implement rotation group and play around with it a bit
This commit is contained in:
Florian Stecker
parent
35932782e9
commit
a8b4bb7c2c
388
draw.c
388
draw.c
@ -46,21 +46,22 @@ int fixedPoints(DrawingContext *ctx, const char *word, vector_t *out)
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{
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gsl_matrix *tmp = getTempMatrix(ctx->ws);
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gsl_matrix *ev = getTempMatrix(ctx->ws);
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gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
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gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
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initializeTriangleGenerators(gen, ctx->cartan);
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initializeTriangleGeneratorsCurrent(gen, ctx);
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gsl_matrix_set_identity(tmp);
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for(int i = 0; i < strlen(word); i++) {
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if(word[i] == ' ')
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continue;
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if(word[i] >= 'a' && word[i] <= 'c')
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multiply_right(tmp, gen[word[i]-'a'], ctx->ws);
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else if(word[i] >= 'A' && word[i] <= 'C')
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multiply_right(tmp, gen[word[i]-'A'+3], ctx->ws);
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}
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int count = real_eigenvectors(tmp, ev, ctx->ws);
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LOOP(i) LOOP(j) out[i].x[j] = gsl_matrix_get(ev, j, i);
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releaseTempMatrices(ctx->ws, 5);
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releaseTempMatrices(ctx->ws, 8);
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return count;
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}
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@ -69,9 +70,9 @@ int wordEigenvalues(DrawingContext *ctx, const char *word, double *out)
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{
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gsl_matrix *tmp = getTempMatrix(ctx->ws);
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gsl_vector *ev = getTempVector(ctx->ws);
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gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
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gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
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initializeTriangleGenerators(gen, ctx->cartan);
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initializeTriangleGeneratorsCurrent(gen, ctx);
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gsl_matrix_set_identity(tmp);
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for(int i = 0; i < strlen(word); i++) {
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@ -83,7 +84,7 @@ int wordEigenvalues(DrawingContext *ctx, const char *word, double *out)
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LOOP(i) out[i] = gsl_vector_get(ev, i);
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releaseTempMatrices(ctx->ws, 4);
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releaseTempMatrices(ctx->ws, 7);
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releaseTempVectors(ctx->ws, 1);
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return count;
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@ -298,8 +299,6 @@ void drawBoxLines(DrawingContext *ctx, const char *word1, const char *word2)
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drawPolygon(ctx, 0, 4, p[0][0], i[0], p[1][0], i[1]);
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}
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void drawBoxStd(DrawingContext *ctx, const char *word, char base)
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{
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char word1[100];
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@ -329,13 +328,13 @@ void drawRotationOrbitFrame(DrawingContext *ctx, gsl_matrix *frame, vector_t sta
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vector_t v[3], w;
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point_t p;
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double parameter, startangle;
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int iterations = 200;
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int iterations = 2000;
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gsl_matrix *inverse = getTempMatrix(ctx->ws);
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gsl_vector *start_v = getTempVector(ctx->ws);
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gsl_vector *start_in_frame = getTempVector(ctx->ws);
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cairo_t *C = ctx->cairo;
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// computeRotationMatrix(ctx, frame, word);
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// computeRotationMatrixFrame(ctx, frame, word);
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LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);
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LOOP(i) gsl_vector_set(start_v, i, start.x[i]);
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@ -371,7 +370,7 @@ void drawRotationOrbit(DrawingContext *ctx, const char *word, vector_t start)
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{
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gsl_matrix *frame = getTempMatrix(ctx->ws);
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computeRotationMatrix(ctx, frame, word);
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computeRotationMatrixFrame(ctx, frame, word);
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drawRotationOrbitFrame(ctx, frame, start);
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releaseTempMatrices(ctx->ws, 1);
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@ -389,7 +388,7 @@ void drawDualRotationOrbit(DrawingContext *ctx, const char *word, vector_t start
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gsl_vector *start_in_frame = getTempVector(ctx->ws);
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cairo_t *C = ctx->cairo;
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computeRotationMatrix(ctx, frame, word);
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computeRotationMatrixFrame(ctx, frame, word);
