv_nsec - starttime.tv_nsec) / 1e9;
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}
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enum mode {
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MODE_HELP,
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MODE_TRACES,
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MODE_EIGENVALUES,
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MODE_SUMMARY,
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MODE_TRACE_IDS
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};
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@ -94,10 +145,13 @@ int main(int argc, char *argv[])
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char buf[100];
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int mode;
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runtime(); // start timer
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// parse arguments
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if(argc < 2 || strcmp(argv[1], "help") == 0)
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mode = MODE_HELP;
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else if(strcmp(argv[1], "traces") == 0)
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mode = MODE_TRACES;
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else if(strcmp(argv[1], "evs") == 0)
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mode = MODE_EIGENVALUES;
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else if(strcmp(argv[1], "summary") == 0)
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mode = MODE_SUMMARY;
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else if(strcmp(argv[1], "trace_ids") == 0)
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@ -106,72 +160,78 @@ int main(int argc, char *argv[])
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mode = MODE_HELP;
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if(mode == MODE_HELP) {
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fprintf(stderr, "Usage: %s <help|traces|summary|trace_ids> [arguments]\n", argv[0]);
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fprintf(stderr, "Usage: %s <help|evs|summary|trace_ids> [arguments]\n", argv[0]);
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fprintf(stderr, "%s help display this page\n", argv[0]);
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fprintf(stderr, "%s traces <n> <qreal> <qimag> enumerate group and output unique trace/trace inverse pairs\n", argv[0]);
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fprintf(stderr, "%s summary <n> <qreal> <qimag> only output max slope etc.\n", argv[0]);
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fprintf(stderr, "%s trace_ids <n> <qreal> <qimag> list of ids of unique traces\n", argv[0]);
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fprintf(stderr, "%s evs <n> <q1> <q2> <q3> <treal> <timag> enumerate group and output unique (log) eigenvalue triples\n", argv[0]);
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fprintf(stderr, "%s summary <n> <q1> <q2> <q3> <treal> <timag> only output max slope etc.\n", argv[0]);
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fprintf(stderr, "%s trace_ids <n> <q1> <q2> <q3> <treal> <timag> list of ids of unique traces\n", argv[0]);
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return 0;
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}
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if(argc < 5) {
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if(argc < 8) {
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fprintf(stderr, "Not enough arguments!\n");
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return 0;
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}
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int n = atoi(argv[2]);
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int nlist, nuniq;
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mpq_t qreal, qimag;
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mpq_inits(qreal, qimag, NULL);
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mpq_set_str(qreal, argv[3], 10);
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mpq_set_str(qimag, argv[4], 10);
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// mpq_set_si(qreal, 50, 10);
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// mpq_set_si(qimag, 1, 10);
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mpq_canonicalize(qreal);
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mpq_canonicalize(qimag);
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/*
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int length = 0;
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LOOP(i, n) {
