florian/triangle_group_limit_set
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity

triangle group code reorganization

Browse Source
This commit is contained in:
Florian Stecker 2019-02-03 13:18:14 +01:00
parent 587a96e54a
commit 1ec2a49983
7 changed files with 937 additions and 705 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

18
Makefile
View File

@ -1,8 +1,8 @@
HEADERS=triangle.h linalg.h queue.h initcairo.h HEADERS=triangle.h linalg.h queue.h initcairo.h main.h
#SPECIAL_OPTIONS=-O0 -g -D_DEBUG SPECIAL_OPTIONS=-O0 -g -D_DEBUG
#SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline #SPECIAL_OPTIONS=-O3 -pg -funroll-loops -fno-inline
SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -Wall -Wno-unused-function -Werror=implicit-function-declaration #SPECIAL_OPTIONS=-O3 -flto -funroll-loops -Winline -Wall -Wno-unused-function -Werror=implicit-function-declaration
#SPECIAL_OPTIONS= #SPECIAL_OPTIONS=
CAIRO_OPTIONS=$(shell pkg-config --cflags cairo) CAIRO_OPTIONS=$(shell pkg-config --cflags cairo)
@ -11,8 +11,8 @@ OPTIONS=$(GENERAL_OPTIONS) $(CAIRO_OPTIONS) $(SPECIAL_OPTIONS)
all: limit_set all: limit_set
limit_set: limit_set.o linalg.o triangle.o initcairo.o limit_set: limit_set.o linalg.o triangle.o initcairo.o draw.o main.o
gcc $(OPTIONS) -o limit_set limit_set.o linalg.o triangle.o initcairo.o -lm -lgsl -lcblas -lcairo -lX11 gcc $(OPTIONS) -o limit_set limit_set.o linalg.o triangle.o initcairo.o draw.o main.o -lm -lgsl -lcblas -lcairo -lX11
linalg.o: linalg.c $(HEADERS) linalg.o: linalg.c $(HEADERS)
gcc $(OPTIONS) -c linalg.c gcc $(OPTIONS) -c linalg.c
@ -26,5 +26,11 @@ limit_set.o: limit_set.c $(HEADERS)
initcairo.o: initcairo.c $(HEADERS) initcairo.o: initcairo.c $(HEADERS)
gcc $(OPTIONS) -c initcairo.c gcc $(OPTIONS) -c initcairo.c
draw.o: draw.c $(HEADERS)
gcc $(OPTIONS) -c draw.c
main.o: main.c $(HEADERS)
gcc $(OPTIONS) -c main.c
clean: clean:
rm -f limit_set linalg.o triangle.o limit_set.o rm -f limit_set linalg.o triangle.o limit_set.o draw.o main.o

407
draw.c Normal file
View File

@ -0,0 +1,407 @@
#include "main.h"
// level 0: helper functions
vector_t cross(vector_t a, vector_t b)
{
vector_t result;
result.x[0] = a.x[1]*b.x[2] - a.x[2]*b.x[1];
result.x[1] = a.x[2]*b.x[0] - a.x[0]*b.x[2];
result.x[2] = a.x[0]*b.x[1] - a.x[1]*b.x[0];
return result;
}
vector_t apply(DrawingContext *ctx, gsl_matrix *m, vector_t x)
{
gsl_vector *tmp = getTempVector(ctx);
gsl_vector *tmp2 = getTempVector(ctx);
vector_t out;
LOOP(i) gsl_vector_set(tmp, i, x.x[i]);
gsl_blas_dgemv(CblasNoTrans, 1.0, m, tmp, 0.0, tmp2);
LOOP(i) out.x[i] = gsl_vector_get(tmp2, i);
releaseTempVectors(ctx, 2);
}
int fixedPoints(DrawingContext *ctx, const char *word, vector_t *out)
{
gsl_matrix *tmp = getTempMatrix(ctx);
gsl_matrix *ev = getTempMatrix(ctx);
gsl_matrix **gen = getTempMatrices(ctx, 3);
initializeTriangleGenerators(gen, ctx->cartan);