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LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);
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LOOP(i) gsl_vector_set(start_v, i, start.x[i]);
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@ -434,7 +433,7 @@ void drawArcWithOutput(DrawingContext *ctx, const char *word, vector_t start, ve
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gsl_vector *vector_in_frame = getTempVector(ctx->ws);
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cairo_t *C = ctx->cairo;
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computeRotationMatrix(ctx, frame, word);
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computeRotationMatrixFrame(ctx, frame, word);
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LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);
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LOOP(i) gsl_vector_set(vector, i, start.x[i]);
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@ -576,9 +575,9 @@ void drawAttractors(DrawingContext *ctx)
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vector_t p[6][3];
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vector_t l[6][3];
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fixedPoints(ctx, "abc", p[0]);
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fixedPoints(ctx, "bca", p[1]);
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fixedPoints(ctx, "cab", p[2]);
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fixedPoints(ctx, "cba", p[0]);
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fixedPoints(ctx, "bac", p[1]);
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fixedPoints(ctx, "acb", p[2]);
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fixedPoints(ctx, "a cab a", p[3]);
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fixedPoints(ctx, "b abc b", p[4]);
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fixedPoints(ctx, "c bca c", p[5]);
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@ -705,200 +704,180 @@ void drawCurvedBox(DrawingContext *ctx, int base, const char *conj, int style)
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}
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}
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groupelement_t *left(const char *word, groupelement_t *g)
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{
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int n = strlen(word);
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for(int i = n-1; i >= 0; i--) {
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if(word[i] == ' ')
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continue;
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g = g->adj[word[i]-'a'];
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if(!g)
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break;
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}
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return g;
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}
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void drawBoxes(DrawingContext *ctx)
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{
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gsl_matrix *rot = getTempMatrix(ctx->ws);
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gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
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gsl_matrix *tmp = getTempMatrix(ctx->ws);
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gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
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gsl_matrix *frame = getTempMatrix(ctx->ws);
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gsl_matrix *frame2 = getTempMatrix(ctx->ws);
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gsl_vector *startpoint_drawbasis = getTempVector(ctx->ws);
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gsl_vector *startpoint_globalbasis = getTempVector(ctx->ws);
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gsl_matrix **elements = getTempMatrices(ctx->ws, ctx->n_group_elements);
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cairo_t *C = ctx->cairo;
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cairo_save(C);
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vector_t p[22][3];
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vector_t l[22][3];
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vector_t alpha[6];
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vector_t ptmp[3];
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char word[100], word2[100];
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fixedPoints(ctx, "abc", p[0]);
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fixedPoints(ctx, "bca", p[1]);
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fixedPoints(ctx, "cab", p[2]);
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fixedPoints(ctx, "bacabab", p[3]);
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fixedPoints(ctx, "bcacabacb", p[4]);
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cairo_set_line_width(C, 2.0/ctx->dim->scalefactor);
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cairo_set_source_rgb(C, 0.6, 0.6, 0.6);
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drawRotationOrbit(ctx, "ab", p[0][0]);
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drawRotationOrbit(ctx, "bc", p[0][0]);
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drawRotationOrbit(ctx, "ca", p[0][0]);
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vector_t p[22][3];
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vector_t fp[3];
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vector_t l[22][3];
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vector_t alpha[6];
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vector_t ptmp[3];
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vector_t start;
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vector_t start2;
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char word[100], word2[100];
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if(ctx->mode >= 2) {
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cairo_set_source_rgb(C, 0.6, 0.6, 1);
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drawRotationOrbit(ctx, "bcabcb", p[1][0]); // bcC
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drawRotationOrbit(ctx, "abcabcba", p[0][0]); // abcC
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// drawRotationOrbit(ctx, "bcabcabacb", p[1][0]); // bcabC''
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// drawRotationOrbit(ctx, "bacabcacab", p[3][0]); // bacaC'
