florian/triangle_group_limit_set
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implementing points and lines

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This commit is contained in:
Florian Stecker 2018-08-14 13:20:54 +02:00
parent a373a8ccf7
commit 09a43c7ac3
3 changed files with 257 additions and 96 deletions
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12
initcairo.c
View File

@ -80,7 +80,7 @@ void waitUpdateTimer(GraphicsInfo *info)
info->frames++; info->frames++;
} }
int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(void*), void *data) int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(cairo_t *, void*), void *data)
{ {
int state; int state;
static int last_x, last_y; static int last_x, last_y;
@ -88,7 +88,7 @@ int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(void*), vo
switch(ev->type) { switch(ev->type) {
case Expose: case Expose:
draw(data); draw(info->ctx, data);
break; break;
case ConfigureNotify: case ConfigureNotify:
@ -124,7 +124,7 @@ int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(void*), vo
} }
last_x = ev->xbutton.x; last_x = ev->xbutton.x;
last_y = ev->xbutton.y; last_y = ev->xbutton.y;
draw(data); draw(info->ctx, data);
break; break;
case MotionNotify: case MotionNotify:
@ -139,7 +139,7 @@ int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(void*), vo
printf("Button1Motion Event, dx: %d, dy: %d\n", dx, dy); printf("Button1Motion Event, dx: %d, dy: %d\n", dx, dy);
draw(data); draw(info->ctx, data);
} else if(ev->xmotion.state & Button1Mask && ev->xmotion.state & ShiftMask) { } else if(ev->xmotion.state & Button1Mask && ev->xmotion.state & ShiftMask) {
double angle = double angle =
atan2((double)ev->xmotion.y - (double)info->height/2, (double)ev->xmotion.x - (double)info->width/2)- atan2((double)ev->xmotion.y - (double)info->height/2, (double)ev->xmotion.x - (double)info->width/2)-
@ -154,7 +154,7 @@ int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(void*), vo
printf("Button1Motion Event, angle: %f\n", angle); printf("Button1Motion Event, angle: %f\n", angle);
draw(data); draw(info->ctx, data);
} }
last_x = ev->xmotion.x; last_x = ev->xmotion.x;
last_y = ev->xmotion.y; last_y = ev->xmotion.y;
@ -172,7 +172,7 @@ int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(void*), vo
} }
int checkEvents(GraphicsInfo *info, int (*process)(GraphicsInfo*, XEvent*, void*), void (*draw)(void*), void *data) // get any events from the queue and the server, process them if neccessary, quit if wanted int checkEvents(GraphicsInfo *info, int (*process)(GraphicsInfo*, XEvent*, void*), void (*draw)(cairo_t *, void*), void *data) // get any events from the queue and the server, process them if neccessary, quit if wanted
{ {
XEvent ev; XEvent ev;

2
initcairo.h
View File

@ -34,6 +34,6 @@ void destroyCairo(GraphicsInfo *info);
void startTimer(GraphicsInfo *info); void startTimer(GraphicsInfo *info);
void waitUpdateTimer(GraphicsInfo *info); void waitUpdateTimer(GraphicsInfo *info);
int checkEvents(GraphicsInfo *info, int (*process)(GraphicsInfo*, XEvent*, void*), void (*draw)(void*), void *data); int checkEvents(GraphicsInfo *info, int (*process)(GraphicsInfo*, XEvent*, void*), void (*draw)(cairo_t *, void*), void *data);
#endif #endif

323
limit_set.c
View File

