switch hyperbolic program to svg
This commit is contained in:
Florian Stecker
parent
7fb5c1f442
commit
bea92930ca
204
hyperbolic.c
204
hyperbolic.c
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@ -8,6 +8,10 @@
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#define POINCARE 1
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#define LOOP(i) for(int i = 0; i < 3; i++)
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#define CUTOFF(x) ((x)>1000.0?1000.0:(x)<-1000.0?-1000.0:(x))
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#define CONV(x) (CUTOFF(x)*490+500)
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#define DCONV(x) (CUTOFF(x)*490)
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void cartan_matrix(gsl_matrix *cartan, double a1, double a2, double a3, double s)
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{
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gsl_matrix_set(cartan, 0, 0, -2);
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@ -104,6 +108,7 @@ void print_tex_header() {
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char *header =
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"\\documentclass{standalone}\n"
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"\\usepackage[utf8]{inputenc}\n"
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"\\usepackage[dvipsnames]{xcolor}\n"
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"\\usepackage{tikz}\n"
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"\\begin{document}\n"
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"\\begin{tikzpicture}[scale=5]\n";
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@ -120,22 +125,43 @@ void print_tex_footer() {
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printf("%s", footer);
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}
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char *poincare_arc(double x1, double x2, double y1, double y2, char *buffer)
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void print_svg_header() {
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char *header =
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"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n"
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"<svg width=\"1000\" height=\"1000\" xmlns=\"http://www.w3.org/2000/svg\">\n";
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printf("%s", header);
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}
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void print_svg_footer() {
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printf("<circle cx=\"%f\" cy=\"%f\" r=\"%f\" style=\"fill:none;stroke-width:3;stroke:black;\" />\n",
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CONV(0.0), CONV(0.0), DCONV(1.0));
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printf("</svg>\n");
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}
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char *poincare_arc(double ax, double ay, double bx, double by, char *buffer)
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{
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double t = (1 - x1*y1 - x2*y2)/(x1*y2 - x2*y1)/2;
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double m1 = x1/2 + y1/2 + t*(y2 - x2); // center of circle
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double m2 = x2/2 + y2/2 + t*(x1 - y1);
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// find m = (a+b)/2 + tc with c orthogonal to a-b and |m|^2 = |m-a|^2 + 1
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// m^2 = m^2 - 2<m,a> + a^2 + 1
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// 0 = -2<m,a> + a^2 + 1 = -<a+b,a> - 2t<c,a> + a^2 + 1 = -<b,a> - 2t<c,a> + 1
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// t = (1 - <a,b>)/<a,c>/2
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double cx = ay - by;
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double cy = bx - ax;
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double t = (1 - ax*bx - ay*by)/(ax*cx + ay*cy)/2;
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double mx = ax/2 + bx/2 + t*cx; // center of circle
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double my = ay/2 + by/2 + t*cy;
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double r = sqrt((ax-mx)*(ax-mx) + (ay-my)*(ay-my));
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//double phix = atan2(x2-m2,x1-m1);
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//double phiy = atan2(y2-m2,y1-m1);
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double r = sqrt((x1-m1)*(x1-m1) + (x2-m2)*(x2-m2));
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double phix = atan2(x2-m2,x1-m1);
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double phiy = atan2(y2-m2,y1-m1);
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// if(phix - phiy > M_PI)
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// phiy += 2*M_PI;
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// else if(phiy - phix > M_PI)
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// phix += 2*M_PI;
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if(phix - phiy > M_PI)
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phiy += 2*M_PI;
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else if(phiy - phix > M_PI)
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phix += 2*M_PI;
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sprintf(buffer, "%f:%f:%f", phix/M_PI*180, phiy/M_PI*180, r);
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// sprintf(buffer, "%f:%f:%f", phix/M_PI*180, phiy/M_PI*180, r);
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sprintf(buffer, "%f %f 0 0 %d %f %f", DCONV(r), DCONV(r), t>0, CONV(bx), CONV(by));
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return buffer;
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}
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@ -151,10 +177,18 @@ void draw_triangle(point *p, gsl_matrix *frame, const char *arguments)
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double x3 = coord(p[2], 0, frame);
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double y3 = coord(p[2], 1, frame);
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printf("\\draw[%s] (%f, %f) arc (%s) arc (%s) arc (%s);\n", arguments, x1, y1,
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// TikZ version