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// drawRotationOrbit(ctx, "bcacabcacacb", p[4][0]); // bcacaC' bcacabacb
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fixedPoints(ctx, "cba", p[0]);
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fixedPoints(ctx, "acb", p[1]);
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fixedPoints(ctx, "bac", p[2]);
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initializeTriangleGeneratorsCurrent(gen, ctx);
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gsl_matrix_set_identity(elements[0]);
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for(int i = 1; i < ctx->n_group_elements; i++) {
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if(ctx->group[i].length % 2)
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continue;
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int letter = ROTATION_LETTER(ctx->group[i].letter, ctx->group[i].parent->letter);
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multiply(gen[letter], elements[ctx->group[i].parent->parent->id], elements[i]);
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}
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cairo_set_source_rgb(C, 1, 0, 1);
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// drawRotationOrbit(ctx, "bacabcacab", p[3][0]); // ababcba
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cairo_set_source_rgb(C, 0, 0, 0);
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fixedPoints(ctx, "abababcbaba", p[3]);
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// drawRotationOrbit(ctx, "abababcabcbababa", p[3][0]); // bab abc bab
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cairo_set_source_rgb(C, 0, 0, 1);
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// fixedPoints(ctx, "cab", p[3]);
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// drawRotationOrbit(ctx, "cabc", p[3][0]);
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// fixedPoints(ctx, "bca", p[3]);
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// drawRotationOrbit(ctx, "bcabcb", p[3][0]);
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// fixedPoints(ctx, "bc abc cb", p[3]);
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// drawRotationOrbit(ctx, "bcabcb", p[3][0]);
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fixedPoints(ctx, "bc bca cb", p[3]);
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// drawRotationOrbit(ctx, "bcbcacbc", p[3][0]);
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gsl_vector_set(startpoint_drawbasis, 0, ctx->marking.x);
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gsl_vector_set(startpoint_drawbasis, 1, ctx->marking.y);
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gsl_vector_set(startpoint_drawbasis, 2, 1);
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solve(ctx->cob, startpoint_drawbasis, startpoint_globalbasis, ctx->ws);
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LOOP(i) start.x[i] = gsl_vector_get(startpoint_globalbasis, i);
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/*
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cairo_set_source_rgb(C, 0, 0, 0);
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strncpy(word,"abc",100);
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for(int i = 0; i < 9; i++) {
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conjugate_word(word, 0, "ab", word2);
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strncpy(word, word2, 100);
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fixedPoints(ctx, word, ptmp);
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drawVector(ctx, ptmp[0]);
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// drawVector(ctx, ptmp[2]);
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fixedPoints(ctx, "ABAB", fp);
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drawCovector(ctx, cross(fp[0], fp[2]));
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drawVector(ctx, fp[1]);
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computeRotationMatrixFrame(ctx, frame, "c");
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drawRotationOrbit(ctx, "c", start); // ba cb ab ac = C A c B
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drawVector(ctx, start);
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computeMatrix(ctx, tmp, "ABABc");
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start2 = apply(tmp, start);
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computeRotationMatrixFrame(ctx, frame, "c");
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multiply(tmp, frame, frame2);
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drawVector(ctx, start2);
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drawRotationOrbitFrame(ctx, frame2, apply(tmp, start));
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computeMatrix(ctx, tmp, "ABABcABABC");
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start2 = apply(tmp, start);
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computeRotationMatrixFrame(ctx, frame, "c");
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multiply(tmp, frame, frame2);
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drawVector(ctx, start2);
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drawRotationOrbitFrame(ctx, frame2, apply(tmp, start));
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*/
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for(groupelement_t *cur = &ctx->group[180]; cur->parent; cur = cur->parent)
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fputc('a'+cur->letter, stdout);
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fputc('\n', stdout);
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queue_t queue;
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queue_init(&queue);
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queue_put(&queue, 0);
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int current;
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groupelement_t *cur, *next;
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for(int i = 0; i < ctx->n_group_elements_combinatorial; i++)
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ctx->group[i].visited = 0;
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cur = &ctx->group[0];
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computeRotationMatrixFrame(ctx, frame, "c");
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for(int i = 0; i < 1000; i++) {
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if(ctx->group[i].length % 2 != 0)
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continue;
