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triangle_group_limit_set
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florian:master
florian:asymmetric_distance

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Author SHA1 Message Date
Florian Stecker 78769593a7 movie command line arguments 2023-02-05 15:10:16 -05:00
Florian Stecker a8b4bb7c2c implement rotation group and play around with it a bit 2022-07-29 14:38:48 +09:00
Florian Stecker 35932782e9 new .gitignore 2022-03-02 10:53:19 -06:00
6 changed files with 685 additions and 572 deletions
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@ -0,0 +1,3 @@
*.o
limit_set
*.pdf

396
draw.c
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@ -46,21 +46,22 @@ int fixedPoints(DrawingContext *ctx, const char *word, vector_t *out)
{
gsl_matrix *tmp = getTempMatrix(ctx->ws);
gsl_matrix *ev = getTempMatrix(ctx->ws);
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
initializeTriangleGenerators(gen, ctx->cartan);
initializeTriangleGeneratorsCurrent(gen, ctx);
gsl_matrix_set_identity(tmp);
for(int i = 0; i < strlen(word); i++) {
if(word[i] == ' ')
continue;
multiply_right(tmp, gen[word[i]-'a'], ctx->ws);
if(word[i] >= 'a' && word[i] <= 'c')
multiply_right(tmp, gen[word[i]-'a'], ctx->ws);
else if(word[i] >= 'A' && word[i] <= 'C')
multiply_right(tmp, gen[word[i]-'A'+3], ctx->ws);
}
int count = real_eigenvectors(tmp, ev, ctx->ws);
LOOP(i) LOOP(j) out[i].x[j] = gsl_matrix_get(ev, j, i);
releaseTempMatrices(ctx->ws, 5);
releaseTempMatrices(ctx->ws, 8);
return count;
}
@ -69,9 +70,9 @@ int wordEigenvalues(DrawingContext *ctx, const char *word, double *out)
{
gsl_matrix *tmp = getTempMatrix(ctx->ws);
gsl_vector *ev = getTempVector(ctx->ws);
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
initializeTriangleGenerators(gen, ctx->cartan);
initializeTriangleGeneratorsCurrent(gen, ctx);
gsl_matrix_set_identity(tmp);
for(int i = 0; i < strlen(word); i++) {
@ -83,7 +84,7 @@ int wordEigenvalues(DrawingContext *ctx, const char *word, double *out)
LOOP(i) out[i] = gsl_vector_get(ev, i);
releaseTempMatrices(ctx->ws, 4);
releaseTempMatrices(ctx->ws, 7);
releaseTempVectors(ctx->ws, 1);
return count;
@ -298,8 +299,6 @@ void drawBoxLines(DrawingContext *ctx, const char *word1, const char *word2)
drawPolygon(ctx, 0, 4, p[0][0], i[0], p[1][0], i[1]);
}
void drawBoxStd(DrawingContext *ctx, const char *word, char base)
{
char word1[100];
@ -329,13 +328,13 @@ void drawRotationOrbitFrame(DrawingContext *ctx, gsl_matrix *frame, vector_t sta
vector_t v[3], w;
point_t p;
double parameter, startangle;
int iterations = 200;
int iterations = 2000;
gsl_matrix *inverse = getTempMatrix(ctx->ws);
gsl_vector *start_v = getTempVector(ctx->ws);
gsl_vector *start_in_frame = getTempVector(ctx->ws);
cairo_t *C = ctx->cairo;
// computeRotationMatrix(ctx, frame, word);
// computeRotationMatrixFrame(ctx, frame, word);
LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);
LOOP(i) gsl_vector_set(start_v, i, start.x[i]);
@ -371,7 +370,7 @@ void drawRotationOrbit(DrawingContext *ctx, const char *word, vector_t start)
{
gsl_matrix *frame = getTempMatrix(ctx->ws);
computeRotationMatrix(ctx, frame, word);
computeRotationMatrixFrame(ctx, frame, word);
drawRotationOrbitFrame(ctx, frame, start);
releaseTempMatrices(ctx->ws, 1);
@ -389,7 +388,7 @@ void drawDualRotationOrbit(DrawingContext *ctx, const char *word, vector_t start
gsl_vector *start_in_frame = getTempVector(ctx->ws);
cairo_t *C = ctx->cairo;
computeRotationMatrix(ctx, frame, word);
computeRotationMatrixFrame(ctx, frame, word);
LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);
LOOP(i) gsl_vector_set(start_v, i, start.x[i]);
@ -434,7 +433,7 @@ void drawArcWithOutput(DrawingContext *ctx, const char *word, vector_t start, ve
gsl_vector *vector_in_frame = getTempVector(ctx->ws);
cairo_t *C = ctx->cairo;
computeRotationMatrix(ctx, frame, word);
computeRotationMatrixFrame(ctx, frame, word);
LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);
LOOP(i) gsl_vector_set(vector, i, start.x[i]);
@ -576,9 +575,9 @@ void drawAttractors(DrawingContext *ctx)
vector_t p[6][3];
vector_t l[6][3];
fixedPoints(ctx, "abc", p[0]);
fixedPoints(ctx, "bca", p[1]);
fixedPoints(ctx, "cab", p[2]);
fixedPoints(ctx, "cba", p[0]);
fixedPoints(ctx, "bac", p[1]);
fixedPoints(ctx, "acb", p[2]);
fixedPoints(ctx, "a cab a", p[3]);
fixedPoints(ctx, "b abc b", p[4]);
fixedPoints(ctx, "c bca c", p[5]);
@ -705,200 +704,180 @@ void drawCurvedBox(DrawingContext *ctx, int base, const char *conj, int style)
}
}
groupelement_t *left(const char *word, groupelement_t *g)
{
int n = strlen(word);
for(int i = n-1; i >= 0; i--) {
if(word[i] == ' ')
continue;
g = g->adj[word[i]-'a'];
if(!g)
break;
}
return g;
}
void drawBoxes(DrawingContext *ctx)
{
gsl_matrix *rot = getTempMatrix(ctx->ws);
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
gsl_matrix *tmp = getTempMatrix(ctx->ws);
gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
gsl_matrix *frame = getTempMatrix(ctx->ws);
gsl_matrix *frame2 = getTempMatrix(ctx->ws);
gsl_vector *startpoint_drawbasis = getTempVector(ctx->ws);
gsl_vector *startpoint_globalbasis = getTempVector(ctx->ws);
gsl_matrix **elements = getTempMatrices(ctx->ws, ctx->n_group_elements);
cairo_t *C = ctx->cairo;
cairo_save(C);
vector_t p[22][3];
vector_t l[22][3];
vector_t alpha[6];
vector_t ptmp[3];
char word[100], word2[100];
fixedPoints(ctx, "abc", p[0]);
fixedPoints(ctx, "bca", p[1]);
fixedPoints(ctx, "cab", p[2]);
fixedPoints(ctx, "bacabab", p[3]);
fixedPoints(ctx, "bcacabacb", p[4]);
cairo_set_line_width(C, 2.0/ctx->dim->scalefactor);
cairo_set_source_rgb(C, 0.6, 0.6, 0.6);
drawRotationOrbit(ctx, "ab", p[0][0]);
drawRotationOrbit(ctx, "bc", p[0][0]);