gsl_matrix_set_identity(tmp);
for(int i = 0; i < strlen(word); i++) {
if(word[i] == ' ')
continue;
multiply_right(tmp, gen[word[i]-'a'], ctx->ws);
}
int count = real_eigenvectors(tmp, ev, ctx->ws);
LOOP(i) LOOP(j) out[i].x[j] = gsl_matrix_get(ev, j, i);
releaseTempMatrices(ctx, 5);
return count;
}
void transformFrameStd(DrawingContext *ctx, vector_t *x, gsl_matrix *out)
{
gsl_matrix *tmp = getTempMatrix(ctx);
gsl_vector *fourth = getTempVector(ctx);
gsl_vector *lambda = getTempVector(ctx);
int s;
LOOP(i) LOOP(j) gsl_matrix_set(out, j, i, x[i].x[j]);
gsl_matrix_memcpy(tmp, out);
gsl_linalg_LU_decomp(tmp, ctx->ws->permutation, &s);
gsl_linalg_LU_solve(tmp, ctx->ws->permutation, fourth, lambda);
LOOP(i) LOOP(j) *gsl_matrix_ptr(out, i, j) *= gsl_vector_get(lambda, j);
gsl_matrix_fprintf(stdout, out, "%f");
releaseTempMatrices(ctx, 1);
releaseTempVectors(ctx, 2);
}
// level 1: the elementary drawing functions, drawPoint, drawSegment2d
void drawPoint(DrawingContext *ctx, point_t p)
{
cairo_t *C = ctx->cairo;
cairo_save(C);
cairo_move_to(C, p.x, p.y);
cairo_close_path(C);
cairo_set_line_cap(C, CAIRO_LINE_CAP_ROUND);
cairo_set_line_width(C, 10.0/ctx->dim->scalefactor);
cairo_stroke(C);
cairo_restore(C);
}
void drawSegment2d(DrawingContext *ctx, point_t a, point_t b)
{
cairo_t *C = ctx->cairo;
cairo_move_to(C, a.x, a.y);
cairo_line_to(C, b.x, b.y);
cairo_stroke(C);
}
// level 2: drawVector, drawCovector, drawSegment
static point_t vectorToPoint(DrawingContext *ctx, vector_t in)
{
double x[3];
point_t out;
LOOP(i) x[i] = 0.0;
LOOP(i) LOOP(j) x[i] += gsl_matrix_get(ctx->cob, i, j) * in.x[j];
out.x = x[0] / x[2];
out.y = x[1] / x[2];
return out;
}
void drawVector(DrawingContext *ctx, vector_t v)
{
drawPoint(ctx, vectorToPoint(ctx, v));
}
static void drawImplicitLine(DrawingContext *ctx, double a, double b, double c)
{
double norm, lambda;
point_t m, s, xminus, xplus;
m.x = ctx->dim->center_x;
m.y = ctx->dim->center_y;
lambda = (a*m.x + b*m.y + c)/(a*a + b*b);
s.x = m.x - lambda*a;
s.y = m.y - lambda*b;
norm = sqrt(a*a + b*b);
xminus.x = s.x - ctx->dim->radius * b / norm;
xminus.y = s.y + ctx->dim->radius * a / norm;
xplus.x = s.x + ctx->dim->radius * b / norm;
xplus.y = s.y - ctx->dim->radius * a / norm;
drawSegment2d(ctx, xminus, xplus);
}
void drawCovector(DrawingContext *ctx, vector_t v)
{
double x[3];
double cofactor;
LOOP(i) x[i] = 0.0;
LOOP(i) LOOP(j) {
cofactor = gsl_matrix_get(ctx->cob, (i+1)%3, (j+1)%3) * gsl_matrix_get(ctx->cob, (i+2)%3, (j+2)%3)
- gsl_matrix_get(ctx->cob, (i+1)%3, (j+2)%3) * gsl_matrix_get(ctx->cob, (i+2)%3, (j+1)%3);
x[i] += cofactor * v.x[j];
}
drawImplicitLine(ctx, x[0], x[1], x[2]);
}
void drawSegment(DrawingContext *ctx, vector_t a, vector_t b)
{
drawSegment2d(ctx, vectorToPoint(ctx, a), vectorToPoint(ctx, b));
}
// level 3: boxes and polygons
void drawPolygon(DrawingContext *ctx, int sides, ...)