@ -21,12 +21,14 @@ 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, gsl_matrix *cartan);
int compareAngle(const void *x, const void *y); int compareAngle(const void *x, const void *y);
int computeLimitCurve(); int computeLimitCurve();
void draw(void *data); void draw(cairo_t *ctx, void *data);
point_t intersect(point_t a, point_t b, point_t c, point_t d); point_t intersect(point_t a, point_t b, point_t c, point_t d);
void drawBoxStd(cairo_t *ctx, const char *word, char base);
void drawBox(cairo_t *ctx, const char *word1, const char *word2);
GraphicsInfo G; GraphicsInfo G;
double parameter = 2.8; double parameter;
int n_group_elements; int n_group_elements;
double *limit_curve; // x, y, angle triples double *limit_curve; // x, y, angle triples
int limit_curve_valid = 0; int limit_curve_valid = 0;
@ -36,6 +38,10 @@ gsl_matrix *gen[3];
gsl_matrix **matrices; gsl_matrix **matrices;
gsl_matrix *cartan, *cob, *coxeter, *coxeter_fixedpoints, *fixedpoints; gsl_matrix *cartan, *cob, *coxeter, *coxeter_fixedpoints, *fixedpoints;
int show_boxes = 0;
int show_attractors = 0;
int show_limit = 1;
int processEvent(GraphicsInfo *info, XEvent *ev, void *data) int processEvent(GraphicsInfo *info, XEvent *ev, void *data)
{ {
int state; int state;
@ -65,9 +71,26 @@ int processEvent(GraphicsInfo *info, XEvent *ev, void *data)
parameter = 2.76375163; parameter = 2.76375163;
limit_curve_valid = computeLimitCurve(); limit_curve_valid = computeLimitCurve();
break; break;
case 'm':
printf("G.matrix.xx = %f;\n", G.matrix.xx);
printf("G.matrix.xy = %f;\n", G.matrix.xy);
printf("G.matrix.x0 = %f;\n", G.matrix.x0);
printf("G.matrix.yx = %f;\n", G.matrix.yx);
printf("G.matrix.yy = %f;\n", G.matrix.yy);
printf("G.matrix.y0 = %f;\n", G.matrix.y0);
printf("G.scalefactor = %f;\n", G.scalefactor);
break;
case 'b':
show_boxes = !show_boxes;
break;
case 'a':
show_attractors = !show_attractors;
break;
case 'l':
show_limit = !show_limit;
} }
draw(0); draw(G.ctx, 0);
} }
return 0; return 0;
@ -144,59 +167,102 @@ point_t intersect(point_t a, point_t b, point_t c, point_t d)
return res; return res;
} }
void draw_segment(point_t a, point_t b) void drawPoint(cairo_t *ctx, point_t p)
{ {
cairo_move_to(G.ctx, a.x, a.y); // not implemented
cairo_line_to(G.ctx, b.x, b.y); cairo_save(ctx);
cairo_stroke(G.ctx); cairo_move_to(ctx, p.x, p.y);
cairo_close_path(ctx);
cairo_set_line_cap(ctx, CAIRO_LINE_CAP_ROUND);
cairo_set_line_width(ctx, 10.0/G.scalefactor);
cairo_stroke(ctx);
cairo_restore(ctx);
} }
void draw_polygon(int sides, point_t a, point_t b, point_t c, point_t d) // only quadrilaterals so far void drawLine(cairo_t *ctx, point_t a, point_t b)
{ {
draw_segment(a, b); // not implemented
draw_segment(b, c);
draw_segment(c, d);
draw_segment(d, a);
} }
void draw_box(const char *word, char base) void drawSegment(cairo_t *ctx, point_t a, point_t b)
{ {
// lower stack[i] reserved for linalg.c is used by multiply_*() cairo_move_to(ctx, a.x, a.y);
gsl_matrix *tmp1 = ws->stack[10]; cairo_line_to(ctx, b.x, b.y);
gsl_matrix *conj = ws->stack[12]; cairo_stroke(ctx);
gsl_matrix *conjinv = ws->stack[13]; }
gsl_matrix *coxeter[3] = { ws->stack[14], ws->stack[15], ws->stack[16] }; // fixed points of coxeter elements
gsl_matrix_set_identity(conj); void drawPolygon(cairo_t *ctx, int sides, point_t a, point_t b, point_t c, point_t d) // only quadrilaterals so far