drawRotationOrbit(ctx, "ca", p[0][0]);
vector_t p[22][3];
vector_t fp[3];
vector_t l[22][3];
vector_t alpha[6];
vector_t ptmp[3];
vector_t start;
vector_t start2;
char word[100], word2[100];
if(ctx->mode >= 2) {
cairo_set_source_rgb(C, 0.6, 0.6, 1);
drawRotationOrbit(ctx, "bcabcb", p[1][0]); // bcC
drawRotationOrbit(ctx, "abcabcba", p[0][0]); // abcC
// drawRotationOrbit(ctx, "bcabcabacb", p[1][0]); // bcabC''
// drawRotationOrbit(ctx, "bacabcacab", p[3][0]); // bacaC'
// drawRotationOrbit(ctx, "bcacabcacacb", p[4][0]); // bcacaC' bcacabacb
fixedPoints(ctx, "cba", p[0]);
fixedPoints(ctx, "acb", p[1]);
fixedPoints(ctx, "bac", p[2]);
initializeTriangleGeneratorsCurrent(gen, ctx);
gsl_matrix_set_identity(elements[0]);
for(int i = 1; i < ctx->n_group_elements; i++) {
if(ctx->group[i].length % 2)
continue;
int letter = ROTATION_LETTER(ctx->group[i].letter, ctx->group[i].parent->letter);
multiply(gen[letter], elements[ctx->group[i].parent->parent->id], elements[i]);
}
cairo_set_source_rgb(C, 1, 0, 1);
// drawRotationOrbit(ctx, "bacabcacab", p[3][0]); // ababcba
cairo_set_source_rgb(C, 0, 0, 0);
fixedPoints(ctx, "abababcbaba", p[3]);
// drawRotationOrbit(ctx, "abababcabcbababa", p[3][0]); // bab abc bab
cairo_set_source_rgb(C, 0, 0, 1);
// fixedPoints(ctx, "cab", p[3]);
// drawRotationOrbit(ctx, "cabc", p[3][0]);
// fixedPoints(ctx, "bca", p[3]);
// drawRotationOrbit(ctx, "bcabcb", p[3][0]);
// fixedPoints(ctx, "bc abc cb", p[3]);
// drawRotationOrbit(ctx, "bcabcb", p[3][0]);
fixedPoints(ctx, "bc bca cb", p[3]);
// drawRotationOrbit(ctx, "bcbcacbc", p[3][0]);
gsl_vector_set(startpoint_drawbasis, 0, ctx->marking.x);
gsl_vector_set(startpoint_drawbasis, 1, ctx->marking.y);
gsl_vector_set(startpoint_drawbasis, 2, 1);
solve(ctx->cob, startpoint_drawbasis, startpoint_globalbasis, ctx->ws);
LOOP(i) start.x[i] = gsl_vector_get(startpoint_globalbasis, i);
/*
cairo_set_source_rgb(C, 0, 0, 0);
strncpy(word,"abc",100);
for(int i = 0; i < 9; i++) {
conjugate_word(word, 0, "ab", word2);
strncpy(word, word2, 100);
fixedPoints(ctx, word, ptmp);
drawVector(ctx, ptmp[0]);
// drawVector(ctx, ptmp[2]);
fixedPoints(ctx, "ABAB", fp);
drawCovector(ctx, cross(fp[0], fp[2]));
drawVector(ctx, fp[1]);
computeRotationMatrixFrame(ctx, frame, "c");
drawRotationOrbit(ctx, "c", start); // ba cb ab ac = C A c B
drawVector(ctx, start);
computeMatrix(ctx, tmp, "ABABc");
start2 = apply(tmp, start);
computeRotationMatrixFrame(ctx, frame, "c");
multiply(tmp, frame, frame2);
drawVector(ctx, start2);
drawRotationOrbitFrame(ctx, frame2, apply(tmp, start));
computeMatrix(ctx, tmp, "ABABcABABC");
start2 = apply(tmp, start);
computeRotationMatrixFrame(ctx, frame, "c");
multiply(tmp, frame, frame2);
drawVector(ctx, start2);
drawRotationOrbitFrame(ctx, frame2, apply(tmp, start));
*/
for(groupelement_t *cur = &ctx->group[180]; cur->parent; cur = cur->parent)
fputc('a'+cur->letter, stdout);
fputc('\n', stdout);
queue_t queue;
queue_init(&queue);
queue_put(&queue, 0);
int current;
groupelement_t *cur, *next;
for(int i = 0; i < ctx->n_group_elements_combinatorial; i++)
ctx->group[i].visited = 0;
cur = &ctx->group[0];
computeRotationMatrixFrame(ctx, frame, "c");
for(int i = 0; i < 1000; i++) {
if(ctx->group[i].length % 2 != 0)
continue;
multiply(elements[i], frame, frame2);
drawRotationOrbitFrame(ctx, frame2, apply(elements[i], start));
}
strncpy(word,"bca",100);
for(int i = 0; i < 9; i++) {
conjugate_word(word, 0, "ab", word2);
strncpy(word, word2, 100);
fixedPoints(ctx, word, ptmp);
drawVector(ctx, ptmp[0]);
// drawVector(ctx, ptmp[2]);
}
/*
while((current = queue_get(&queue)) != -1) {
cur = &ctx->group[current];
if(cur->visited > 4)
continue;
strncpy(word,"abc",100);
for(int i = 0; i < 9; i++) {
conjugate_word(word, 0, "bc", word2);
strncpy(word, word2, 100);
fixedPoints(ctx, word, ptmp);
drawVector(ctx, ptmp[0]);
}
strncpy(word,"cab",100);
for(int i = 0; i < 9; i++) {
conjugate_word(word, 0, "bc", word2);
strncpy(word, word2, 100);
fixedPoints(ctx, word, ptmp);
drawVector(ctx, ptmp[0]);
}
strncpy(word,"cab",100);
for(int i = 0; i < 9; i++) {
conjugate_word(word, 0, "ca", word2);
strncpy(word, word2, 100);
fixedPoints(ctx, word, ptmp);
drawVector(ctx, ptmp[0]);
}
strncpy(word,"abc",100);
for(int i = 0; i < 9; i++) {
conjugate_word(word, 0, "ca", word2);
strncpy(word, word2, 100);
fixedPoints(ctx, word, ptmp);
drawVector(ctx, ptmp[0]);
if(cur->id < ctx->n_group_elements) {
multiply(elements[cur->id], frame, frame2);
drawRotationOrbitFrame(ctx, frame2, apply(elements[cur->id], start));
}
next = left("ab ab", cur);
if(next && next->visited == 0) {
queue_put(&queue, next->id);
next->visited = cur->visited+1;
}
next = left("cbac cbac", cur);
if(next && next->visited == 0) {
queue_put(&queue, next->id);
next->visited = cur->visited+1;
}
next = left("cacbca cacbca", cur);
if(next && next->visited == 0) {
queue_put(&queue, next->id);
next->visited = cur->visited+1;
}
next = left("cabcacbcac cabcacbcac", cur);
if(next && next->visited == 0) {
queue_put(&queue, next->id);
next->visited = cur->visited+1;
}
next = left("acbcacba acbcacba", cur);
if(next && next->visited == 0) {
queue_put(&queue, next->id);
next->visited = cur->visited+1;
}
next = left("bcacbc bcacbc", cur);
if(next && next->visited == 0) {
queue_put(&queue, next->id);
next->visited = cur->visited+1;
}
}
*/
/*
cairo_set_source_rgb(C, 1, 0, 0);
drawVector(ctx, p[0][0]);
cairo_set_source_rgb(C, 0, 0.6, 0);
drawVector(ctx, p[1][0]);
cairo_set_source_rgb(C, 0, 0, 1);
drawVector(ctx, p[2][0]);
*/
/*
fixedPoints(ctx, "ab abc ba", p[4]);
fixedPoints(ctx, "abab abc baba", p[5]);
fixedPoints(ctx, "ababab abc bababa", p[6]);
fixedPoints(ctx, "abababab abc babababa", p[7]);
fixedPoints(ctx, "babababa abc abababab", p[8]);