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if(group->elements[i].length > length) {
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printf("Elements up to length %d: %d\n", length, i);
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length = group->elements[i].length;
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}
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}
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return 0;
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*/
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/*
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LOOP(i, n) {
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groupelement_t *cur = &group->elements[i];
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groupelement_t *other;
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cur->conjugacy_class = cur; // start with itself and reduce if possible
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LOOP(j, 3) {
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if(cur->left[j] && cur->left[j]->right[j]) {
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other = cur->left[j]->right[j];
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if(other->id < cur->id)
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cur->conjugacy_class = other->conjugacy_class;
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}
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if(cur->right[j] && cur->right[j]->left[j]) {
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other = cur->right[j]->left[j];
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if(other->id < cur->id)
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cur->conjugacy_class = other->conjugacy_class;
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}
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}
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}
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*/
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int q[3];
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mpq_t treal, timag;
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q[0] = atoi(argv[3]);
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q[1] = atoi(argv[4]);
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q[2] = atoi(argv[5]);
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mpq_inits(treal, timag, NULL);
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mpq_set_str(treal, argv[6], 10);
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mpq_set_str(timag, argv[7], 10);
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mpq_canonicalize(treal);
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mpq_canonicalize(timag);
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// enumerate group
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INFO("generate group\n");
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group_t *group = coxeter_init_triangle(5, 5, 5, n);
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// read list of elements we need to compute, or just fill it with all elements
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INFO("prepare list\n");
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int *idlist = malloc(n*sizeof(int));
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char *id_file = getenv("IDLIST");
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if(id_file != NULL) {
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nlist = read_idlist(id_file, idlist);
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// sort and symmetrize the list
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qsort(idlist, nlist, sizeof(int), compare_int);
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int ninverses = 0;
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LOOP(i, nlist) {
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int id = idlist[i];
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int invid = group->elements[id].inverse->id;
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if(!bsearch(&invid, idlist, nlist, sizeof(int), compare_int)) {
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idlist[nlist+ninverses] = invid;
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ninverses++;
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}
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}
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nlist += ninverses;
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qsort(idlist, nlist, sizeof(int), compare_int);
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} else {
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// just list all elements which have inverses
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nlist = 0;