{
va_list args;
vector_t first, prev, current;
va_start(args, sides);
first = va_arg(args, vector_t);
current = first;
for(int i = 0; i < sides-1; i++) {
prev = current;
current = va_arg(args, vector_t);
drawSegment(ctx, prev, current);
}
drawSegment(ctx, current, first);
va_end(args);
}
void drawTriangle(DrawingContext *ctx, const char *word)
{
vector_t p[3];
fixedPoints(ctx, word, p);
drawPolygon(ctx, 3, p[0], p[1], p[2]);
}
void drawBox(DrawingContext *ctx, const char *word1, const char *word2)
{
vector_t p[2][3],i[2];
fixedPoints(ctx, word1, p[0]);
fixedPoints(ctx, word2, p[1]);
// intersect attracting line with neutral line of the other element
for(int j = 0; j < 2; j++)
i[j] = cross(cross(p[j%2][0],p[j%2][1]),cross(p[(j+1)%2][0],p[(j+1)%2][2]));
drawPolygon(ctx, 4, p[0][0], i[0], p[1][0], i[1]);
}
void drawBoxStd(DrawingContext *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;
LOOP(i) word1[len+i] = (base-'A'+6+i+1)%3+'a';
LOOP(i) word2[len+i] = (base-'A'+6-i-1)%3+'a';
// printf("Words: %s %s\n", word1, word2);
drawBox(ctx, word1, word2);
}
// level 4: draw the actual image components
void drawReflectors(DrawingContext *ctx)
{
vector_t v[3];
cairo_set_source_rgb(ctx->cairo, 0, 0, 0);
LOOP(i) LOOP(j) { v[i].x[j] = (i==j) ? 1.0 : 0.0; }
LOOP(i) drawVector(ctx, v[i]);
LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(ctx->cartan, i, j);
LOOP(i) drawCovector(ctx, v[i]);
}
void drawAttractors(DrawingContext *ctx)
{
vector_t p[3][3];
vector_t l[3][3];
fixedPoints(ctx, "abc", p[0]);
fixedPoints(ctx, "bca", p[1]);
fixedPoints(ctx, "cab", p[2]);
double color[3][3] = {{1,0,0},{0,0.7,0},{0,0,1}};
LOOP(i) LOOP(j) l[i][j] = cross(p[i][(3-j)%3], p[i][(4-j)%3]);
LOOP(i) LOOP(j) {
cairo_set_source_rgb(ctx->cairo, color[i][0], color[i][1], color[i][2]);
drawVector(ctx, p[i][j]);
}
LOOP(i) LOOP(j) {
cairo_set_source_rgb(ctx->cairo, color[i][0], color[i][1], color[i][2]);
drawCovector(ctx, l[i][j]);
}
}
void drawBoxes(DrawingContext *ctx)
{
cairo_t *C = ctx->cairo;
/*
cairo_set_source_rgb(C, 1, 0, 0);
drawTriangle(ctx, "abc");
cairo_set_source_rgb(C, 0, 0, 1);
drawTriangle(ctx, "aca abc aca");
drawTriangle(ctx, "acac abc caca");
drawTriangle(ctx, "acaca abc acaca");
cairo_set_source_rgb(C, 0, 0.8, 0);
drawTriangle(ctx, "cac abc cac");
drawTriangle(ctx, "caca abc acac");
drawTriangle(ctx, "cacac abc cacac");
*/
cairo_set_source_rgb(C, 1, 0, 0);
drawBoxStd(ctx, "c", 'C');
drawBoxStd(ctx, "", 'B');
drawBoxStd(ctx, "a", 'A');
drawBoxStd(ctx, "", 'C');
drawBoxStd(ctx, "b", 'B');
cairo_set_source_rgb(C, 0, 0, 0);
drawBoxStd(ctx, "ca", 'A');
drawBoxStd(ctx, "cac", 'C');
drawBoxStd(ctx, "caca", 'A');
drawBoxStd(ctx, "acac", 'C');
drawBoxStd(ctx, "aca", 'A');
drawBoxStd(ctx, "ac", 'C');
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');
drawBoxStd(ctx, "caca cb", 'B');
drawBoxStd(ctx, "caca cbc", 'C');
drawBoxStd(ctx, "caca cbcb", 'B');
drawBoxStd(ctx, "caca bcbc", 'C');
drawBoxStd(ctx, "caca bcb", 'B');
drawBoxStd(ctx, "caca bc", 'C');
cairo_set_source_rgb(C, 1, 0, 1);
drawBoxStd(ctx, "ca bc", 'C');
drawBoxStd(ctx, "ca bcb", 'B');
drawBoxStd(ctx, "ca bcbc", 'C');
drawBoxStd(ctx, "ca cbcb", 'B');
drawBoxStd(ctx, "ca cbc", 'C');
drawBoxStd(ctx, "ca cb", 'B');
cairo_set_source_rgb(C, 0, 1, 0);
// drawBoxStd(ctx, "ca bc", 'C');
drawBoxStd(ctx, "cabc ba", 'A');
drawBoxStd(ctx, "cabc bab", 'B');
drawBoxStd(ctx, "cabc baba", 'A');
drawBoxStd(ctx, "cabc abab", 'B');
drawBoxStd(ctx, "cabc aba", 'A');
drawBoxStd(ctx, "cabc ab", 'B');
}
void drawLimitCurve(DrawingContext *ctx)
{
cairo_t *C = ctx->cairo;
cairo_save(C);
int previous_inside = 0;
for(int i = 0; i < ctx->n_group_elements; i++) {
double x = ctx->limit_curve[3*i];
double y = ctx->limit_curve[3*i+1];
cairo_user_to_device(C, &x, &y);
if(-x < ctx->dim->width && x < 3*ctx->dim->width && -y < ctx->dim->height && y < 3*ctx->dim->height) {
if(ctx->limit_with_lines) {