fixedPoints(ctx, "bababa abc ababab", p[9]);
fixedPoints(ctx, "baba abc abab", p[10]);
fixedPoints(ctx, "ba abc ab", p[11]);
fixedPoints(ctx, "bca", p[12]);
fixedPoints(ctx, "b abc b", p[13]);
fixedPoints(ctx, "bab abc bab", p[14]);
fixedPoints(ctx, "babab abc babab", p[15]);
fixedPoints(ctx, "bababab abc bababab", p[16]);
fixedPoints(ctx, "abababab bca babababa", p[17]);
fixedPoints(ctx, "ababab bca bababa", p[18]);
fixedPoints(ctx, "abab bca baba", p[19]);
fixedPoints(ctx, "ab bca ba", p[20]);
*/
// initializeTriangleGenerators(gen, ctx->cartan);
// for(int i = 0; i < 22; i++) LOOP(j) l[i][j] = cross(p[i][(3-j)%3], p[i][(4-j)%3]);
// LOOP(i) LOOP(j) alpha[i].x[j] = gsl_matrix_get(ctx->cartan, i, j);
/*
gsl_matrix_set(frame, 0, 0, 2.0);
gsl_matrix_set(frame, 0, 1, 0.0);
gsl_matrix_set(frame, 0, 2, 1.0);
gsl_matrix_set(frame, 1, 0, -1.0);
gsl_matrix_set(frame, 1, 1, sqrt(3));
gsl_matrix_set(frame, 1, 2, 1.0);
gsl_matrix_set(frame, 2, 0, -1.0);
gsl_matrix_set(frame, 2, 1, -sqrt(3));
gsl_matrix_set(frame, 2, 2, 1.0);*/
// drawRotationOrbitFrame(ctx, frame, p[0][0]);
// drawRotationOrbit(ctx, "bc", p[0][0]);
// drawRotationOrbit(ctx, "ca", p[0][0]);
/*
for(int i = 0; i < 18; i++) {
if(i == 0)
cairo_set_source_rgb(C, 1, 0, 0);
else if(i == 8)
cairo_set_source_rgb(C, 0, 0, 1);
else if(i == 9)
cairo_set_source_rgb(C, 0, 0.6, 0);
else
cairo_set_source_rgb(C, 0, 0, 0);
drawVector(ctx, p[3+i][0]);
// drawCovector(ctx, l[3+i][0]);
}
*/
// drawRotationOrbit(ctx, "ab", cross(l[0][0], l[2][1]));
// drawRotationOrbit(ctx, "abca", p[0][0]);
// drawRotationOrbit(ctx, "a", p[1][0]);
// drawRotationOrbit(ctx, "b", p[2][0]);
cairo_restore(C);
releaseTempMatrices(ctx->ws, 5);
releaseTempMatrices(ctx->ws, 9 + ctx->n_group_elements);
releaseTempVectors(ctx->ws, 2);
}
void drawBoxes2(DrawingContext *ctx)
{
gsl_matrix *rot = getTempMatrix(ctx->ws);
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
cairo_t *C = ctx->cairo;
cairo_save(C);
initializeTriangleGenerators(gen, ctx->cartan);
initializeTriangleGeneratorsCurrent(gen, ctx);
vector_t p[4][3];
fixedPoints(ctx, "abc", p[0]);
fixedPoints(ctx, "bca", p[1]);
fixedPoints(ctx, "cab", p[2]);
fixedPoints(ctx, "cba", p[0]);
fixedPoints(ctx, "acb", p[1]);
fixedPoints(ctx, "bac", p[2]);
cairo_set_line_width(C, 2.5/ctx->dim->scalefactor);
@ -1262,13 +1241,13 @@ void drawBoxes2(DrawingContext *ctx)
*/
cairo_restore(C);
releaseTempMatrices(ctx->ws, 4);
releaseTempMatrices(ctx->ws, 7);
}
void drawRotatedReflectors(DrawingContext *ctx)
{
gsl_matrix *rot = getTempMatrix(ctx->ws);
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
cairo_t *C = ctx->cairo;
vector_t fp[3], fp2[3];
vector_t w;
@ -1276,7 +1255,7 @@ void drawRotatedReflectors(DrawingContext *ctx)
cairo_set_source_rgb(C, 0.7, 0.7, 0.7);
initializeTriangleGenerators(gen, ctx->cartan);
initializeTriangleGeneratorsCurrent(gen, ctx);
LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(ctx->cartan, i, j);
multiply(gen[0], gen[1], rot);
@ -1297,7 +1276,7 @@ void drawRotatedReflectors(DrawingContext *ctx)
fixedPoints(ctx, "cacabac", fp2);
drawRotationOrbit(ctx, "ac", fp[0]);
releaseTempMatrices(ctx->ws, 4);
releaseTempMatrices(ctx->ws, 7);
}
void drawDualLimitCurve(DrawingContext *ctx)
@ -1307,12 +1286,36 @@ void drawDualLimitCurve(DrawingContext *ctx)
cairo_save(C);
cairo_set_source_rgb(C, 0.5, 0.5, 1);
int n = 18;
vector_t p[n][3];
vector_t l[n][3];
vector_t ptmp[3], ltmp[3];
gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
gsl_matrix **elements = getTempMatrices(ctx->ws, ctx->n_group_elements);
fixedPoints(ctx, "abc", p[0]);
// wordEigenvalues(ctx, "abc", ev);
// LOOP(i) LOOP(j) gsl_matrix_set(coxeter_fixedpoints, j, i, cox[0][i].x[j]);
initializeTriangleGeneratorsCurrent(gen, ctx);
gsl_matrix_set_identity(elements[0]);
for(int i = 1; i < ctx->n_group_elements; i++)
multiply(gen[ctx->group[i].letter], elements[ctx->group[i].parent->id], elements[i]);
vector_t p[3], l[3], v;
fixedPoints(ctx, "cba", p);
drawVector(ctx, p[0]);
drawVector(ctx, p[1]);
drawVector(ctx, p[2]);
LOOP(i) l[i] = cross(p[(i+1)%3], p[(i+2)%3]);
for(int i = 0; i < ctx->n_group_elements; i++) {
v = apply_transpose(elements[i], l[0]);
drawCovector(ctx, v);
}
releaseTempMatrices(ctx->ws, 3 + ctx->n_group_elements);
// releaseTempVectors(ctx->ws, 4);
/*
fixedPoints(ctx, "ab abc ba", p[1]);
fixedPoints(ctx, "abab abc baba", p[2]);
fixedPoints(ctx, "ababab abc bababa", p[3]);
@ -1331,6 +1334,7 @@ void drawDualLimitCurve(DrawingContext *ctx)
fixedPoints(ctx, "bababa bca ababab", p[15]);
fixedPoints(ctx, "baba bca abab", p[16]);
fixedPoints(ctx, "ba bca ab", p[17]);
*/
/*
fixedPoints(ctx, "abc", p[0]);
@ -1368,6 +1372,7 @@ void drawDualLimitCurve(DrawingContext *ctx)
// drawCovector(ctx, l[i][2]);
}*/
/*
fixedPoints(ctx, "abc", ptmp);
drawCovector(ctx, cross(ptmp[0], ptmp[1]));
fixedPoints(ctx, "bca", ptmp);
@ -1380,6 +1385,7 @@ void drawDualLimitCurve(DrawingContext *ctx)
drawCovector(ctx, cross(ptmp[0], ptmp[1]));
fixedPoints(ctx, "acaba", ptmp);
drawCovector(ctx, cross(ptmp[0], ptmp[1]));
*/
cairo_restore(C);
}
@ -1435,7 +1441,7 @@ void drawLimitCurve(DrawingContext *ctx)
void drawCoxeterOrbit(DrawingContext *ctx)
{
gsl_matrix *rot = getTempMatrix(ctx->ws);
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
gsl_vector *eval = getTempVector(ctx->ws);
gsl_matrix *coxeter_fixedpoints = getTempMatrix(ctx->ws);
gsl_vector *startpoint_coxeterbasis = getTempVector(ctx->ws);
@ -1452,7 +1458,7 @@ void drawCoxeterOrbit(DrawingContext *ctx)
int first = 1;
cairo_save(C);
initializeTriangleGenerators(gen, ctx->cartan);
initializeTriangleGeneratorsCurrent(gen, ctx);
cairo_set_source_rgb(C, 0, 0, 1);
@ -1463,7 +1469,7 @@ void drawCoxeterOrbit(DrawingContext *ctx)