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LOOP(i, n) {
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if(group->elements[i].inverse)
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idlist[nlist++] = i;
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}
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}
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// get generator matrices
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INFO("make generators\n");
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mat gen[3];
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LOOP(i, 3) mat_init(gen[i], 3, QT_GAUSS_SQRT5);
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generators_triangle_reflection_group_555_complex(gen, 2, 2, 2, qreal, qimag);
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generators_triangle_reflection_group_555_complex(gen, q[0], q[1], q[2], treal, timag);
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// compute the traces of all elements in idlist
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INFO("enumerate traces\n");
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struct tracedata *traces;
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int nuniq = enumerate_coxeter_group_traces(group, gen, &traces);
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nuniq = enumerate_coxeter_group_traces(group, gen, &traces, idlist, nlist, 1);
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// compute eigenvalues out of traces
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INFO("compute eigenvalues\n");
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mps_context *solver = mps_context_new();
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mps_monomial_poly *poly = mps_monomial_poly_new(solver, 3);
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mps_context_set_output_prec(solver, 20); // relative precision
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@ -198,7 +258,14 @@ int main(int argc, char *argv[])
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if(fabs(ev_abs2[0]) < fabs(ev_abs2[1]))
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SWAP(double, ev_abs2[0], ev_abs2[1]);
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if(log(ev_abs2[0]) < 1e-3) // we regard this as a finite order element
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if(mode == MODE_TRACE_IDS) {
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// we only want to record unordered pairs here
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if(CMP(traces[i].tr, traces[i].trinv) >= 0)
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printf("%d\n", traces[i].id);
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continue;
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}
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if(log(ev_abs2[0]) < 1e-6) // we regard this as a finite order element
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continue;
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double slope = - log(ev_abs2[0]) / log(ev_abs2[2]);
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@ -207,28 +274,31 @@ int main(int argc, char *argv[])
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max_slope_id = traces[i].id;
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}
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if(mode == MODE_TRACES) {
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if(mode == MODE_EIGENVALUES) {
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printf("%d %f %f %f\n",
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traces[i].id, log(ev_abs2[0]), log(ev_abs2[1]), log(ev_abs2[2]));
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} else if(mode == MODE_TRACE_IDS) {
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printf("%d\n", traces[i].id);
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traces[i].id, log(ev_abs2[0])/2, log(ev_abs2[1])/2, log(ev_abs2[2])/2);
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}
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}
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// output summary
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coxeter_snprint(buf, sizeof(buf), &group->elements[max_slope_id]);
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if(mode == MODE_SUMMARY) {
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gmp_fprintf(stdout, "%f %f %d %d %f %s\n", mpq_get_d(qreal), mpq_get_d(qimag), n, nuniq, max_slope, buf);
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} else {
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gmp_fprintf(stderr, "q = %Qd + i*%Qd\tElements: %d\tTraces: %d\tMaximal slope: %f at %s\n", qreal, qimag, n, nuniq, max_slope, buf);