if(!previous_inside)
cairo_move_to(C, ctx->limit_curve[3*i], ctx->limit_curve[3*i+1]);
else
cairo_line_to(C, ctx->limit_curve[3*i], ctx->limit_curve[3*i+1]);
} else {
cairo_move_to(C, ctx->limit_curve[3*i], ctx->limit_curve[3*i+1]);
cairo_close_path(C);
}
previous_inside = 1;
} else {
previous_inside = 0;
}
}
if(!ctx->limit_with_lines) { // draw dots instead of lines
cairo_set_line_cap(C, CAIRO_LINE_CAP_ROUND);
cairo_set_line_width(C, 3.0/ctx->dim->scalefactor);
}
cairo_set_source_rgb(C, 0, 0, 0);
cairo_stroke(C);
cairo_restore(C);
}
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", log(ctx->parameter), ctx->parameter);
cairo_show_text(ctx->cairo, buf);
}
// level 5: put everything together
void draw(DrawingContext *ctx)
{
cairo_t *C = ctx->cairo;
cairo_set_source_rgb(C, 1, 1, 1);
cairo_paint(C);
cairo_set_matrix(C, &ctx->dim->matrix);
// defaults; use save/restore whenever these are changed
cairo_set_line_width(C, 1.0/ctx->dim->scalefactor);
cairo_set_font_size(C, 16);
cairo_set_line_join(C, CAIRO_LINE_JOIN_BEVEL);
cairo_set_line_cap(C, CAIRO_LINE_CAP_ROUND);
if(ctx->limit_curve_valid) {
if(ctx->show_limit)
drawLimitCurve(ctx);
if(ctx->show_boxes)
drawBoxes(ctx);
if(ctx->show_attractors)
drawAttractors(ctx);
if(ctx->show_reflectors)
drawReflectors(ctx);
}
cairo_identity_matrix(C); // text is in screen coordinates
drawText(ctx);
cairo_surface_flush(cairo_get_target(C));
}

81
initcairo.c
View File

@ -12,28 +12,11 @@ static Bool alwaysTruePredicate(Display *display, XEvent *event, XPointer arg)
return true; return true;
} }
// this computes center, radius and scalefactor out of ctx->matrix
void updateDimensions(DrawingContext *ctx)
{
double det = ctx->matrix.xx * ctx->matrix.yy - ctx->matrix.xy * ctx->matrix.yx;
double cx = (double)ctx->width/2;
double cy = (double)ctx->height/2;
double r = 2*sqrt((cx*cx + cy*cy)/det); // this is not safe anymore if we have non-uniform scaling
// don't use cairo_device_to_user() since the matrix might not be our CTM yet
cx -= ctx->matrix.x0;
cy -= ctx->matrix.y0;
ctx->center_x = ( ctx->matrix.yy * cx - ctx->matrix.xy * cy) / det;
ctx->center_y = (- ctx->matrix.yx * cx + ctx->matrix.xx * cy) / det;
ctx->radius = r;
ctx->scalefactor = sqrt(det);
}
GraphicsInfo *initCairo(int screen, int mask, int width, int height, const char *name) GraphicsInfo *initCairo(int screen, int mask, int width, int height, const char *name)
{ {
GraphicsInfo *info = malloc(sizeof(GraphicsInfo)); GraphicsInfo *info = malloc(sizeof(GraphicsInfo));
DrawingContext *ctx = malloc(sizeof(DrawingContext)); DimensionsInfo *dim = malloc(sizeof(DimensionsInfo));
info->context = ctx; info->dim = dim;
mask |= StructureNotifyMask | ExposureMask | KeyPressMask | ButtonPressMask | PointerMotionMask; mask |= StructureNotifyMask | ExposureMask | KeyPressMask | ButtonPressMask | PointerMotionMask;
@ -65,10 +48,11 @@ GraphicsInfo *initCairo(int screen, int mask, int width, int height, const char
int stride = cairo_format_stride_for_width(CAIRO_FORMAT_ARGB32, width); int stride = cairo_format_stride_for_width(CAIRO_FORMAT_ARGB32, width);
info->buffer = malloc(stride*height); info->buffer = malloc(stride*height);
info->buffer_surface = cairo_image_surface_create_for_data(info->buffer, CAIRO_FORMAT_ARGB32, width, height, stride); info->buffer_surface = cairo_image_surface_create_for_data(info->buffer, CAIRO_FORMAT_ARGB32, width, height, stride);
info->context->cairo = cairo_create(info->buffer_surface); info->buffer_context = cairo_create(info->buffer_surface);
cairo_matrix_init_identity(&info->context->matrix); cairo_matrix_init_identity(&info->dim->matrix);
info->context->width = width; info->dim->width = width;
info->context->height = height; info->dim->height = height;
updateDimensions(info->dim);
info->wm_delete_window = XInternAtom(info->display, "WM_DELETE_WINDOW", 0); info->wm_delete_window = XInternAtom(info->display, "WM_DELETE_WINDOW", 0);