wordEigenvalues(ctx, "abc", ev);
LOOP(i) LOOP(j) gsl_matrix_set(coxeter_fixedpoints, j, i, cox[0][i].x[j]);
initializeTriangleGenerators(gen, ctx->cartan);
initializeTriangleGeneratorsCurrent(gen, ctx);
gsl_matrix_set_identity(elements[0]);
for(int i = 1; i < ctx->n_group_elements; i++)
multiply(gen[ctx->group[i].letter], elements[ctx->group[i].parent->id], elements[i]);
@ -1477,7 +1483,7 @@ void drawCoxeterOrbit(DrawingContext *ctx)
gsl_vector_set(startpoint_drawbasis, 2, 1);
solve(ctx->cob, startpoint_drawbasis, startpoint_globalbasis, ctx->ws);
solve(coxeter_fixedpoints, startpoint_globalbasis, startpoint_coxeterbasis, ctx->ws);
// solve(coxeter_fixedpoints, startpoint_globalbasis, startpoint_coxeterbasis, ctx->ws);
// LOOP(i) start.x[i] = gsl_vector_get(startpoint_coxeterbasis, i);
LOOP(i) start.x[i] = gsl_vector_get(startpoint_globalbasis, i);
@ -1517,7 +1523,7 @@ void drawCoxeterOrbit(DrawingContext *ctx)
// LOOP(i) drawVector(ctx, abcb[i]);
cairo_restore(C);
releaseTempMatrices(ctx->ws, 5 + ctx->n_group_elements);
releaseTempMatrices(ctx->ws, 8 + ctx->n_group_elements);
releaseTempVectors(ctx->ws, 4);
}
@ -1526,7 +1532,7 @@ void drawText(DrawingContext *ctx)
cairo_move_to(ctx->cairo, 15, 30);
cairo_set_source_rgb(ctx->cairo, 0, 0, 0);
char buf[100];
sprintf(buf, "t = exp(%.8f) = %.8f, marking = (%.5f, %.5f)", log(ctx->parameter), ctx->parameter, ctx->marking.x, ctx->marking.y);
sprintf(buf, "t = exp(%.8f) = %.8f, s = exp(%.8f) = %.8f, marking = (%.5f, %.5f)", log(ctx->parameter), ctx->parameter, log(ctx->parameter2), ctx->parameter2, ctx->marking.x, ctx->marking.y);
cairo_show_text(ctx->cairo, buf);
}

107
limit_set.c
View File

@ -5,6 +5,7 @@ static int compareAngle(const void *x, const void *y)
return ((double*)x)[2] > ((double*)y)[2] ? 1 : -1;
}
// might need a rewrite
void cartanMatrix(gsl_matrix *cartan, double a1, double a2, double a3, double s)
{
gsl_matrix_set(cartan, 0, 0, 2);
@ -20,11 +21,58 @@ void cartanMatrix(gsl_matrix *cartan, double a1, double a2, double a3, double s)
gsl_matrix_set(cartan, 2, 2, 2);
}
void initializeTriangleGenerators(gsl_matrix **gen, gsl_matrix *cartan)
void initializeTriangleGenerators(gsl_matrix **gen, double a1, double a2, double a3, double s, double t, workspace_t *ws)
{
LOOP(i) gsl_matrix_set_identity(gen[i]);
LOOP(i) LOOP(j) *gsl_matrix_ptr(gen[i], j, j) = -1.0;
LOOP(i) LOOP(j) *gsl_matrix_ptr(gen[i], i, j) += gsl_matrix_get(cartan, i, j);
gsl_matrix *reflection_gen[3];
LOOP(i) {
reflection_gen[i] = gsl_matrix_alloc(3, 3);
gsl_matrix_set_identity(reflection_gen[i]);
}
double rho[3];
rho[0] = sqrt(s*s + 2*s*cos(a1) + 1);
rho[1] = sqrt(s*s + 2*s*cos(a2) + 1);
rho[2] = sqrt(s*s + 2*s*cos(a3) + 1);
gsl_matrix_set(reflection_gen[0], 0, 0, -1.0);
gsl_matrix_set(reflection_gen[0], 0, 1, rho[2]*t);
gsl_matrix_set(reflection_gen[0], 0, 2, rho[1]/t);
gsl_matrix_set(reflection_gen[1], 1, 0, rho[2]/t);
gsl_matrix_set(reflection_gen[1], 1, 1, -1.0);
gsl_matrix_set(reflection_gen[1], 1, 2, rho[0]*t);
gsl_matrix_set(reflection_gen[2], 2, 0, rho[1]*t);
gsl_matrix_set(reflection_gen[2], 2, 1, rho[0]/t);
gsl_matrix_set(reflection_gen[2], 2, 2, -1.0);
LOOP(i) {
gsl_matrix_set_identity(gen[i]);
gsl_matrix_set(gen[i], (i+1)%3, (i+1)%3, s);
gsl_matrix_set(gen[i], (i+2)%3, (i+2)%3, 1/s);
gsl_matrix_set_identity(gen[i+3]);
gsl_matrix_set(gen[i+3], (i+1)%3, (i+1)%3, 1/s);
gsl_matrix_set(gen[i+3], (i+2)%3, (i+2)%3, s);
}
LOOP(i) {
multiply_left(reflection_gen[i], gen[(i+2)%3], ws);
multiply_right(gen[(i+2)%3], reflection_gen[(i+1)%3], ws);
multiply_left(reflection_gen[(i+1)%3], gen[(i+2)%3+3], ws);
multiply_right(gen[(i+2)%3+3], reflection_gen[i], ws);
}
LOOP(i) gsl_matrix_free(reflection_gen[i]);
}
void initializeTriangleGeneratorsCurrent(gsl_matrix **gen, DrawingContext *ctx)
{
double angle[3];
LOOP(i) angle[i] = 2*M_PI*ctx->k[i]/ctx->p[i];
initializeTriangleGenerators(gen, angle[0], angle[1], angle[2], ctx->parameter2, ctx->parameter, ctx->ws);
}
int computeLimitCurve(DrawingContext *ctx)
@ -38,7 +86,7 @@ int computeLimitCurve(DrawingContext *ctx)
gsl_matrix *coxeter = getTempMatrix(ctx->ws);
gsl_matrix *coxeter_fixedpoints = getTempMatrix(ctx->ws);
gsl_matrix *fixedpoints = getTempMatrix(ctx->ws);
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
gsl_matrix **elements = getTempMatrices(ctx->ws, ctx->n_group_elements);
groupelement_t *group = ctx->group;
int success = 0;
@ -50,31 +98,43 @@ int computeLimitCurve(DrawingContext *ctx)
// do first in the Fuchsian positive case to get the angles
cartanMatrix(cartan_pos, M_PI/ctx->p[0], M_PI/ctx->p[1], M_PI/ctx->p[2], 1.0);
initializeTriangleGenerators(gen, cartan_pos);
initializeTriangleGenerators(gen, 2*M_PI/ctx->p[0], 2*M_PI/ctx->p[1], 2*M_PI/ctx->p[2], 1.0, 1.0, ctx->ws);
gsl_matrix_set_identity(elements[0]);
for(int i = 1; i < ctx->n_group_elements; i++)
multiply(gen[group[i].letter], elements[group[i].parent->id], elements[i]);
for(int i = 1; i < ctx->n_group_elements; i++) {
if(group[i].length % 2)
continue;
int letter = ROTATION_LETTER(group[i].letter, group[i].parent->letter);
multiply(gen[letter], elements[group[i].parent->parent->id], elements[i]);
}
diagonalize_symmetric_form(cartan_pos, cob_pos, ws);
multiply_many(ws, coxeter_pos, 3, gen[0], gen[1], gen[2]);
multiply_many(ws, coxeter_pos, 3, gen[2], gen[1], gen[0]);
int ev_count_pos = real_eigenvectors(coxeter_pos, coxeter_fixedpoints_pos, ws);
if(ev_count_pos != 3)
goto error_out;
int n = 0;
for(int i = 0; i < ctx->n_group_elements; i++) {
if(group[i].length % 2)
continue;
multiply_many(ws, fixedpoints_pos, 3, cob_pos, elements[i], coxeter_fixedpoints_pos);
ctx->limit_curve[3*i+2] = atan2(
ctx->limit_curve[3*n+2] = atan2(