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gmp_fprintf(stdout, "%f %f %d %d %d %f %s\n", mpq_get_d(treal), mpq_get_d(timag), n, nlist, nuniq, max_slope, buf);
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} else if(mode == MODE_EIGENVALUES) {
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gmp_fprintf(stderr, "q = %.2f + i*%.2f\tn = %d\tnlist = %d\tnuniq = %d\tMaximal slope: %f at %s\n", mpq_get_d(treal), mpq_get_d(timag), n, nlist, nuniq, max_slope, buf);
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} else if(mode == MODE_TRACE_IDS) {
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gmp_fprintf(stderr, "q = %.2f + i*%.2f\tElements: %d\tTraces: %d\n", mpq_get_d(treal), mpq_get_d(timag), n, nuniq);
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}
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mps_monomial_poly_free(solver, MPS_POLYNOMIAL(poly));
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// clean up
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INFO("clean up\n");
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// mps_monomial_poly_free(solver, MPS_POLYNOMIAL(poly));
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mps_context_free(solver);
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enumerate_tracedata_clear(traces, nuniq);
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free(idlist);
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LOOP(i, 3) mat_clear(gen[i]);
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coxeter_clear(group);
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mpq_clears(qreal, qimag, NULL);
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mpq_clears(treal, timag, NULL);
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return 0;
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}
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9
compute_picture.sh
Executable file
9
compute_picture.sh
Executable file
@ -0,0 +1,9 @@
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#!/bin/bash
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for i in $(seq -50 50); do
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for j in $(seq 0 50); do
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if [ $i -ne 0 ] || [ $j -ne 0 ]; then
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IDLIST=output/idlist_13 ./complex_anosov summary 15124 1 1 1 $i/50 $j/50
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fi
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done
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done
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134
enumerate.c
134
enumerate.c
@ -3,25 +3,84 @@
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#include <stdlib.h>
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#define LOOP(i,n) for(int i = 0; i < (n); i++)
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// #define INFO(msg, ...) fprintf(stderr, "[%10.3f] " msg, runtime(), ##__VA_ARGS__)
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#define INFO(msg, ...)
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void enumerate_coxeter_group(group_t *group, mat *gen, mat *matrices)
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static int compare_int(const void *a, const void *b)
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{
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TYPE t = GETTYPE(gen[0]->x[0]);
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const int *aa = a;
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const int *bb = b;
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return (*aa > *bb) - (*aa < *bb);
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}
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static int index_in_list(const int *list, int n, int key)
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{
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int *ptr = bsearch(&key, list, n, sizeof(int), compare_int);
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if(ptr)
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return ptr - list;
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else
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return -1;
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}
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// idlist is assumed to be sorted and symmetric
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void enumerate_coxeter_group(group_t *group, mat *gen, mat *matrices, const int *idlist, int nlist)
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{
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TYPE type = GETTYPE(gen[0]->x[0]);