info->wm_protocols = XInternAtom(info->display, "WM_PROTOCOLS", 0); info->wm_protocols = XInternAtom(info->display, "WM_PROTOCOLS", 0);
@ -81,7 +65,7 @@ GraphicsInfo *initCairo(int screen, int mask, int width, int height, const char
void destroyCairo(GraphicsInfo *info) void destroyCairo(GraphicsInfo *info)
{ {
cairo_destroy(info->context->cairo); cairo_destroy(info->buffer_context);
cairo_destroy(info->front_context); cairo_destroy(info->front_context);
cairo_surface_destroy(info->surface); cairo_surface_destroy(info->surface);
cairo_surface_destroy(info->buffer_surface); cairo_surface_destroy(info->buffer_surface);
@ -89,7 +73,7 @@ void destroyCairo(GraphicsInfo *info)
XDestroyWindow(info->display, info->win); XDestroyWindow(info->display, info->win);
XFreeColormap(info->display, info->cmap); XFreeColormap(info->display, info->cmap);
XCloseDisplay(info->display); XCloseDisplay(info->display);
free(info->context); free(info->dim);
free(info); free(info);
} }
@ -119,7 +103,7 @@ void waitUpdateTimer(GraphicsInfo *info)
info->frames++; info->frames++;
} }
int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(DrawingContext *)) int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(void *))
{ {
int state; int state;
static int last_x, last_y; static int last_x, last_y;
@ -133,17 +117,18 @@ int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(DrawingCon
case ConfigureNotify: case ConfigureNotify:
printf("ConfigureNotify Event, new dimensions: %d %d %d %d\n", ev->xconfigure.x, ev->xconfigure.y, ev->xconfigure.width, ev->xconfigure.height); printf("ConfigureNotify Event, new dimensions: %d %d %d %d\n", ev->xconfigure.x, ev->xconfigure.y, ev->xconfigure.width, ev->xconfigure.height);
info->context->width = ev->xconfigure.width; info->dim->width = ev->xconfigure.width;
info->context->height = ev->xconfigure.height; info->dim->height = ev->xconfigure.height;
cairo_xlib_surface_set_size(info->surface, info->context->width, info->context->height); updateDimensions(info->dim);
cairo_xlib_surface_set_size(info->surface, info->dim->width, info->dim->height);
cairo_destroy(info->context->cairo); cairo_destroy(info->buffer_context);
cairo_surface_destroy(info->buffer_surface); cairo_surface_destroy(info->buffer_surface);
free(info->buffer); free(info->buffer);
stride = cairo_format_stride_for_width(CAIRO_FORMAT_ARGB32, info->context->width); stride = cairo_format_stride_for_width(CAIRO_FORMAT_ARGB32, info->dim->width);
info->buffer = malloc(stride*info->context->height); info->buffer = malloc(stride*info->dim->height);
info->buffer_surface = cairo_image_surface_create_for_data(info->buffer, CAIRO_FORMAT_ARGB32, info->context->width, info->context->height, stride); info->buffer_surface = cairo_image_surface_create_for_data(info->buffer, CAIRO_FORMAT_ARGB32, info->dim->width, info->dim->height, stride);
info->context->cairo = cairo_create(info->buffer_surface); info->buffer_context = cairo_create(info->buffer_surface);
return STATUS_REDRAW; return STATUS_REDRAW;
@ -160,7 +145,7 @@ int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(DrawingCon
cairo_matrix_translate(&transform, ev->xbutton.x, ev->xbutton.y); cairo_matrix_translate(&transform, ev->xbutton.x, ev->xbutton.y);
cairo_matrix_scale(&transform, 5.0/4.0, 5.0/4.0); cairo_matrix_scale(&transform, 5.0/4.0, 5.0/4.0);
cairo_matrix_translate(&transform, -ev->xbutton.x, -ev->xbutton.y); cairo_matrix_translate(&transform, -ev->xbutton.x, -ev->xbutton.y);
cairo_matrix_multiply(&info->context->matrix, &info->context->matrix, &transform); cairo_matrix_multiply(&info->dim->matrix, &info->dim->matrix, &transform);
status = STATUS_REDRAW; status = STATUS_REDRAW;
} else if(ev->xbutton.button == 5) { } else if(ev->xbutton.button == 5) {
cairo_matrix_t transform; cairo_matrix_t transform;
@ -168,12 +153,13 @@ int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(DrawingCon