gsl_matrix_set_identity(conjinv); {
drawSegment(ctx, a, b);
drawSegment(ctx, b, c);
drawSegment(ctx, c, d);
drawSegment(ctx, d, a);
}
void fixedPoints(const char *word, point_t *out)
{
gsl_matrix *tmp = ws->stack[10];
gsl_matrix *ev = ws->stack[11];
gsl_matrix_set_identity(tmp);
for(int i = 0; i < strlen(word); i++) { for(int i = 0; i < strlen(word); i++) {
if(word[i] == ' ') if(word[i] == ' ')
continue; continue;
multiply_right(conj, gen[word[i]-'a'], ws); multiply_right(tmp, gen[word[i]-'a'], ws);
multiply_left(gen[word[i]-'a'], conjinv, ws);
} }
eigenvectors(tmp, ev, ws);
multiply_left(cob, ev, ws);
for(int i = 0; i < 3; i++) { LOOP(i) out[i].x = gsl_matrix_get(ev, 0, i) / gsl_matrix_get(ev, 2, i);
multiply_many(ws, tmp1, 5, conj, gen[(base-'A'+i)%3], gen[(base-'A'+i+1)%3], gen[(base-'A'+i+2)%3], conjinv); LOOP(i) out[i].y = gsl_matrix_get(ev, 1, i) / gsl_matrix_get(ev, 2, i);
eigenvectors(tmp1, coxeter[i], ws); }
multiply_left(cob, coxeter[i], ws);
void drawAttractorConnection(cairo_t *ctx, const char *word1, const char *word2)
{
point_t p1[3], p2[3];
fixedPoints(word1, p1);
fixedPoints(word2, p2);
drawSegment(ctx, p1[0], p2[0]);
}
void drawBox(cairo_t *ctx, const char *word1, const char *word2)
{
point_t p[2][3],i[2];
fixedPoints(word1, p[0]);
fixedPoints(word2, p[1]);
// intersect attracting line with neutral line of the other element
for(int j = 0; j < 2; j++)
i[j] = intersect(p[j%2][0],p[j%2][1],p[(j+1)%2][0],p[(j+1)%2][2]);
drawPolygon(ctx, 4, p[0][0], i[0], p[1][0], i[1]);
}
void drawBoxStd(cairo_t *ctx, const char *word, char base)
{
char word1[100];
char word2[100];
int len = strlen(word);
if(len*2 + 4 > 100)
return;
for(int i = 0; i < len; i++) {
word1[i] = word1[2*len+2-i] = word[i];
word2[i] = word2[2*len+2-i] = word[i];
} }
word1[2*len+3] = 0;
word2[2*len+3] = 0;
point_t p_a[3],p_m[3],p_r[3],p_i[4]; LOOP(i) word1[len+i] = (base-'A'+6+i+1)%3+'a';
LOOP(i) word2[len+i] = (base-'A'+6-i-1)%3+'a';
LOOP(i) p_a[i].x = gsl_matrix_get(coxeter[i], 0, 0) / gsl_matrix_get(coxeter[i], 2, 0); // printf("Words: %s %s\n", word1, word2);
LOOP(i) p_a[i].y = gsl_matrix_get(coxeter[i], 1, 0) / gsl_matrix_get(coxeter[i], 2, 0);
LOOP(i) p_m[i].x = gsl_matrix_get(coxeter[i], 0, 1) / gsl_matrix_get(coxeter[i], 2, 1);
LOOP(i) p_m[i].y = gsl_matrix_get(coxeter[i], 1, 1) / gsl_matrix_get(coxeter[i], 2, 1);
LOOP(i) p_r[i].x = gsl_matrix_get(coxeter[i], 0, 2) / gsl_matrix_get(coxeter[i], 2, 2);
LOOP(i) p_r[i].y = gsl_matrix_get(coxeter[i], 1, 2) / gsl_matrix_get(coxeter[i], 2, 2);
p_i[0] = intersect(p_a[1], p_r[1], p_m[0], p_r[0]); drawBox(ctx, word1, word2);
p_i[1] = intersect(p_a[0], p_r[0], p_a[2], p_r[2]);
p_i[2] = intersect(p_a[1], p_m[1], p_a[2], p_r[2]);
p_i[3] = intersect(p_a[0], p_r[0], p_a[1], p_m[1]);
draw_polygon(4, p_a[1], p_i[0], p_r[0], p_i[3]);
} }
int computeLimitCurve() int computeLimitCurve()
@ -248,31 +314,132 @@ int computeLimitCurve()
return 1; return 1;
} }
void draw(void *data) void drawBoxes(cairo_t *ctx)
{
cairo_set_source_rgb(ctx, 1, 0, 0);
drawBoxStd(ctx, "c", 'C');
drawBoxStd(ctx, "", 'B');
drawBoxStd(ctx, "a", 'A');
drawBoxStd(ctx, "", 'C');
// drawBoxStd(ctx, "", 'A');
drawBoxStd(ctx, "b", 'B');
cairo_set_source_rgb(ctx, 0, 0, 1);
drawBoxStd(ctx, "ca", 'A');