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mat_workspace *ws;
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ws = mat_workspace_init(3, t);
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// mark elements which we need to compute
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int ncompute = 0;
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LOOP(i, group->size) group->elements[i].need_to_compute = 0;
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LOOP(i, nlist) {
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groupelement_t *cur = &group->elements[idlist[i]];
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while(cur && cur->need_to_compute == 0) {
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cur->need_to_compute = 1;
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ncompute++;
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cur = cur->parent;
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}
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}
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INFO("need to compute %d elements for %d elements in list\n", ncompute, nlist);
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mat_identity(matrices[0]);
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for(int i = 1; i < group->size; i++) {
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if(!group->elements[i].inverse)
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continue;
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// compute them depth first
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int maxlen = group->elements[group->size-1].length;
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int parent = group->elements[i].parent->id;
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int letter = group->elements[i].letter;
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groupelement_t **stack = malloc((maxlen+1)*sizeof(groupelement_t));
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int *letter_stack = malloc((maxlen+1)*sizeof(int));
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mat *matrix_stack = malloc((maxlen+1)*sizeof(mat));
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int level = 0;
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mat_multiply(ws, matrices[i], matrices[parent], gen[letter]);
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LOOP(i, maxlen+1) mat_init(matrix_stack[i], 3, type);
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ws = mat_workspace_init(3, type);
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stack[0] = &group->elements[0];
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mat_identity(matrix_stack[0]);
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letter_stack[0] = 0;
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while(level >= 0) {
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int letter = letter_stack[level];
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groupelement_t *next = stack[level]->left[letter];
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if(next && next->length > level && next->need_to_compute) {
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mat_multiply(ws, matrix_stack[level+1], gen[letter], matrix_stack[level]);
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int id = next->id;
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int listid = index_in_list(idlist, nlist, id);
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if(listid != -1)
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mat_copy(matrices[listid], matrix_stack[level+1]);
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next->need_to_compute = 0;
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stack[level+1] = next;
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letter_stack[level+1] = 0;
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level++;
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} else {
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letter = ++letter_stack[level];
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while(letter >= group->rank) { // done with this level, go back down
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level--;
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if(level < 0)
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break;
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letter = ++letter_stack[level];
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}
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}
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}
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LOOP(i, maxlen+1) mat_clear(matrix_stack[i]);
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mat_workspace_clear(ws);