cairo_matrix_translate(&transform, ev->xbutton.x, ev->xbutton.y); cairo_matrix_translate(&transform, ev->xbutton.x, ev->xbutton.y);
cairo_matrix_scale(&transform, 4.0/5.0, 4.0/5.0); cairo_matrix_scale(&transform, 4.0/5.0, 4.0/5.0);
cairo_matrix_translate(&transform, -ev->xbutton.x, -ev->xbutton.y); cairo_matrix_translate(&transform, -ev->xbutton.x, -ev->xbutton.y);
cairo_matrix_multiply(&info->context->matrix, &info->context->matrix, &transform); cairo_matrix_multiply(&info->dim->matrix, &info->dim->matrix, &transform);
status = STATUS_REDRAW; status = STATUS_REDRAW;
} }
last_x = ev->xbutton.x; last_x = ev->xbutton.x;
last_y = ev->xbutton.y; last_y = ev->xbutton.y;
updateDimensions(info->dim);
return status; return status;
case MotionNotify: case MotionNotify:
@ -184,7 +170,7 @@ int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(DrawingCon
cairo_matrix_t transform; cairo_matrix_t transform;
cairo_matrix_init_identity(&transform); cairo_matrix_init_identity(&transform);
cairo_matrix_translate(&transform, dx, dy); cairo_matrix_translate(&transform, dx, dy);
cairo_matrix_multiply(&info->context->matrix, &info->context->matrix, &transform); cairo_matrix_multiply(&info->dim->matrix, &info->dim->matrix, &transform);
status = STATUS_REDRAW; status = STATUS_REDRAW;
} else if(ev->xmotion.state & Button1Mask && ev->xmotion.state & ShiftMask) { } else if(ev->xmotion.state & Button1Mask && ev->xmotion.state & ShiftMask) {
double width = (double) cairo_xlib_surface_get_width(info->surface); double width = (double) cairo_xlib_surface_get_width(info->surface);
@ -199,7 +185,7 @@ int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(DrawingCon
cairo_matrix_translate(&transform, width/2, height/2); cairo_matrix_translate(&transform, width/2, height/2);
cairo_matrix_rotate(&transform, angle); cairo_matrix_rotate(&transform, angle);
cairo_matrix_translate(&transform, -width/2, -height/2); cairo_matrix_translate(&transform, -width/2, -height/2);
cairo_matrix_multiply(&info->context->matrix, &info->context->matrix, &transform); cairo_matrix_multiply(&info->dim->matrix, &info->dim->matrix, &transform);
status = STATUS_REDRAW; status = STATUS_REDRAW;
} }
@ -219,7 +205,7 @@ int processStandardEvent(GraphicsInfo *info, XEvent *ev, void (*draw)(DrawingCon
return STATUS_NOTHING; return STATUS_NOTHING;
} }
int checkEvents(GraphicsInfo *info, int (*process)(GraphicsInfo*, XEvent*), void (*draw)(DrawingContext*)) // 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 (*draw)(void *)) // get any events from the queue and the server, process them if neccessary, quit if wanted
{ {
XEvent ev; XEvent ev;
int x11_fd; int x11_fd;
@ -264,3 +250,20 @@ int checkEvents(GraphicsInfo *info, int (*process)(GraphicsInfo*, XEvent*), void
return status; return status;
} }
// this computes center, radius and scalefactor out of ctx->matrix
void updateDimensions(DimensionsInfo *dim)
{
double det = dim->matrix.xx * dim->matrix.yy - dim->matrix.xy * dim->matrix.yx;
double cx = (double)dim->width/2;
double cy = (double)dim->height/2;
double r = 2*sqrt((cx*cx + cy*cy)/det); // this is not safe anymore if we have non-uniform scaling
// don't use cairo_device_to_user() since the matrix might not be our CTM yet
cx -= dim->matrix.x0;
cy -= dim->matrix.y0;
dim->center_x = ( dim->matrix.yy * cx - dim->matrix.xy * cy) / det;
dim->center_y = (- dim->matrix.yx * cx + dim->matrix.xx * cy) / det;
dim->radius = r;
dim->scalefactor = sqrt(det);
}

10
initcairo.h
View File

@ -17,7 +17,6 @@
#define STATUS_QUIT 2 #define STATUS_QUIT 2
typedef struct { typedef struct {
cairo_t *cairo;
cairo_matrix_t matrix; cairo_matrix_t matrix;
unsigned int width; unsigned int width;
unsigned int height; unsigned int height;
@ -27,10 +26,9 @@ typedef struct {
double center_x; double center_x;
double center_y; double center_y;
double radius; double radius;