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multiply(elements[i], frame, frame2);
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drawRotationOrbitFrame(ctx, frame2, apply(elements[i], start));
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}
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strncpy(word,"bca",100);
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for(int i = 0; i < 9; i++) {
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conjugate_word(word, 0, "ab", word2);
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strncpy(word, word2, 100);
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fixedPoints(ctx, word, ptmp);
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drawVector(ctx, ptmp[0]);
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// drawVector(ctx, ptmp[2]);
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/*
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while((current = queue_get(&queue)) != -1) {
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cur = &ctx->group[current];
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if(cur->visited > 4)
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continue;
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if(cur->id < ctx->n_group_elements) {
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multiply(elements[cur->id], frame, frame2);
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drawRotationOrbitFrame(ctx, frame2, apply(elements[cur->id], start));
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}
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strncpy(word,"abc",100);
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for(int i = 0; i < 9; i++) {
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conjugate_word(word, 0, "bc", word2);
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strncpy(word, word2, 100);
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fixedPoints(ctx, word, ptmp);
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drawVector(ctx, ptmp[0]);
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next = left("ab ab", cur);
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if(next && next->visited == 0) {
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queue_put(&queue, next->id);
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next->visited = cur->visited+1;
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}
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strncpy(word,"cab",100);
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for(int i = 0; i < 9; i++) {
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conjugate_word(word, 0, "bc", word2);
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strncpy(word, word2, 100);
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fixedPoints(ctx, word, ptmp);
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drawVector(ctx, ptmp[0]);
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next = left("cbac cbac", cur);
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if(next && next->visited == 0) {
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queue_put(&queue, next->id);
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next->visited = cur->visited+1;
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}
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strncpy(word,"cab",100);
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for(int i = 0; i < 9; i++) {
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conjugate_word(word, 0, "ca", word2);
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strncpy(word, word2, 100);
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fixedPoints(ctx, word, ptmp);
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drawVector(ctx, ptmp[0]);
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next = left("cacbca cacbca", cur);
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if(next && next->visited == 0) {
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queue_put(&queue, next->id);
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next->visited = cur->visited+1;
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}
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next = left("cabcacbcac cabcacbcac", cur);
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if(next && next->visited == 0) {
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queue_put(&queue, next->id);
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next->visited = cur->visited+1;
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}
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next = left("acbcacba acbcacba", cur);
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if(next && next->visited == 0) {
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queue_put(&queue, next->id);
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next->visited = cur->visited+1;
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}
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next = left("bcacbc bcacbc", cur);
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if(next && next->visited == 0) {
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queue_put(&queue, next->id);
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next->visited = cur->visited+1;
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}
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strncpy(word,"abc",100);
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for(int i = 0; i < 9; i++) {
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conjugate_word(word, 0, "ca", word2);
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strncpy(word, word2, 100);
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fixedPoints(ctx, word, ptmp);
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drawVector(ctx, ptmp[0]);
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}
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*/
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/*
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cairo_set_source_rgb(C, 1, 0, 0);
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drawVector(ctx, p[0][0]);
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cairo_set_source_rgb(C, 0, 0.6, 0);
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drawVector(ctx, p[1][0]);
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cairo_set_source_rgb(C, 0, 0, 1);
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drawVector(ctx, p[2][0]);
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*/
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/*
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fixedPoints(ctx, "ab abc ba", p[4]);