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}
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|
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@ -48,44 +107,45 @@ static int compare_tracedata_id(const void *a, const void *b)
|
||||
return ida > idb ? 1 : ida < idb ? -1 : 0;
|
||||
}
|
||||
|
||||
int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **traces_out)
|
||||
int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **traces_out, const int *idlist, int nlist, int unique)
|
||||
{
|
||||
TYPE t = GETTYPE(gen[0]->x[0]);
|
||||
int n = group->size;
|
||||
int nuniq;
|
||||
|
||||
mat *matrices = malloc(n*sizeof(mat));
|
||||
struct tracedata *traces = malloc(n*sizeof(struct tracedata));
|
||||
struct tracedata **distinct_traces = malloc(n*sizeof(struct tracedata*));
|
||||
mat *matrices = malloc(nlist*sizeof(mat));
|
||||
struct tracedata *traces = malloc(nlist*sizeof(struct tracedata));
|
||||
struct tracedata **distinct_traces = malloc(nlist*sizeof(struct tracedata*));
|
||||
|
||||
LOOP(i, n) mat_init(matrices[i], 3, t);
|
||||
enumerate_coxeter_group(group, gen, matrices);
|
||||
LOOP(i, nlist) mat_init(matrices[i], 3, t);
|
||||
enumerate_coxeter_group(group, gen, matrices, idlist, nlist);
|
||||
|
||||
LOOP(i, n) {
|
||||
LOOP(i, nlist) {
|
||||
INIT(traces[i].tr, t);
|
||||
INIT(traces[i].trinv, t);
|
||||
}
|
||||
LOOP(i, n) {
|
||||
if(!group->elements[i].inverse)
|
||||
continue;
|
||||
int inv_id_in_list = index_in_list(idlist, nlist, group->elements[idlist[i]].inverse->id);
|
||||
mat_trace(traces[i].tr, matrices[i]);
|
||||
mat_trace(traces[i].trinv, matrices[group->elements[i].inverse->id]);
|
||||
traces[i].id = i;
|
||||
mat_trace(traces[i].trinv, matrices[inv_id_in_list]);
|
||||
traces[i].id = idlist[i];
|
||||
distinct_traces[i] = &traces[i];
|
||||
}
|
||||
|
||||
qsort(distinct_traces, n, sizeof(struct tracedata*), compare_tracedata);
|
||||
if(unique) {
|
||||
qsort(distinct_traces, nlist, sizeof(struct tracedata*), compare_tracedata);
|
||||
|
||||
int nuniq = 0;
|
||||
LOOP(i, n) {
|
||||
if(i == 0 || compare_tracedata(&distinct_traces[i], &distinct_traces[nuniq-1]) != 0) {
|
||||
distinct_traces[nuniq] = distinct_traces[i];
|
||||
nuniq++;
|
||||
} else {
|
||||
int oldlength = group->elements[distinct_traces[nuniq-1]->id].length;
|
||||
int newlength = group->elements[distinct_traces[i]->id].length;
|
||||
if(newlength < oldlength)
|
||||
distinct_traces[nuniq-1]->id = distinct_traces[i]->id;
|
||||
nuniq = 0;
|
||||
LOOP(i, nlist) {
|
||||
if(i == 0 || compare_tracedata(&distinct_traces[i], &distinct_traces[nuniq-1]) != 0) {
|
||||
distinct_traces[nuniq] = distinct_traces[i];
|
||||
nuniq++;
|
||||
} else {
|
||||
int oldlength = group->elements[distinct_traces[nuniq-1]->id].length;
|
||||
int newlength = group->elements[distinct_traces[i]->id].length;
|
||||
if(newlength < oldlength)
|
||||
distinct_traces[nuniq-1]->id = distinct_traces[i]->id;
|
||||
}
|
||||
}
|
||||
} else {
|
||||
nuniq = nlist;
|
||||
}
|
||||
|
||||
qsort(distinct_traces, nuniq, sizeof(struct tracedata*), compare_tracedata_id);
|
||||
@ -99,8 +159,8 @@ int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **
|
||||
unique_traces[i].id = distinct_traces[i]->id;
|
||||
}
|
||||
|
||||
LOOP(i, n) mat_clear(matrices[i]);
|
||||
LOOP(i, n) {
|
||||
LOOP(i, nlist) mat_clear(matrices[i]);
|
||||
LOOP(i, nlist) {
|
||||
CLEAR(traces[i].tr);
|
||||
CLEAR(traces[i].trinv);
|
||||
}
|
||||
|
||||
@ -12,8 +12,8 @@ struct tracedata {
|
||||
NUMBER trinv;
|
||||
};
|
||||
|
||||
void enumerate_coxeter_group(group_t *group, mat *gen, mat *matrices);
|
||||
int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **traces_out);
|
||||
void enumerate_coxeter_group(group_t *group, mat *gen, mat *matrices, const int *idlist, int nlist);
|
||||
int enumerate_coxeter_group_traces(group_t *group, mat *gen, struct tracedata **traces_out, const int *idlist, int nlist, int unique);
|
||||
|
||||
void enumerate_tracedata_clear(struct tracedata *traces, int n);
|
||||
|
||||
|
||||
62
generators.c
62
generators.c
@ -3,39 +3,39 @@
|
||||
|
||||
#define LOOP(i,n) for(int i = 0; i < (n); i++)
|
||||
|
||||
void generators_triangle_reflection_generic(mat *gen, NUMBER rho1, NUMBER rho2, NUMBER rho3, NUMBER q)
|
||||
void generators_triangle_reflection_generic(mat *gen, NUMBER sqrho1, NUMBER sqrho2, NUMBER sqrho3, NUMBER t)
|
||||
{
|
||||
NUMBER tmp;
|
||||
NUMBER qinv;
|
||||
TYPE t = GETTYPE(rho1);
|
||||
NUMBER tinv;
|
||||
TYPE type = GETTYPE(sqrho1);
|
||||
|
||||
INIT(tmp, t);
|
||||
INIT(qinv, t);
|
||||
INV(qinv, q);
|
||||
INIT(tmp, type);
|
||||
INIT(tinv, type);
|
||||
INV(tinv, t);
|
||||
|
||||
LOOP(i, 3) {
|
||||
mat_init(gen[i], 3, t);
|
||||
mat_init(gen[i], 3, type);
|
||||