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/* printf("\\draw[%s] (%f, %f) arc (%s) arc (%s) arc (%s);\n", arguments, x1, y1,
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poincare_arc(x1, y1, x2, y2, buffer1),
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poincare_arc(x2, y2, x3, y3, buffer2),
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poincare_arc(x3, y3, x1, y1, buffer3));
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poincare_arc(x3, y3, x1, y1, buffer3)); */
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// SVG version
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printf("<path d=\"M %f %f A %s A %s A %s Z\" style=\"%s\" />\n", CONV(x1), CONV(y1),
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poincare_arc(x1, y1, x2, y2, buffer1),
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poincare_arc(x2, y2, x3, y3, buffer2),
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poincare_arc(x3, y3, x1, y1, buffer3),
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arguments);
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#else
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printf("\\draw[%s] (%f, %f) -- (%f, %f) -- (%f, %f) -- cycle;\n", arguments,
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@ -174,25 +208,42 @@ void draw_line(point p1, point p2, gsl_matrix *frame, const char *arguments)
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double y2 = coord(p2, 1, frame);
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#ifdef POINCARE
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printf("\\draw[%s] (%f, %f) arc (%s);\n", arguments, x1, y1,
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poincare_arc(x1, y1, x2, y2, buffer));
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// printf("\\draw[%s] (%f, %f) arc (%s);\n", arguments, x1, y1,
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// poincare_arc(x1, y1, x2, y2, buffer));
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printf("<path d=\"M %f %f A %s\" style=\"%s\"/>\n", CONV(x1), CONV(y1),
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poincare_arc(x1, y1, x2, y2, buffer), arguments);
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#else
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printf("\\draw[%s] (%f, %f) -- (%f, %f);\n", arguments, x1, y1, x2, y2);
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#endif
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}
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int main()
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void compute_word(workspace_t *ws, gsl_matrix *result, gsl_matrix **gen, const char *word, int modifier)
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{
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gsl_matrix_set_identity(result);
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for(int i = 0; word[i] != 0; i++)
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multiply_right(result, gen[(word[i]-'a'+modifier)%3], ws);
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}
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int main(int argc, const char *argv[])
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{
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groupelement_t *group;
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gsl_matrix **matrices;
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gsl_matrix *cartan;
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gsl_matrix *gen[3];
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gsl_matrix *coxeter[3];
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gsl_matrix *coxeter2[3];
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gsl_matrix *coxeter_eigenvectors[3];
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gsl_matrix *coxeter_eigenvectors2[3];
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gsl_matrix *frame;
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workspace_t *ws;
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int elements = 2000;
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int p = 4, q = 4, r = 4;
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if(argc < 5) {
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fprintf(stderr, "Usage: %s <p> <q> <r> <n_elements>\n", argv[0]);
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exit(1);
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}
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int elements = atoi(argv[4]);
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int p = atoi(argv[1]), q = atoi(argv[2]), r = atoi(argv[3]);
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group = malloc(elements*sizeof(groupelement_t));
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matrices = malloc(elements*sizeof(gsl_matrix*));
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@ -203,6 +254,8 @@ int main()
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LOOP(i) gen[i] = gsl_matrix_alloc(3, 3);
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LOOP(i) coxeter[i] = gsl_matrix_alloc(3, 3);
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LOOP(i) coxeter_eigenvectors[i] = gsl_matrix_alloc(3, 3);
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LOOP(i) coxeter2[i] = gsl_matrix_alloc(3, 3);
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LOOP(i) coxeter_eigenvectors2[i] = gsl_matrix_alloc(3, 3);
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ws = workspace_alloc(3);
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generate_triangle_group(group, elements, p, q, r);
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@ -214,8 +267,16 @@ int main()
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for(int i = 1; i < elements; i++)
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multiply(matrices[group[i].parent->id], gen[group[i].letter], matrices[i]);
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LOOP(i) multiply_many(ws, coxeter[i], 3, gen[i%3], gen[(i+1)%3], gen[(i+2)%3]);
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// LOOP(i) multiply_many(ws, coxeter[i], 3, gen[i%3], gen[(i+1)%3], gen[(i+2)%3]); // coxeter
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// LOOP(i) multiply_many(ws, coxeter[i], 4, gen[i%3], gen[(i+1)%3], gen[i%3], gen[(i+2)%3]); // abcb
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LOOP(i) compute_word(ws, coxeter[i], gen, "abcb", i);