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fixedPoints(ctx, "abab abc baba", p[5]);
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fixedPoints(ctx, "ababab abc bababa", p[6]);
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fixedPoints(ctx, "abababab abc babababa", p[7]);
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fixedPoints(ctx, "babababa abc abababab", p[8]);
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fixedPoints(ctx, "bababa abc ababab", p[9]);
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fixedPoints(ctx, "baba abc abab", p[10]);
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fixedPoints(ctx, "ba abc ab", p[11]);
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fixedPoints(ctx, "bca", p[12]);
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fixedPoints(ctx, "b abc b", p[13]);
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fixedPoints(ctx, "bab abc bab", p[14]);
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fixedPoints(ctx, "babab abc babab", p[15]);
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fixedPoints(ctx, "bababab abc bababab", p[16]);
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fixedPoints(ctx, "abababab bca babababa", p[17]);
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fixedPoints(ctx, "ababab bca bababa", p[18]);
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fixedPoints(ctx, "abab bca baba", p[19]);
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fixedPoints(ctx, "ab bca ba", p[20]);
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*/
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// initializeTriangleGenerators(gen, ctx->cartan);
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// for(int i = 0; i < 22; i++) LOOP(j) l[i][j] = cross(p[i][(3-j)%3], p[i][(4-j)%3]);
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// LOOP(i) LOOP(j) alpha[i].x[j] = gsl_matrix_get(ctx->cartan, i, j);
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/*
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gsl_matrix_set(frame, 0, 0, 2.0);
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gsl_matrix_set(frame, 0, 1, 0.0);
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gsl_matrix_set(frame, 0, 2, 1.0);
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gsl_matrix_set(frame, 1, 0, -1.0);
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gsl_matrix_set(frame, 1, 1, sqrt(3));
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gsl_matrix_set(frame, 1, 2, 1.0);
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gsl_matrix_set(frame, 2, 0, -1.0);
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gsl_matrix_set(frame, 2, 1, -sqrt(3));
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gsl_matrix_set(frame, 2, 2, 1.0);*/
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// drawRotationOrbitFrame(ctx, frame, p[0][0]);
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// drawRotationOrbit(ctx, "bc", p[0][0]);
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// drawRotationOrbit(ctx, "ca", p[0][0]);
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/*
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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
107
limit_set.c
@ -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;
|
||||
}
|
||||
|
||||
48
main.c
48
main.c
@ -18,6 +18,7 @@ DrawingContext *screen_context;
|
||||
void setupContext(DrawingContext *ctx, int argc, char *argv[])
|
||||
{
|
||||
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]);
|
||||
@ -28,6 +29,10 @@ void setupContext(DrawingContext *ctx, int argc, char *argv[])
|
||||
ctx->parameter = atof(argv[7]);
|
||||
else
|
||||
ctx->parameter = 1.0;
|
||||
if(argc > 8)
|
||||
ctx->parameter2 = atof(argv[8]);
|
||||
else
|
||||
ctx->parameter2 = 1.0;
|
||||
// ctx->parameter = 2.77;
|
||||
// ctx->parameter = 0.1;
|
||||
ctx->show_boxes = 0;
|
||||
@ -39,8 +44,8 @@ void setupContext(DrawingContext *ctx, int argc, char *argv[])
|
||||
ctx->show_dual_limit = 0;
|
||||
ctx->show_text = 1;
|
||||
ctx->mode = 0;
|
||||
ctx->use_rotation_basis = 0;
|
||||
ctx->limit_with_lines = 1;
|
||||
ctx->use_rotation_basis = 2;
|
||||
ctx->limit_with_lines = 0;
|
||||
ctx->use_repelling = 0;
|
||||
ctx->show_marking = 1;
|
||||
ctx->marking.x = -0.73679;
|
||||
@ -50,8 +55,8 @@ void setupContext(DrawingContext *ctx, int argc, char *argv[])
|
||||
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);
|
||||
@ -70,21 +75,30 @@ void destroyContext(DrawingContext *ctx)
|
||||
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");
|
||||
|
||||
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);
|
||||
}
|
||||
|
||||
releaseTempMatrices(ctx->ws, 6);
|
||||
}
|
||||
|
||||
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, 4);
|
||||
releaseTempMatrices(ctx->ws, 1);
|
||||
}
|
||||
|
||||
void computeBoxTransform(DrawingContext *ctx, char *word1, char *word2, gsl_matrix *result)
|
||||
@ -159,10 +173,10 @@ void updateMatrices(DrawingContext *ctx)
|
||||
} 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");
|
||||
computeRotationMatrixFrame(ctx, tmp, "C");
|
||||
invert(tmp, ctx->cob, ctx->ws);
|
||||
} else if(ctx->use_rotation_basis % 5 == 3) {
|
||||
computeBoxTransform(ctx, "bca", "abc", ctx->cob);
|
||||
computeBoxTransform(ctx, "acb", "cba", ctx->cob);
|
||||
// computeBoxTransform(ctx, "cab", "bca", ctx->cob);
|
||||
// computeBoxTransform(ctx, "acb", "cba", ctx->cob);
|
||||
} else {
|
||||
@ -258,12 +272,12 @@ int processEvent(GraphicsInfo *info, XEvent *ev)
|
||||
computeLimitCurve(screen_context);
|
||||
break;
|
||||
case XK_Left:
|
||||
screen_context->parameter /= exp(0.00002);
|
||||
screen_context->parameter2 /= exp(0.002);
|
||||
updateMatrices(screen_context);
|
||||
computeLimitCurve(screen_context);
|
||||
break;
|
||||
case XK_Right:
|
||||
screen_context->parameter *= exp(0.00002);
|
||||
screen_context->parameter2 *= exp(0.002);
|
||||
updateMatrices(screen_context);
|
||||
computeLimitCurve(screen_context);
|
||||
break;
|
||||
|
||||
15
main.h
15
main.h
@ -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 +35,9 @@ typedef struct {
|
||||
// a priori parameter
|
||||
int p[3],k[3];
|
||||
double parameter;
|
||||
double parameter2;
|
||||
int n_group_elements;
|
||||
int n_group_elements_combinatorial;
|
||||
int show_boxes;
|
||||
int show_boxes2;
|
||||
int show_attractors;
|
||||
@ -66,7 +73,8 @@ 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 +104,8 @@ 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)
|
||||
|
||||
@ -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);
|
||||
|
||||
Loading…
Reference in New Issue
Block a user