} DrawingContext; } DimensionsInfo;
typedef struct { typedef struct {
DrawingContext *context;
Display *display; Display *display;
Window win; Window win;
Colormap cmap; Colormap cmap;
@ -40,11 +38,13 @@ typedef struct {
cairo_t *front_context; cairo_t *front_context;
cairo_surface_t *buffer_surface; cairo_surface_t *buffer_surface;
cairo_t *buffer_context;
unsigned char *buffer; unsigned char *buffer;
struct timeval start_time; struct timeval start_time;
unsigned long frames; unsigned long frames;
double elapsed, frametime; double elapsed, frametime;
DimensionsInfo *dim;
} GraphicsInfo; } GraphicsInfo;
GraphicsInfo *initCairo(int screen, int mask, int width, int height, const char *name); GraphicsInfo *initCairo(int screen, int mask, int width, int height, const char *name);
@ -52,7 +52,7 @@ 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 (*draw)(DrawingContext *)); int checkEvents(GraphicsInfo *info, int (*process)(GraphicsInfo*, XEvent*), void (*draw)(void *));
void updateDimensions(DrawingContext *ctx); void updateDimensions(DimensionsInfo *ctx);
#endif #endif

719
limit_set.c
View File

@ -1,59 +1,9 @@
#include <math.h> #include "main.h"
#include <stdio.h>
#include <time.h>
#include <sys/time.h>
#include <cairo/cairo-pdf.h>
#include <X11/XKBlib.h>
#include "initcairo.h" static int compareAngle(const void *x, const void *y)
#include "triangle.h" {
#include "linalg.h" return ((double*)x)[2] > ((double*)y)[2] ? 1 : -1;
}
#define LOOP(i) for(int i = 0; i < 3; i++)
typedef struct {
double x;
double y;
} point_t;
void cartanMatrix(gsl_matrix *cartan, double a1, double a2, double a3, double s);
void initializeTriangleGenerators(gsl_matrix **gen, gsl_matrix *cartan);
point_t intersect(point_t a, point_t b, point_t c, point_t d);
void drawPoint(DrawingContext *ctx, point_t p);
void drawSegment(DrawingContext *ctx, point_t a, point_t b);
void drawLine(DrawingContext *ctx, point_t a, point_t b);
void drawImplicitLine(DrawingContext *ctx, double a, double b, double c);
void drawPolygon(DrawingContext *ctx, int sides, ...);
void drawAttractorConnection(DrawingContext *ctx, const char *word1, const char *word2);
void drawBox(DrawingContext *ctx, const char *word1, const char *word2);
void drawBoxStd(DrawingContext *ctx, const char *word, char base);
int compareAngle(const void *x, const void *y);
int computeLimitCurve();
void drawBoxes(DrawingContext *ctx);
void drawReflectors(DrawingContext *ctx);
void drawAttractors(DrawingContext *ctx);
void draw(DrawingContext *ctx);
void setup();
void destroy();
void print(DrawingContext *screen);
int processEvent(GraphicsInfo *info, XEvent *ev);
double parameter;
int n_group_elements;
double *limit_curve; // x, y, angle triples
int limit_curve_valid = 0;
groupelement_t *group;
workspace_t *ws;
gsl_matrix *gen[3];
gsl_matrix **matrices;
gsl_matrix *cartan, *cob, *coxeter, *coxeter_fixedpoints, *fixedpoints;
int show_boxes = 0;
int show_attractors = 0;
int show_reflectors = 0;
int show_limit = 1;
int limit_with_lines = 1;
int use_repelling = 1;
void cartanMatrix(gsl_matrix *cartan, double a1, double a2, double a3, double s) void cartanMatrix(gsl_matrix *cartan, double a1, double a2, double a3, double s)
{ {
@ -76,622 +26,73 @@ void initializeTriangleGenerators(gsl_matrix **gen, gsl_matrix *cartan)
LOOP(i) LOOP(j) *gsl_matrix_ptr(gen[i], i, j) += gsl_matrix_get(cartan, i, j); LOOP(i) LOOP(j) *gsl_matrix_ptr(gen[i], i, j) += gsl_matrix_get(cartan, i, j);
} }
// intersect the lines a-b and c-d int computeLimitCurve(DrawingContext *ctx)
point_t intersect(point_t a, point_t b, point_t c, point_t d)
{ {
point_t res; workspace_t *ws = ctx->ws;
double t = ((c.y-d.y)*(c.x-a.x) - (c.x-d.x)*(c.y-a.y)) / ((b.x-a.x)*(c.y-d.y) - (b.y-a.y)*(c.x-d.x)); gsl_matrix *cartan_pos = getTempMatrix(ctx);
res.x = (1-t)*a.x + t*b.x; gsl_matrix *cob_pos = getTempMatrix(ctx);