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/* LOOP(i) multiply_many(ws, coxeter[i], 10,
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gen[i%3], gen[(i+1)%3], gen[(i+2)%3],
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gen[i%3], gen[(i+1)%3], gen[(i+2)%3],
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gen[i%3], gen[(i+1)%3], gen[(i+2)%3],
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gen[(i+1)%3]); // (abc)^3 b */
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LOOP(i) eigenvectors(coxeter[i], coxeter_eigenvectors[i], ws);
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LOOP(i) eigenvectors(coxeter2[i], coxeter_eigenvectors2[i], ws);
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/*
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for(int i = 0; i < elements; i++) {
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@ -230,12 +291,19 @@ int main()
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point coxeter_attracting[3];
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point coxeter_repelling[3];
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point coxeter_axes[3];
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point coxeter2_attracting[3];
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point coxeter2_repelling[3];
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point coxeter2_axes[3];
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point edge_midpoints[3];
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point reflection_lines[3];
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point triangle_points[3];
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point transformed[3];
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point transformed2[3];
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point transformed3[3];
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point transformed4[3];
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point transformed5[3];
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point transformed6[3];
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point center;
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LOOP(i) coxeter_attracting[i] = column(coxeter_eigenvectors[i], 0);
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LOOP(i) coxeter_repelling[i] = column(coxeter_eigenvectors[i], 2);
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@ -243,8 +311,35 @@ int main()
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LOOP(i) edge_midpoints[i] = incidence(coxeter_axes[(i+1)%3], coxeter_axes[(i+2)%3]);
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LOOP(i) reflection_lines[i] = row(cartan, i);
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LOOP(i) triangle_points[i] = incidence(reflection_lines[(i+1)%3], reflection_lines[(i+2)%3]);
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LOOP(i) coxeter2_attracting[i] = column(coxeter_eigenvectors2[i], 0);
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LOOP(i) coxeter2_repelling[i] = column(coxeter_eigenvectors2[i], 2);
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LOOP(i) coxeter2_axes[i] = incidence(coxeter2_attracting[i], coxeter2_repelling[i]);
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print_tex_header();
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print_svg_header();
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// let's correct the frame of reference by using hyperbolic transformations
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center = apply(frame, triangle_points[2]);
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double angle = atan2(center.x[1], center.x[0]);
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double boost = atanh(-sqrt(center.x[0]*center.x[0]+center.x[1]*center.x[1])/center.x[2]);
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gsl_matrix *frame_correction = gsl_matrix_alloc(3, 3);
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gsl_matrix_set_identity(frame_correction);
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/*
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gsl_matrix_set(frame_correction, 0, 0, cos(angle-M_PI/2));
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gsl_matrix_set(frame_correction, 0, 1, sin(angle-M_PI/2));
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gsl_matrix_set(frame_correction, 1, 0, -sin(angle-M_PI/2));
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gsl_matrix_set(frame_correction, 1, 1, cos(angle-M_PI/2));
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gsl_matrix_set(frame_correction, 2, 2, 1);
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// multiply_left(frame_correction, frame, ws);
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gsl_matrix_set_identity(frame_correction);
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gsl_matrix_set(frame_correction, 0, 0, cosh(-boost));
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gsl_matrix_set(frame_correction, 0, 2, sinh(-boost));
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gsl_matrix_set(frame_correction, 1, 1, 1);
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gsl_matrix_set(frame_correction, 2, 0, sinh(-boost));
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gsl_matrix_set(frame_correction, 2, 2, cosh(-boost));
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multiply_left(frame_correction, frame, ws);
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*/
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gsl_matrix_free(frame_correction);
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// int indices[10] = {0, 1, 6, 10, 30, 46, 124, 185, 484, 717};
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// int indices[10] = {0, 1, 4, 10, 22};
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@ -254,16 +349,69 @@ int main()
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continue;
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LOOP(i) transformed[i] = apply(matrices[k], triangle_points[i]);
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draw_triangle(transformed, frame, "black,fill=black!10,line width=0pt");
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// draw_triangle(transformed, frame, "black,fill=black!10,line width=0pt");
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draw_triangle(transformed, frame, "fill:#cfcfcf;");
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// draw_triangle(transformed, frame, "fill:#000000;");