mat_zero(gen[i]);
|
||||
LOOP(j, 3) {
|
||||
SET_INT(*mat_ref(gen[i], j, j), i == j ? 1 : -1);
|
||||
}
|
||||
}
|
||||
|
||||
MUL(tmp, q, rho1);
|
||||
MUL(tmp, t, sqrho1);
|
||||
NEG(*mat_ref(gen[2], 1, 2), tmp);
|
||||
MUL(tmp, q, rho2);
|
||||
NEG(*mat_ref(gen[0], 2, 0), tmp);
|
||||
MUL(tmp, q, rho3);
|
||||
NEG(*mat_ref(gen[1], 0, 1), tmp);
|
||||
NEG(*mat_ref(gen[0], 2, 0), sqrho2);
|
||||
NEG(*mat_ref(gen[1], 0, 1), sqrho3);
|
||||
|
||||
NEG(*mat_ref(gen[1], 2, 1), qinv);
|
||||
NEG(*mat_ref(gen[2], 0, 2), qinv);
|
||||
NEG(*mat_ref(gen[0], 1, 0), qinv);
|
||||
MUL(tmp, tinv, sqrho1);
|
||||
NEG(*mat_ref(gen[1], 2, 1), tmp);
|
||||
NEG(*mat_ref(gen[2], 0, 2), sqrho2);
|
||||
NEG(*mat_ref(gen[0], 1, 0), sqrho3);
|
||||
|
||||
CLEAR(tmp);
|
||||
CLEAR(qinv);
|
||||
CLEAR(tinv);
|
||||
}
|
||||
|
||||
// warning: this is not compatible anymore!
|
||||
int generators_triangle_reflection_group(mat *gen, int p1, int p2, int p3, int q1, int q2, int q3, mpq_t t)
|
||||
{
|
||||
int p[3] = {p1, p2, p3};
|
||||
@ -107,23 +107,23 @@ int generators_triangle_reflection_group_555_complex(mat *gen, int q1, int q2, i
|
||||
|
||||
int q[3] = {q1, q2, q3};
|
||||
|
||||
NUMBER rho[3];
|
||||
LOOP(i, 3) INIT(rho[i], QT_GAUSS_SQRT5);
|
||||
NUMBER sqrho[3];
|
||||
LOOP(i, 3) INIT(sqrho[i], QT_GAUSS_SQRT5);
|
||||
|
||||
// compute rho1, rho2, rho3
|
||||
// compute sqrho1, sqrho2, sqrho3
|
||||
LOOP(i, 3) {
|
||||
if(q[i] == 1) {
|
||||
// 4cos(pi/5)^2 = 3/2 + 1/2*sqrt(5)
|
||||
mpq_set_si(rho[i]->a[0], 3, 2);
|
||||
mpq_set_si(rho[i]->a[1], 7, 12);
|
||||
mpq_set_si(rho[i]->a[2], 0, 1);
|
||||
mpq_set_si(rho[i]->a[3], -1, 24);
|
||||
// 2cos(pi/5) = 1/2 + 1/2*sqrt(5) = 1/2 + 7/12 a - 1/24 a^3
|
||||
mpq_set_si(sqrho[i]->a[0], 1, 2);
|
||||
mpq_set_si(sqrho[i]->a[1], 7, 12);
|
||||
mpq_set_si(sqrho[i]->a[2], 0, 1);
|
||||
mpq_set_si(sqrho[i]->a[3], -1, 24);
|
||||
} else if(q[i] == 2) {
|
||||
// 4cos(pi/5)^2 = 3/2 - 1/2*sqrt(5)
|
||||
mpq_set_si(rho[i]->a[0], 3, 2);
|
||||
mpq_set_si(rho[i]->a[1], -7, 12);
|
||||
mpq_set_si(rho[i]->a[2], 0, 1);
|
||||
mpq_set_si(rho[i]->a[3], 1, 24);
|
||||
// 2cos(pi/5) = -1/2 + 1/2*sqrt(5)
|
||||
mpq_set_si(sqrho[i]->a[0], -1, 2);
|
||||
mpq_set_si(sqrho[i]->a[1], 7, 12);
|
||||
mpq_set_si(sqrho[i]->a[2], 0, 1);
|
||||
mpq_set_si(sqrho[i]->a[3], -1, 24);
|
||||
} else {
|
||||
return 0;
|
||||
}
|
||||
@ -138,9 +138,9 @@ int generators_triangle_reflection_group_555_complex(mat *gen, int q1, int q2, i
|
||||
mpq_set_si(param->a[3], 1, 12);
|
||||
mpq_mul(param->a[3], param->a[3], timag);
|
||||
|
||||
generators_triangle_reflection_generic(gen, rho[0], rho[1], rho[2], param);
|
||||
generators_triangle_reflection_generic(gen, sqrho[0], sqrho[1], sqrho[2], param);
|
||||
|
||||
LOOP(i, 3) CLEAR(rho[i]);
|
||||
LOOP(i, 3) CLEAR(sqrho[i]);
|
||||
CLEAR(param);
|
||||
|
||||
return 1;
|
||||
|
||||
67
make_picture.py
Executable file
67
make_picture.py
Executable file
@ -0,0 +1,67 @@
|
||||
#!/usr/bin/python
|
||||
|
||||
import sys
|
||||
import math
|
||||
|
||||
def sharpen(x):
|
||||
alpha = 1
|
||||
y = abs(2*x-1)**alpha # between 0 and 1
|
||||
if x > 0.499 and x < 0.501:
|
||||
return 0.5
|
||||
elif x > 0.5:
|
||||
return (y+1)/2
|
||||
else:
|
||||
return (1-y)/2
|
||||
|
||||
f = open(sys.argv[1])
|
||||
lines = [x.split() for x in f]
|
||||
f.close()
|
||||
|
||||
res1 = int(sys.argv[2]) # 400 pixel per unit
|
||||
res2 = int(sys.argv[3]) # 50 pixel in picture (acutally one quadrant)
|
||||
|
||||
data = {(round(float(l[0])*res1), round(float(l[1])*res1)) : float(l[5]) for l in lines}
|
||||
data[(0,0)] = 2.0
|
||||
|
||||
print("P3")
|
||||
print("1000 1000")
|
||||
print("255")
|
||||
|
||||
for i in range (-500,500):
|
||||
for j in range(-500,500):
|
||||
x = j/500*res2
|
||||
y = i/500*res2
|
||||
|
||||
if y < 0:
|
||||
y = -y
|
||||
|
||||
x0 = math.floor(x)
|
||||
y0 = math.floor(y)
|
||||
x1 = math.ceil(x)
|
||||
y1 = math.ceil(y)
|
||||
tx = sharpen(x-x0)
|
||||
ty = sharpen(y-y0)
|
||||
|
||||
if not (x0,y0) in data or not (x0,y1) in data or not (x1,y0) in data or not (x1,y1) in data:
|
||||
value = 0
|
||||
else:
|
||||
value = 0.0
|
||||
value += data[(x0,y0)]*(1-tx)*(1-ty)
|
||||
value += data[(x0,y1)]*(1-tx)*ty
|
||||
value += data[(x1,y0)]*tx*(1-ty)
|
||||
value += data[(x1,y1)]*tx*ty
|
||||
value -= 1
|
||||
|
||||
value = 0 if value < 0 else 1 if value > 1 else value
|
||||
|
||||
r = round(255*math.sqrt(value))
|
||||
g = round(255*(value)**3)
|
||||
b = round(255*math.sin(2*math.pi*(value)))
|
||||
|
||||
r = 0 if r < 0 else 255 if r > 255 else r
|
||||
g = 0 if g < 0 else 255 if g > 255 else g
|
||||
b = 0 if b < 0 else 255 if b > 255 else b
|
||||
|
||||
print("%d %d %d" % (r,g,b))
|
||||
|
||||
#print(data)
|
||||
Loading…
Reference in New Issue
Block a user