gsl_matrix_get(fixedpoints_pos, 2, column)/gsl_matrix_get(fixedpoints_pos, 0, column),
gsl_matrix_get(fixedpoints_pos, 1, column)/gsl_matrix_get(fixedpoints_pos, 0, column));
n++;
}
// now do it again to calculate x and y coordinates
initializeTriangleGenerators(gen, ctx->cartan);
initializeTriangleGeneratorsCurrent(gen, ctx);
gsl_matrix_set_identity(elements[0]);
for(int i = 1; i < ctx->n_group_elements; i++)
multiply(gen[group[i].letter], elements[group[i].parent->id], elements[i]);
for(int i = 1; i < ctx->n_group_elements; i++) {
if(group[i].length % 2)
continue;
int letter = ROTATION_LETTER(group[i].letter, group[i].parent->letter);
multiply(gen[letter], elements[group[i].parent->parent->id], elements[i]);
}
multiply_many(ws, coxeter, 3, gen[0], gen[1], gen[2]);
multiply_many(ws, coxeter, 3, gen[2], gen[1], gen[0]);
int ev_count = real_eigenvectors(coxeter, coxeter_fixedpoints, ws);
if(ev_count == 1)
@ -82,11 +142,17 @@ int computeLimitCurve(DrawingContext *ctx)
if(ev_count == 0)
goto error_out;
ctx->limit_curve_count = 0;
for(int i = 0; i < ctx->n_group_elements; i++) {
if(group[i].length % 2)
continue;
multiply_many(ws, fixedpoints, 3, ctx->cob, elements[i], coxeter_fixedpoints);
x = ctx->limit_curve[3*i ] = gsl_matrix_get(fixedpoints, 0, column)/gsl_matrix_get(fixedpoints, 2, column);
y = ctx->limit_curve[3*i+1] = gsl_matrix_get(fixedpoints, 1, column)/gsl_matrix_get(fixedpoints, 2, column);
x = ctx->limit_curve[3*ctx->limit_curve_count ] = gsl_matrix_get(fixedpoints, 0, column)/gsl_matrix_get(fixedpoints, 2, column);
y = ctx->limit_curve[3*ctx->limit_curve_count+1] = gsl_matrix_get(fixedpoints, 1, column)/gsl_matrix_get(fixedpoints, 2, column);
ctx->limit_curve_count++;
if((x - ctx->marking.x)*(x - ctx->marking.x) + (y - ctx->marking.y)*(y - ctx->marking.y) < 25e-10)
{
@ -95,19 +161,16 @@ int computeLimitCurve(DrawingContext *ctx)
fputc('a' + cur->letter, stdout); // bcbcbca, bacbcacab, bc bca cb
fputc('\n',stdout);
}
// bca abc acb = abc
}
qsort(ctx->limit_curve, ctx->n_group_elements, 3*sizeof(double), compareAngle);
qsort(ctx->limit_curve, ctx->limit_curve_count, 3*sizeof(double), compareAngle);
ctx->limit_curve_count = ctx->n_group_elements;
// ctx->limit_curve_count = ctx->n_group_elements;
success = 1;
error_out:
releaseTempMatrices(ctx->ws, 11+ctx->n_group_elements);
releaseTempMatrices(ctx->ws, 14+ctx->n_group_elements);
return success;
}

731
main.c
View File

@ -11,447 +11,474 @@
#include "linalg.h"
#define TOGGLE(a) do { (a) = !(a); } while(0)
#define SIGN(x) ((x) > 0 ? 1.0 : -1.0)
DrawingContext *screen_context;
// setup everything except cairo and dim, which will be provided by the graphics system
void setupContext(DrawingContext *ctx, int argc, char *argv[])
{
ctx->n_group_elements = NUM_GROUP_ELEMENTS;
ctx->p[0] = atoi(argv[1]);
ctx->p[1] = atoi(argv[2]);
ctx->p[2] = atoi(argv[3]);
ctx->k[0] = atoi(argv[4]);
ctx->k[1] = atoi(argv[5]);
ctx->k[2] = atoi(argv[6]);
if(argc > 7)
ctx->parameter = atof(argv[7]);
else
ctx->parameter = 1.0;
// ctx->parameter = 2.77;
// ctx->parameter = 0.1;
ctx->show_boxes = 0;
ctx->show_boxes2 = 0;
ctx->show_attractors = 0;
ctx->show_reflectors = 0;
ctx->show_rotated_reflectors = 0;
ctx->show_limit= 0;
ctx->show_dual_limit= 0;
ctx->show_text = 1;
ctx->mode = 0;
ctx->use_rotation_basis = 0;
ctx->limit_with_lines = 1;
ctx->use_repelling = 0;
ctx->show_marking = 1;
ctx->marking.x = -0.73679;
ctx->marking.y = -0.01873;
ctx->show_coxeter_orbit = 0;
ctx->n_group_elements = NUM_GROUP_ELEMENTS;
ctx->n_group_elements_combinatorial = NUM_GROUP_ELEMENTS_COMBINATORIAL;
ctx->p[0] = atoi(argv[1]);
ctx->p[1] = atoi(argv[2]);
ctx->p[2] = atoi(argv[3]);
ctx->k[0] = atoi(argv[4]);
ctx->k[1] = atoi(argv[5]);
ctx->k[2] = atoi(argv[6]);
if(argc > 7)
ctx->parameter = atof(argv[7]);
else
ctx->parameter = 1.0;
if(argc > 8)
ctx->parameter2 = atof(argv[8]);
else
ctx->parameter2 = 1.0;
if(argc > 12) {
ctx->movie_filename = argv[9];
ctx->movie_parameter_duration = atof(argv[10]);
ctx->movie_parameter2_duration = atof(argv[11]);
ctx->movie_n_frames = atoi(argv[12]);
} else {
ctx->movie_n_frames = 0;
}
// ctx->parameter = 2.77;
// ctx->parameter = 0.1;
ctx->show_boxes = 0;
ctx->show_boxes2 = 0;
ctx->show_attractors = 0;
ctx->show_reflectors = 0;
ctx->show_rotated_reflectors = 0;
ctx->show_limit = 0;
ctx->show_dual_limit = 0;
ctx->show_text = 1;
ctx->mode = 0;
ctx->use_rotation_basis = 1;
ctx->limit_with_lines = 0;
ctx->use_repelling = 0;
ctx->show_marking = 0;
ctx->marking.x = -0.73679;
ctx->marking.y = -0.01873;
ctx->show_coxeter_orbit = 0;
ctx->limit_curve = malloc(3*ctx->n_group_elements*sizeof(double));
ctx->limit_curve_count = -1;
ctx->limit_curve = malloc(3*ctx->n_group_elements*sizeof(double));
ctx->limit_curve_count = -1;
ctx->group = malloc(ctx->n_group_elements*sizeof(groupelement_t));
generate_triangle_group(ctx->group, ctx->n_group_elements, ctx->p[0], ctx->p[1], ctx->p[2]);
ctx->group = malloc(ctx->n_group_elements_combinatorial*sizeof(groupelement_t));
generate_triangle_group(ctx->group, ctx->n_group_elements_combinatorial, ctx->p[0], ctx->p[1], ctx->p[2]);
// the temporary stuff
ctx->cartan = gsl_matrix_alloc(3, 3);
ctx->cob = gsl_matrix_alloc(3, 3);
ctx->ws = workspace_alloc(3);
// the temporary stuff
ctx->cartan = gsl_matrix_alloc(3, 3);
ctx->cob = gsl_matrix_alloc(3, 3);
ctx->ws = workspace_alloc(3);
}
void destroyContext(DrawingContext *ctx)
{
free(ctx->limit_curve);
free(ctx->group);
free(ctx->limit_curve);
free(ctx->group);
gsl_matrix_free(ctx->cartan);
gsl_matrix_free(ctx->cob);
gsl_matrix_free(ctx->cartan);
gsl_matrix_free(ctx->cob);
workspace_free(ctx->ws);
workspace_free(ctx->ws);
}
void computeRotationMatrix(DrawingContext *ctx, gsl_matrix *result, const char *type)