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}
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for(int k = 0; k < 2000; k++) {
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if(group[k].length % 2)
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continue;
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for(int k = 0; k < elements; k++) {
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// if(group[k].length % 2)
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// continue;
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LOOP(i) transformed[i] = apply(matrices[k], coxeter_attracting[i]);
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LOOP(i) transformed[i] = apply(matrices[k], edge_midpoints[(i+2)%3]);
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LOOP(i) transformed2[i] = apply(matrices[k], coxeter_repelling[i]);
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LOOP(i) transformed3[i] = apply(matrices[k], coxeter_repelling[(i+1)%3]);
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LOOP(i) transformed4[i] = apply(matrices[k], coxeter_attracting[i%3]);
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LOOP(i) transformed5[i] = apply(matrices[k], coxeter2_repelling[i]);
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LOOP(i) transformed6[i] = apply(matrices[k], coxeter2_attracting[i%3]);
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//LOOP(i) draw_line(transformed2[i], transformed4[i], frame, "red");
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draw_line(transformed2[0], transformed4[0], frame, "fill:none;stroke:red;stroke-width:1;");
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// draw_line(transformed2[1], transformed4[1], frame, "fill:none;stroke:blue;stroke-width:1;");
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// draw_line(transformed2[2], transformed4[2], frame, "fill:none;stroke:darkgreen;stroke-width:1;");
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// draw_line(transformed5[0], transformed6[0], frame, "fill:none;stroke:blue;stroke-width:1;");
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// draw_line(transformed5[1], transformed6[1], frame, "fill:none;stroke:blue;stroke-width:1;");
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// draw_line(transformed5[2], transformed6[2], frame, "fill:none;stroke:blue;stroke-width:1;");
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// draw_line(transformed2[1], transformed4[1], frame, "fill:none;stroke:darkgreen;stroke-width:1;");
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// draw_line(transformed2[2], transformed4[2], frame, "fill:none;stroke:blue;stroke-width:1;");
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// LOOP(i) draw_line(transformed[i], transformed3[i], frame, "red");
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// LOOP(i) transformed[i] = apply(matrices[k], coxeter_attracting[i]);
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// draw_line(transformed[1], transformed[2], frame, "red");
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}
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print_tex_footer();
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/*
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draw_line(apply(matrices[0], coxeter_repelling[0]),
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apply(matrices[0], coxeter_attracting[0]),
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frame, "fill:none;stroke:red;stroke-width:1;");
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draw_line(apply(matrices[1], coxeter_repelling[0]),
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apply(matrices[1], coxeter_attracting[0]),
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frame, "fill:none;stroke:red;stroke-width:1;");
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draw_line(apply(matrices[2], coxeter_repelling[0]),
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apply(matrices[2], coxeter_attracting[0]),
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frame, "fill:none;stroke:red;stroke-width:1;");
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draw_line(apply(matrices[3], coxeter_repelling[0]),
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apply(matrices[3], coxeter_attracting[0]),
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frame, "fill:none;stroke:red;stroke-width:1;");
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draw_line(apply(matrices[4], coxeter_repelling[0]),
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apply(matrices[4], coxeter_attracting[0]),
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frame, "fill:none;stroke:red;stroke-width:1;");
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draw_line(apply(matrices[5], coxeter_repelling[0]),
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apply(matrices[5], coxeter_attracting[0]),
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frame, "fill:none;stroke:red;stroke-width:1;");
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draw_line(apply(matrices[14], coxeter_repelling[0]),
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apply(matrices[14], coxeter_attracting[0]),
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frame, "fill:none;stroke:red;stroke-width:1;");
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draw_line(apply(matrices[15], coxeter_repelling[0]),
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apply(matrices[15], coxeter_attracting[0]),
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frame, "fill:none;stroke:red;stroke-width:1;");
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draw_line(apply(matrices[22], coxeter_repelling[0]),
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apply(matrices[22], coxeter_attracting[0]),
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frame, "fill:none;stroke:red;stroke-width:1;");
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draw_line(apply(matrices[23], coxeter_repelling[0]),
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apply(matrices[23], coxeter_attracting[0]),
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frame, "fill:none;stroke:red;stroke-width:1;");
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*/
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print_svg_footer();
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}
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