drawBoxStd(ctx, "cac", 'C');
drawBoxStd(ctx, "caca", 'A');
// drawBoxStd(ctx, "cacac", 'C');
// drawBoxStd(ctx, "acac", 'A');
// drawBoxStd(ctx, "aca", 'C');
cairo_set_source_rgb(ctx, 0, 1, 0);
drawBoxStd(ctx, "ac", 'C');
// drawBoxStd(ctx, "aca", 'A');
drawBoxStd(ctx, "acac", 'C');
// drawBoxStd(ctx, "acaca", 'A');
// drawBoxStd(ctx, "caca", 'C');
// drawBoxStd(ctx, "cac", 'A');
cairo_set_source_rgb(ctx, 1, 0, 1);
drawBoxStd(ctx, "aca cb", 'B');
drawBoxStd(ctx, "aca cbc", 'C');
drawBoxStd(ctx, "aca cbcb", 'B');
drawBoxStd(ctx, "aca bcbc", 'C');
drawBoxStd(ctx, "aca bcb", 'B');
drawBoxStd(ctx, "aca bc", 'C');
/*
cairo_set_source_rgb(ctx, 1, 0, 1);
drawAttractorConnection("acb", "acaba");
drawAttractorConnection("acaba", "acacbca");
drawAttractorConnection("ac acb ca", "ac acaba ca");
drawAttractorConnection("ac acaba ca", "ac acacbca ca");
drawAttractorConnection("acac acb caca", "acac acaba caca");
drawAttractorConnection("acac acaba caca", "acac acacbca caca");
drawAttractorConnection("caca acb acac", "caca acaba acac");
// drawAttractorConnection("caca acaba acac", "caca acacbca acac");
drawAttractorConnection("ca acb ac", "ca acaba ac");
drawAttractorConnection("ca acaba ac", "ca acacbca ac");
cairo_set_source_rgb(ctx, 0, 1, 0);
drawAttractorConnection("cab", "cacbc");
drawAttractorConnection("cacbc", "cacabac");
drawAttractorConnection("ca cab ac", "ca cacbc ac");
drawAttractorConnection("ca cacbc ac", "ca cacabac ac");
drawAttractorConnection("caca cab acac", "caca cacbc acac");
drawAttractorConnection("caca cacbc acac", "caca cacabac acac");
drawAttractorConnection("acac cab caca", "acac cacbc caca");
drawAttractorConnection("acac cacbc caca", "acac cacabac caca");
// drawAttractorConnection("ac cab ca", "ac cacbc ca");
drawAttractorConnection("ac cacbc ca", "ac cacabac ca");
*/
// finer box test
/*
cairo_set_source_rgb(ctx, 0, 1, 0);
drawBox("acb", "acabacaca");
drawBox("acabacaca", "acaba");
// drawBox("acb", "acaba");
drawBox("acaba", "acacbacac");
drawBox("acacbacac", "acacbca");
drawBox("acacbca", "cacacbcac");
drawBox("cacacbcac", "acacabaca");
drawBox("acacabaca", "cacabac");
drawBox("cacabac", "cacabcaca");
drawBox("cacabcaca", "cacbc");
// drawBox("cacbc", "cab");
drawBox("cacbc", "cacbcacac");
drawBox("cacbcacac", "cab"); // strange
*/
}
void drawAttractors(cairo_t *ctx)
{
point_t p[3][3];
fixedPoints("abc", p[0]);
fixedPoints("bca", p[1]);
fixedPoints("cab", p[2]);
cairo_set_source_rgb(ctx, 0, 0, 0);
LOOP(i) LOOP(j) drawPoint(ctx, p[i][j]);
LOOP(i) LOOP(j) drawLine(ctx, p[i][j], p[i][(j+1)%3]);
}
void draw(cairo_t *ctx, void *data)
{ {
struct timeval current_time; struct timeval current_time;
gettimeofday(&current_time, 0); gettimeofday(&current_time, 0);
double start_time = current_time.tv_sec + current_time.tv_usec*1e-6; double start_time = current_time.tv_sec + current_time.tv_usec*1e-6;
cairo_push_group(G.ctx); cairo_push_group(ctx);
cairo_set_source_rgb(G.ctx, 1, 1, 1); cairo_set_source_rgb(ctx, 1, 1, 1);
cairo_paint(G.ctx); cairo_paint(ctx);
cairo_set_matrix(G.ctx, &G.matrix); cairo_set_matrix(ctx, &G.matrix);
// defaults; use save/restore whenever these are changed
cairo_set_line_width(ctx, 1.0/G.scalefactor);
cairo_set_font_size(ctx, 16);
cairo_set_line_join(ctx, CAIRO_LINE_JOIN_BEVEL);