void computeMatrix(DrawingContext *ctx, gsl_matrix *result, const char *type)
{
gsl_matrix *tmp = getTempMatrix(ctx->ws);
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
// ERROR(strlen(type) != 2, "Invalid call of computeRotationMatrix()\n");
// ERROR(strlen(type) != 2, "Invalid call of computeRotationMatrix()\n");
initializeTriangleGenerators(gen, ctx->cartan);
gsl_matrix_set_identity(tmp);
for(int i = 0; i < strlen(type); i++)
multiply_right(tmp, gen[type[i]-'a'], ctx->ws);
initializeTriangleGeneratorsCurrent(gen, ctx);
gsl_matrix_set_identity(result);
for(int i = 0; i < strlen(type); i++) {
if(type[i] >= 'a' && type[i] <= 'c')
multiply_right(result, gen[type[i]-'a'], ctx->ws);
else if(type[i] >= 'A' && type[i] <= 'C')
multiply_right(result, gen[type[i]-'A'+3], ctx->ws);
}
rotation_frame(tmp, result, ctx->ws);
releaseTempMatrices(ctx->ws, 6);
}
releaseTempMatrices(ctx->ws, 4);
void computeRotationMatrixFrame(DrawingContext *ctx, gsl_matrix *result, const char *type)
{
gsl_matrix *tmp = getTempMatrix(ctx->ws);
computeMatrix(ctx, tmp, type);
rotation_frame(tmp, result, ctx->ws);
releaseTempMatrices(ctx->ws, 1);
}
void computeBoxTransform(DrawingContext *ctx, char *word1, char *word2, gsl_matrix *result)
{
vector_t p[2][3],i[2];
vector_t std[4] = {
{-1, -1, 1},
{-1, 1, 1},
{1, 1, 1},
{1, -1, 1}
};
vector_t p[2][3],i[2];
vector_t std[4] = {
{-1, -1, 1},
{-1, 1, 1},
{1, 1, 1},
{1, -1, 1}
};
gsl_vector **vertices = getTempVectors(ctx->ws, 4);
gsl_vector **std_vertices = getTempVectors(ctx->ws, 4);
gsl_matrix *tmp = getTempMatrix(ctx->ws);
gsl_matrix *to_frame = getTempMatrix(ctx->ws);
gsl_matrix *to_std_frame = getTempMatrix(ctx->ws);
gsl_vector **vertices = getTempVectors(ctx->ws, 4);
gsl_vector **std_vertices = getTempVectors(ctx->ws, 4);
gsl_matrix *tmp = getTempMatrix(ctx->ws);
gsl_matrix *to_frame = getTempMatrix(ctx->ws);
gsl_matrix *to_std_frame = getTempMatrix(ctx->ws);
fixedPoints(ctx, word1, p[0]);
fixedPoints(ctx, word2, p[1]);
fixedPoints(ctx, word1, p[0]);
fixedPoints(ctx, word2, p[1]);
// intersect attracting line with neutral line of the other element
for(int j = 0; j < 2; j++)
i[j] = cross(cross(p[j%2][0],p[j%2][1]),cross(p[(j+1)%2][0],p[(j+1)%2][2]));
// intersect attracting line with neutral line of the other element
for(int j = 0; j < 2; j++)
i[j] = cross(cross(p[j%2][0],p[j%2][1]),cross(p[(j+1)%2][0],p[(j+1)%2][2]));
// box consists of p[0][0], i[0], p[1][0], i[1]
// box consists of p[0][0], i[0], p[1][0], i[1]
for(int i = 0; i < 4; i++)
vectorToGsl(std[i], std_vertices[i]);
for(int i = 0; i < 4; i++)
vectorToGsl(std[i], std_vertices[i]);
vectorToGsl(p[0][0], vertices[0]);
vectorToGsl(i[0], vertices[1]);
vectorToGsl(p[1][0], vertices[2]);
vectorToGsl(i[1], vertices[3]);
vectorToGsl(p[0][0], vertices[0]);
vectorToGsl(i[0], vertices[1]);
vectorToGsl(p[1][0], vertices[2]);
vectorToGsl(i[1], vertices[3]);
projective_frame(std_vertices, to_std_frame, ctx->ws);
projective_frame(vertices, to_frame, ctx->ws);
invert(to_frame, tmp, ctx->ws);
multiply(to_std_frame, tmp, result);
projective_frame(std_vertices, to_std_frame, ctx->ws);
projective_frame(vertices, to_frame, ctx->ws);
invert(to_frame, tmp, ctx->ws);
multiply(to_std_frame, tmp, result);
/*
LOOP(i) {
LOOP(j) {
printf("%.4f ", gsl_matrix_get(result, i, j));
}
printf("\n");
}*/
/*
LOOP(i) {
LOOP(j) {
printf("%.4f ", gsl_matrix_get(result, i, j));
}
printf("\n");
}*/
releaseTempVectors(ctx->ws, 8);
releaseTempMatrices(ctx->ws, 3);
releaseTempVectors(ctx->ws, 8);
releaseTempMatrices(ctx->ws, 3);
}
void updateMatrices(DrawingContext *ctx)
{
double angle[3];
LOOP(i) angle[i] = M_PI*ctx->k[i]/ctx->p[i];
cartanMatrix(ctx->cartan, angle[0], angle[1], angle[2], ctx->parameter);
double angle[3];
LOOP(i) angle[i] = M_PI*ctx->k[i]/ctx->p[i];
cartanMatrix(ctx->cartan, angle[0], angle[1], angle[2], ctx->parameter);
gsl_matrix *tmp = getTempMatrix(ctx->ws);
gsl_matrix *tmp = getTempMatrix(ctx->ws);
int nmodes = 5;
if(ctx->use_rotation_basis % 5 == 0) {
gsl_matrix_set(tmp, 0, 0, 0.0);
gsl_matrix_set(tmp, 0, 1, sqrt(3.0)/2.0);
gsl_matrix_set(tmp, 0, 2, -sqrt(3.0)/2.0);
gsl_matrix_set(tmp, 1, 0, 1.0);
gsl_matrix_set(tmp, 1, 1, -0.5);
gsl_matrix_set(tmp, 1, 2, -0.5);
gsl_matrix_set(tmp, 2, 0, 1.0);
gsl_matrix_set(tmp, 2, 1, 1.0);
gsl_matrix_set(tmp, 2, 2, 1.0);
gsl_matrix_memcpy(ctx->cob, tmp);
} else if(ctx->use_rotation_basis % 5 == 1) {
gsl_matrix_memcpy(ctx->cob, ctx->cartan); // is this a good choice of basis for any reason?
} else if(ctx->use_rotation_basis % 5 == 2) {
computeRotationMatrix(ctx, tmp, "ba");
invert(tmp, ctx->cob, ctx->ws);
} else if(ctx->use_rotation_basis % 5 == 3) {
computeBoxTransform(ctx, "bca", "abc", ctx->cob);
// computeBoxTransform(ctx, "cab", "bca", ctx->cob);
// computeBoxTransform(ctx, "acb", "cba", ctx->cob);
} else {
cartanMatrix(tmp, M_PI/ctx->p[0], M_PI/ctx->p[1], M_PI/ctx->p[2], 1.0);
diagonalize_symmetric_form(tmp, ctx->cob, ctx->ws);
}
if(ctx->use_rotation_basis % nmodes == 0) {
gsl_matrix_set(tmp, 0, 0, 0.0);
gsl_matrix_set(tmp, 0, 1, sqrt(3.0)/2.0);
gsl_matrix_set(tmp, 0, 2, -sqrt(3.0)/2.0);
gsl_matrix_set(tmp, 1, 0, 1.0);
gsl_matrix_set(tmp, 1, 1, -0.5);
gsl_matrix_set(tmp, 1, 2, -0.5);
gsl_matrix_set(tmp, 2, 0, 1.0);
gsl_matrix_set(tmp, 2, 1, 1.0);
gsl_matrix_set(tmp, 2, 2, 1.0);
gsl_matrix_memcpy(ctx->cob, tmp);
} else if(ctx->use_rotation_basis % nmodes == 1) {
gsl_matrix_set(tmp, 0, 0, 1.0);
gsl_matrix_set(tmp, 0, 1, -1.0);
gsl_matrix_set(tmp, 0, 2, 0.0);
gsl_matrix_set(tmp, 1, 0, 1.0);
gsl_matrix_set(tmp, 1, 1, 1.0);
gsl_matrix_set(tmp, 1, 2, 0.0);
gsl_matrix_set(tmp, 2, 0, 0.0);
gsl_matrix_set(tmp, 2, 1, 0.0);
gsl_matrix_set(tmp, 2, 2, 1.0);
gsl_matrix_memcpy(ctx->cob, ctx->cartan); // is this a good choice of basis for any reason?