cairo_set_line_cap(ctx, CAIRO_LINE_CAP_ROUND);
if(limit_curve_valid) { if(limit_curve_valid) {
if(show_limit) {
int last_inside = 0; int last_inside = 0;
for(int i = 0; i < n_group_elements; i++) { for(int i = 0; i < n_group_elements; i++) {
double x = limit_curve[3*i]; double x = limit_curve[3*i];
double y = limit_curve[3*i+1]; double y = limit_curve[3*i+1];
cairo_user_to_device(G.ctx, &x, &y); cairo_user_to_device(ctx, &x, &y);
if(-x < G.width && x < 3*G.width && -y < G.height && y < 3*G.height) { if(-x < G.width && x < 3*G.width && -y < G.height && y < 3*G.height) {
if(!last_inside) { if(!last_inside) {
cairo_move_to(G.ctx, limit_curve[3*i], limit_curve[3*i+1]); cairo_move_to(ctx, limit_curve[3*i], limit_curve[3*i+1]);
} else { } else {
cairo_line_to(G.ctx, limit_curve[3*i], limit_curve[3*i+1]); cairo_line_to(ctx, limit_curve[3*i], limit_curve[3*i+1]);
} }
last_inside = 1; last_inside = 1;
} else { } else {
@ -280,46 +447,28 @@ void draw(void *data)
} }
} }
cairo_set_line_width(G.ctx, 1.0/G.scalefactor); cairo_set_source_rgb(ctx, 0, 0, 0);
cairo_set_line_join(G.ctx, CAIRO_LINE_JOIN_BEVEL); cairo_stroke(ctx);
cairo_set_source_rgb(G.ctx, 0, 0, 0);
cairo_stroke(G.ctx);
cairo_set_source_rgb(G.ctx, 1, 0, 0);
// draw_box("c", 'C');
draw_box("", 'B');
draw_box("a", 'A');
// draw_box("", 'C');
cairo_set_source_rgb(G.ctx, 0, 0, 1);
draw_box("ca", 'A');
draw_box("cac", 'C');
draw_box("caca", 'A');
draw_box("cacac", 'C');
draw_box("acac", 'A');
draw_box("aca", 'C');
cairo_set_source_rgb(G.ctx, 0, 1, 0);
draw_box("ac", 'C');
draw_box("aca", 'A');
draw_box("acac", 'C');
draw_box("acaca", 'A');
draw_box("caca", 'C');
draw_box("cac", 'A');
} }
cairo_identity_matrix(G.ctx); if(show_boxes)
drawBoxes(ctx);
cairo_move_to(G.ctx, 15, 30); if(show_attractors)
cairo_set_source_rgb(G.ctx, 0, 0, 0); drawAttractors(ctx);
cairo_set_font_size(G.ctx, 16); }
cairo_identity_matrix(ctx);
cairo_move_to(ctx, 15, 30);
cairo_set_source_rgb(ctx, 0, 0, 0);
char buf[100]; char buf[100];
sprintf(buf, "t = %.8f", parameter); sprintf(buf, "t = %.8f", parameter);
cairo_show_text(G.ctx, buf); cairo_show_text(ctx, buf);
cairo_pop_group_to_source(G.ctx); cairo_pop_group_to_source(ctx);
cairo_paint(G.ctx); cairo_paint(ctx);
cairo_surface_flush(G.sfc); cairo_surface_flush(cairo_get_target(ctx));
gettimeofday(&current_time, 0); gettimeofday(&current_time, 0);
double end_time = current_time.tv_sec + current_time.tv_usec*1e-6; double end_time = current_time.tv_sec + current_time.tv_usec*1e-6;
@ -328,16 +477,28 @@ void draw(void *data)
int main() int main()
{ {
parameter = 3.0;
setup(); setup();
limit_curve_valid = computeLimitCurve(); limit_curve_valid = computeLimitCurve();
if(!initCairo(0, KeyPressMask, 200, 200, "Triangle group", &G)) if(!initCairo(0, KeyPressMask, 200, 200, "Triangle group", &G))
return 1; return 1;
/*
cairo_matrix_init_identity(&G.matrix); cairo_matrix_init_identity(&G.matrix);
G.matrix.xx = G.matrix.yy = G.scalefactor = 1100.0; G.matrix.xx = G.matrix.yy = G.scalefactor = 1100.0;
G.matrix.x0 = 1150.0; G.matrix.x0 = 1150.0;
G.matrix.y0 = 900.0; G.matrix.y0 = 900.0;
*/
G.matrix.xx = 837.930824;
G.matrix.xy = -712.651341;
G.matrix.x0 = 180.427716;
G.matrix.yx = 712.651341;
G.matrix.yy = 837.930824;
G.matrix.y0 = 1412.553240;
G.scalefactor = 1100.000000;
startTimer(&G); startTimer(&G);