multiply_left(tmp, ctx->cob, ctx->ws);
} else if(ctx->use_rotation_basis % nmodes == 2) {
computeRotationMatrixFrame(ctx, tmp, "C");
invert(tmp, ctx->cob, ctx->ws);
} else if(ctx->use_rotation_basis % nmodes == 3) {
computeBoxTransform(ctx, "acb", "cba", ctx->cob);
// computeBoxTransform(ctx, "cab", "bca", ctx->cob);
// computeBoxTransform(ctx, "acb", "cba", ctx->cob);
} else {
cartanMatrix(tmp, M_PI/ctx->p[0], M_PI/ctx->p[1], M_PI/ctx->p[2], 1.0);
diagonalize_symmetric_form(tmp, ctx->cob, ctx->ws);
}
releaseTempMatrices(ctx->ws, 1);
releaseTempMatrices(ctx->ws, 1);
}
void output_info(DrawingContext *ctx)
{
vector_t p[4][3];
point_t pt;
vector_t p[4][3];
point_t pt;
fixedPoints(ctx, "abc", p[0]);
fixedPoints(ctx, "bca", p[1]);
fixedPoints(ctx, "cab", p[2]);
fixedPoints(ctx, "abc", p[0]);
fixedPoints(ctx, "bca", p[1]);
fixedPoints(ctx, "cab", p[2]);
pt = vectorToPoint(ctx, p[0][0]);
printf("(abc)-+ = (%f %f)\n", pt.x, pt.y);
pt = vectorToPoint(ctx, p[1][0]);
printf("(bca)-+ = (%f %f)\n", pt.x, pt.y);
pt = vectorToPoint(ctx, p[0][0]);
printf("(abc)-+ = (%f %f)\n", pt.x, pt.y);
pt = vectorToPoint(ctx, p[1][0]);
printf("(bca)-+ = (%f %f)\n", pt.x, pt.y);
}
void print(DrawingContext *screen)
{
DrawingContext file;
DimensionsInfo dim;
cairo_surface_t *surface;
DrawingContext file;
DimensionsInfo dim;
cairo_surface_t *surface;
char filename[100];
time_t t = time(NULL);
strftime(filename, sizeof(filename), "screenshot_%Y%m%d_%H%M%S.pdf", localtime(&t));
char filename[100];
time_t t = time(NULL);
strftime(filename, sizeof(filename), "screenshot_%Y%m%d_%H%M%S.pdf", localtime(&t));
memcpy(&file, screen, sizeof(file));
memcpy(&file, screen, sizeof(file));
dim.width = screen->dim->width;
dim.height = screen->dim->width / sqrt(2.0);
dim.matrix = screen->dim->matrix;
dim.matrix.y0 += ((double)dim.height - (double)screen->dim->height) / 2.0; // recenter vertically
updateDimensions(&dim);
file.dim = &dim;
dim.width = screen->dim->width;
dim.height = screen->dim->width / sqrt(2.0);
dim.matrix = screen->dim->matrix;
dim.matrix.y0 += ((double)dim.height - (double)screen->dim->height) / 2.0; // recenter vertically
updateDimensions(&dim);
file.dim = &dim;
surface = cairo_pdf_surface_create(filename, (double)dim.width, (double)dim.height);
surface = cairo_pdf_surface_create(filename, (double)dim.width, (double)dim.height);
file.cairo = cairo_create(surface);
draw(&file);
draw(&file);
cairo_destroy(file.cairo);
cairo_surface_destroy(surface);
cairo_destroy(file.cairo);
cairo_surface_destroy(surface);
printf("Wrote sceenshot to file: %s\n", filename);
printf("Wrote sceenshot to file: %s\n", filename);
}
int processEvent(GraphicsInfo *info, XEvent *ev)
{
int state;
unsigned long key;
char filename[100];
int state;
unsigned long key;
char filename[100];
// fprintf(stderr, "Event: %d\n", ev->type);
// fprintf(stderr, "Event: %d\n", ev->type);
switch(ev->type) {
case ButtonPress:
state = ev->xbutton.state & (ShiftMask | LockMask | ControlMask);
switch(ev->type) {
case ButtonPress:
state = ev->xbutton.state & (ShiftMask | LockMask | ControlMask);
if(ev->xbutton.button == 1 && state & ShiftMask) {
screen_context->marking.x = (double)ev->xbutton.x;
screen_context->marking.y = (double)ev->xbutton.y;
printf("mouse button pressed: %f, %f\n", screen_context->marking.x, screen_context->marking.y);
cairo_set_matrix(screen_context->cairo, &screen_context->dim->matrix);
cairo_device_to_user(screen_context->cairo, &screen_context->marking.x, &screen_context->marking.y);
printf("mouse button pressed transformed: %f, %f\n", screen_context->marking.x, screen_context->marking.y);
return STATUS_REDRAW;
}
break;
if(ev->xbutton.button == 1 && state & ShiftMask) {
screen_context->marking.x = (double)ev->xbutton.x;
screen_context->marking.y = (double)ev->xbutton.y;
printf("mouse button pressed: %f, %f\n", screen_context->marking.x, screen_context->marking.y);
cairo_set_matrix(screen_context->cairo, &screen_context->dim->matrix);
cairo_device_to_user(screen_context->cairo, &screen_context->marking.x, &screen_context->marking.y);
printf("mouse button pressed transformed: %f, %f\n", screen_context->marking.x, screen_context->marking.y);
return STATUS_REDRAW;
}
break;
case KeyPress:
state = ev->xkey.state & (ShiftMask | LockMask | ControlMask);
key = XkbKeycodeToKeysym(ev->xkey.display, ev->xkey.keycode, 0, !!(state & ShiftMask));
printf("Key pressed: %ld\n", key);
case KeyPress:
state = ev->xkey.state & (ShiftMask | LockMask | ControlMask);
key = XkbKeycodeToKeysym(ev->xkey.display, ev->xkey.keycode, 0, !!(state & ShiftMask));
printf("Key pressed: %ld\n", key);
switch(key) {
case XK_Down:
screen_context->parameter /= exp(0.002);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Up:
screen_context->parameter *= exp(0.002);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Left:
screen_context->parameter /= exp(0.00002);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Right:
screen_context->parameter *= exp(0.00002);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Page_Down:
screen_context->parameter /= exp(0.02);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Page_Up:
screen_context->parameter *= exp(0.02);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case ' ':
screen_context->parameter = 5.57959706;
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Return:
// screen_context->parameter = 2.76375163;
screen_context->parameter = 5.29063366;
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case 'm':
printf("matrix.xx = %f;\n", info->dim->matrix.xx);
printf("matrix.xy = %f;\n", info->dim->matrix.xy);
printf("matrix.x0 = %f;\n", info->dim->matrix.x0);
printf("matrix.yx = %f;\n", info->dim->matrix.yx);
printf("matrix.yy = %f;\n", info->dim->matrix.yy);
printf("matrix.y0 = %f;\n", info->dim->matrix.y0);
break;
case 'i':
output_info(screen_context);
break;
case 'b':
TOGGLE(screen_context->show_boxes);
break;
case 'B':
TOGGLE(screen_context->show_boxes2);
break;
case 'a':
TOGGLE(screen_context->show_attractors);
break;
case 'r':
TOGGLE(screen_context->show_reflectors);
break;
case 'x':
TOGGLE(screen_context->show_rotated_reflectors);
break;
case 'L':
TOGGLE(screen_context->limit_with_lines);
break;
case 'l':
TOGGLE(screen_context->show_limit);
break;
case 'd':
TOGGLE(screen_context->show_dual_limit);
break;
case 'R':
screen_context->use_rotation_basis++;
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case 'p':
print(screen_context);
break;
case 'M':
/*
screen_context->limit_with_lines = 0;
double parameter_start = screen_context->parameter;
for(int i = 0; i <= 1300; i++) {
if(i < 400)
screen_context->parameter = exp(log(parameter_start)+0.002*i);
else if(i < 500)
screen_context->parameter = exp(log(parameter_start)+0.002*400);
else
screen_context->parameter = exp(log(parameter_start)+0.002*(900-i));
updateMatrices(screen_context);
computeLimitCurve(screen_context);
draw(screen_context);
sprintf(filename, "movie3/test%03d.png", i);
cairo_surface_write_to_png(info->buffer_surface, filename);
printf("Finished drawing %s\n", filename);
}
*/
screen_context->limit_with_lines = 0;
double parameter_start = screen_context->parameter;
for(int i = 0; i <= 1300; i++) {
if(i < 400)
screen_context->parameter = exp(0.003*i);
else if(i < 500)
screen_context->parameter = exp(0.003*400);
else
screen_context->parameter = exp(0.003*(900-i));
updateMatrices(screen_context);
computeLimitCurve(screen_context);
draw(screen_context);
sprintf(filename, "movie5/test%03d.png", i);
cairo_surface_write_to_png(info->buffer_surface, filename);
printf("Finished drawing %s\n", filename);
}
switch(key) {
case XK_Down:
if(ev->xkey.state & ShiftMask)
screen_context->parameter /= exp(0.00005);
else
screen_context->parameter /= exp(0.002);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Up:
if(ev->xkey.state & ShiftMask)
screen_context->parameter *= exp(0.00005);
else
screen_context->parameter *= exp(0.002);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Left:
if(ev->xkey.state & ShiftMask)
screen_context->parameter2 /= exp(0.00005);
else
screen_context->parameter2 /= exp(0.002);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Right:
if(ev->xkey.state & ShiftMask)
screen_context->parameter2 *= exp(0.00005);
else
screen_context->parameter2 *= exp(0.002);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Page_Down:
screen_context->parameter /= exp(0.02);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Page_Up:
screen_context->parameter *= exp(0.02);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case ' ':
screen_context->parameter = 5.57959706;
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Return:
// screen_context->parameter = 2.76375163;
screen_context->parameter = 5.29063366;
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case 'm':
printf("matrix.xx = %f;\n", info->dim->matrix.xx);
printf("matrix.xy = %f;\n", info->dim->matrix.xy);
printf("matrix.x0 = %f;\n", info->dim->matrix.x0);
printf("matrix.yx = %f;\n", info->dim->matrix.yx);
printf("matrix.yy = %f;\n", info->dim->matrix.yy);
printf("matrix.y0 = %f;\n", info->dim->matrix.y0);
break;
case 'i':
output_info(screen_context);
break;
case 'b':
TOGGLE(screen_context->show_boxes);
break;
case 'B':
TOGGLE(screen_context->show_boxes2);
break;
case 'a':
TOGGLE(screen_context->show_attractors);
break;
case 'r':
TOGGLE(screen_context->show_reflectors);
break;
case 'x':
TOGGLE(screen_context->show_rotated_reflectors);
break;
case 'L':
TOGGLE(screen_context->limit_with_lines);
break;
case 'l':
TOGGLE(screen_context->show_limit);
break;
case 'd':
TOGGLE(screen_context->show_dual_limit);
break;
case 'R':
screen_context->use_rotation_basis++;
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case 'p':
print(screen_context);
break;
case 'M':
screen_context->limit_with_lines = 0;
double parameter_start = screen_context->parameter;
double parameter2_start = screen_context->parameter2;
for(int i = 0; i <= screen_context->movie_n_frames; i++) {
screen_context->parameter = SIGN(parameter_start)*exp(log(fabs(parameter_start)) +
i*screen_context->movie_parameter_duration/screen_context->movie_n_frames);
screen_context->parameter2 = SIGN(parameter2_start)*exp(log(fabs(parameter2_start)) +
i*screen_context->movie_parameter2_duration/screen_context->movie_n_frames);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
draw(screen_context);
sprintf(filename, "output/%s%03d.png", screen_context->movie_filename, i);
cairo_surface_write_to_png(info->buffer_surface, filename);
printf("Finished drawing %s\n", filename);
}
case 'f':
TOGGLE(screen_context->use_repelling);
computeLimitCurve(screen_context);
break;
case 't':
TOGGLE(screen_context->show_text);
break;
case 'c':
TOGGLE(screen_context->show_coxeter_orbit);
break;
case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9': case '0':
screen_context->mode = key - '0';
break;
}
return STATUS_REDRAW;
case 'f':
TOGGLE(screen_context->use_repelling);
computeLimitCurve(screen_context);
break;
case 't':
TOGGLE(screen_context->show_text);
break;
case 'c':
TOGGLE(screen_context->show_coxeter_orbit);
break;
case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9': case '0':
screen_context->mode = key - '0';
break;
}
return STATUS_NOTHING;
return STATUS_REDRAW;
}
return STATUS_NOTHING;
}
int main(int argc, char *argv[])
{
GraphicsInfo *info;
GraphicsInfo *info;
screen_context = malloc(sizeof(DrawingContext));
setupContext(screen_context, argc, argv);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
screen_context = malloc(sizeof(DrawingContext));
setupContext(screen_context, argc, argv);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
info = initCairo(0, KeyPressMask, 200, 200, "Triangle group");
if(!info)
return 1;
info = initCairo(0, KeyPressMask, 200, 200, "Triangle group");
if(!info)
return 1;
/*
info->dim->matrix.xx = 274.573171;
info->dim->matrix.xy = 0.000000;
info->dim->matrix.x0 = 583.073462;
info->dim->matrix.yx = 0.000000;
info->dim->matrix.yy = 274.573171;
info->dim->matrix.y0 = 777.225293;
*/
/*
info->dim->matrix.xx = 274.573171;
info->dim->matrix.xy = 0.000000;
info->dim->matrix.x0 = 583.073462;
info->dim->matrix.yx = 0.000000;
info->dim->matrix.yy = 274.573171;
info->dim->matrix.y0 = 777.225293;
*/
info->dim->matrix.xx = 274.573171;
info->dim->matrix.xy = 0.000000;
info->dim->matrix.x0 = 910.073462;
info->dim->matrix.yx = 0.000000;
info->dim->matrix.yy = 274.573171;
info->dim->matrix.y0 = 509.225293;
info->dim->matrix.xx = 274.573171;
info->dim->matrix.xy = 0.000000;
info->dim->matrix.x0 = 910.073462;
info->dim->matrix.yx = 0.000000;
info->dim->matrix.yy = 274.573171;
info->dim->matrix.y0 = 509.225293;
updateDimensions(info->dim);
updateDimensions(info->dim);
screen_context->dim = info->dim;
screen_context->cairo = info->buffer_context;
screen_context->dim = info->dim;
screen_context->cairo = info->buffer_context;
startTimer(info);
startTimer(info);
while(1) {
int result = checkEvents(info, processEvent, NULL);
if(result == STATUS_QUIT)
return 0;
else if(result == STATUS_REDRAW) {
struct timeval current_time;
double start_time, intermediate_time, end_time;
gettimeofday(&current_time, 0);
start_time = current_time.tv_sec + current_time.tv_usec*1e-6;
while(1) {
int result = checkEvents(info, processEvent, NULL);
if(result == STATUS_QUIT)
return 0;
else if(result == STATUS_REDRAW) {
struct timeval current_time;
double start_time, intermediate_time, end_time;
gettimeofday(&current_time, 0);
start_time = current_time.tv_sec + current_time.tv_usec*1e-6;
draw(screen_context);
draw(screen_context);
gettimeofday(&current_time, 0);
intermediate_time = current_time.tv_sec + current_time.tv_usec*1e-6;
gettimeofday(&current_time, 0);
intermediate_time = current_time.tv_sec + current_time.tv_usec*1e-6;
cairo_set_source_surface(info->front_context, info->buffer_surface, 0, 0);
cairo_paint(info->front_context);
cairo_set_source_surface(info->front_context, info->buffer_surface, 0, 0);
cairo_paint(info->front_context);
gettimeofday(&current_time, 0);
end_time = current_time.tv_sec + current_time.tv_usec*1e-6;
printf("drawing finished in %.2f milliseconds, of which %.2f milliseconds were buffer switching\n", (end_time - start_time) * 1000, (end_time - intermediate_time) * 1000);
}
waitUpdateTimer(info);
gettimeofday(&current_time, 0);
end_time = current_time.tv_sec + current_time.tv_usec*1e-6;
printf("drawing finished in %.2f milliseconds, of which %.2f milliseconds were buffer switching\n", (end_time - start_time) * 1000, (end_time - intermediate_time) * 1000);
}
waitUpdateTimer(info);
}
free(screen_context);
destroyCairo(info);
destroyContext(screen_context);
free(screen_context);
destroyCairo(info);
destroyContext(screen_context);
return 0;
return 0;
}

19
main.h
View File

@ -11,7 +11,12 @@
#define ERROR(condition, msg, ...) if(condition){fprintf(stderr, msg, ##__VA_ARGS__); exit(1);}
#define LOOP(i) for(int i = 0; i < 3; i++)
#define NUM_GROUP_ELEMENTS 50000
#define NUM_GROUP_ELEMENTS 10000
#define NUM_GROUP_ELEMENTS_COMBINATORIAL 100000
// (0,1) -> 2, (1,2) -> 0, (2,0) -> 1
// (1,0) -> 5, (2,1) -> 3, (0,2) -> 4
#define ROTATION_LETTER(x,y) (((y)-(x)+3)%3 == 1 ? ((y)+1)%3 : ((x)+1)%3+3)
typedef struct {
double x[3];
@ -30,7 +35,13 @@ typedef struct {
// a priori parameter
int p[3],k[3];
double parameter;
double parameter2;
char *movie_filename;
double movie_parameter_duration;
double movie_parameter2_duration;
int movie_n_frames;
int n_group_elements;
int n_group_elements_combinatorial;
int show_boxes;
int show_boxes2;
int show_attractors;
@ -66,7 +77,8 @@ typedef enum {
// implemented in limit_set.c
void cartanMatrix(gsl_matrix *cartan, double a1, double a2, double a3, double s);
void initializeTriangleGenerators(gsl_matrix **gen, gsl_matrix *cartan);
void initializeTriangleGenerators(gsl_matrix **gen, double a1, double a2, double a3, double s, double t, workspace_t *ws);
void initializeTriangleGeneratorsCurrent(gsl_matrix **gen, DrawingContext *ctx);
int computeLimitCurve(DrawingContext *ctx);
// implemented in draw.c
@ -96,7 +108,8 @@ void setupContext(DrawingContext *ctx, int argc, char *argv[]);
void destroyContext(DrawingContext *ctx);
void print(DrawingContext *screen);
int processEvent(GraphicsInfo *info, XEvent *ev);
void computeRotationMatrix(DrawingContext *ctx, gsl_matrix *result, const char *type);
void computeMatrix(DrawingContext *ctx, gsl_matrix *result, const char *type);
void computeRotationMatrixFrame(DrawingContext *ctx, gsl_matrix *result, const char *type);
void updateMatrices(DrawingContext *ctx);
static vector_t vectorFromGsl(gsl_vector *v)

1
triangle.h
View File

@ -14,6 +14,7 @@ typedef struct _groupelement {
struct _groupelement *parent;
struct _groupelement *inverse;
int letter;
int visited;
} groupelement_t;
int generate_triangle_group(groupelement_t *group, int size, int k1, int k2, int k3);