res.y = (1-t)*a.y + t*b.y; gsl_matrix *coxeter_pos = getTempMatrix(ctx);
return res; gsl_matrix *coxeter_fixedpoints_pos = getTempMatrix(ctx);
gsl_matrix *fixedpoints_pos = getTempMatrix(ctx);
gsl_matrix *coxeter = getTempMatrix(ctx);
gsl_matrix *coxeter_fixedpoints = getTempMatrix(ctx);
gsl_matrix *fixedpoints = getTempMatrix(ctx);
gsl_matrix **gen = getTempMatrices(ctx, 3);
gsl_matrix **elements = getTempMatrices(ctx, ctx->n_group_elements);
groupelement_t *group = ctx->group;
int success = 0;
int column = ctx->use_repelling ? 2 : 0;
ctx->limit_curve_valid = 0;
// 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);
gsl_matrix_set_identity(elements[0]);
for(int i = 1; i < ctx->n_group_elements; i++)
multiply(elements[group[i].parent->id], gen[group[i].letter], elements[i]);
diagonalize_symmetric_form(cartan_pos, cob_pos, ws);
multiply_many(ws, coxeter_pos, 3, gen[0], gen[1], gen[2]);
int ev_count_pos = real_eigenvectors(coxeter_pos, coxeter_fixedpoints_pos, ws);
if(ev_count_pos != 3)
goto error_out;
for(int i = 0; i < ctx->n_group_elements; i++) {
multiply_many(ws, fixedpoints_pos, 3, cob_pos, elements[i], coxeter_fixedpoints_pos);
ctx->limit_curve[3*i+2] = atan2(
gsl_matrix_get(fixedpoints_pos, 0, column)/gsl_matrix_get(fixedpoints_pos, 2, column),
gsl_matrix_get(fixedpoints_pos, 1, column)/gsl_matrix_get(fixedpoints_pos, 2, column));
} }
void drawPoint(DrawingContext *ctx, point_t p) // now do it again to calculate x and y coordinates
{ initializeTriangleGenerators(gen, ctx->cartan);
cairo_t *C = ctx->cairo; gsl_matrix_set_identity(elements[0]);
for(int i = 1; i < ctx->n_group_elements; i++)
cairo_save(C); multiply(elements[group[i].parent->id], gen[group[i].letter], elements[i]);
cairo_move_to(C, p.x, p.y);
cairo_close_path(C);
cairo_set_line_cap(C, CAIRO_LINE_CAP_ROUND);
cairo_set_line_width(C, 10.0/ctx->scalefactor);
cairo_stroke(C);
cairo_restore(C);
}
void drawSegment(DrawingContext *ctx, point_t a, point_t b)
{
cairo_t *C = ctx->cairo;
cairo_move_to(C, a.x, a.y);
cairo_line_to(C, b.x, b.y);
cairo_stroke(C);
}
void drawLine(DrawingContext *ctx, point_t a, point_t b)
{
// not implemented
point_t c, xplus, xminus;
double normb;
double scalbc;
c.x = ctx->center_x;
c.y = ctx->center_y;
b.x -= a.x;
b.y -= a.y;
c.x -= a.x;
c.y -= a.y;
normb = sqrt(b.x*b.x + b.y*b.y);
b.x /= normb;
b.y /= normb;
scalbc = b.x*c.x + b.y*c.y;
xplus.x = a.x + (scalbc + ctx->radius)*b.x;
xplus.y = a.y + (scalbc + ctx->radius)*b.y;
xminus.x = a.x + (scalbc - ctx->radius)*b.x;
xminus.y = a.y + (scalbc - ctx->radius)*b.y;
drawSegment(ctx, xminus, xplus);
}
void drawImplicitLine(DrawingContext *ctx, double a, double b, double c)
{
// not implemented
double norm, lambda;
point_t m, s, xminus, xplus;
m.x = ctx->center_x;
m.y = ctx->center_y;
lambda = (a*m.x + b*m.y + c)/(a*a + b*b);
s.x = m.x - lambda*a;
s.y = m.y - lambda*b;
norm = sqrt(a*a + b*b);
xminus.x = s.x - ctx->radius * b / norm;
xminus.y = s.y + ctx->radius * a / norm;
xplus.x = s.x + ctx->radius * b / norm;
xplus.y = s.y - ctx->radius * a / norm;
drawSegment(ctx, xminus, xplus);
}
void drawPolygon(DrawingContext *ctx, int sides, ...)
{
va_list args;
point_t first, prev, current;
va_start(args, sides);
first = va_arg(args, point_t);
current = first;
for(int i = 0; i < sides-1; i++) {
prev = current;
current = va_arg(args, point_t);
drawSegment(ctx, prev, current);
}
drawSegment(ctx, current, first);
va_end(args);
}
int 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++) {
if(word[i] == ' ')
continue;
multiply_right(tmp, gen[word[i]-'a'], ws);
}
int count = real_eigenvectors(tmp, ev, ws);
multiply_left(cob, ev, ws);
LOOP(i) out[i].x = gsl_matrix_get(ev, 0, i) / gsl_matrix_get(ev, 2, i);
LOOP(i) out[i].y = gsl_matrix_get(ev, 1, i) / gsl_matrix_get(ev, 2, i);
return count;
}
void drawAttractorConnection(DrawingContext *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 drawTriangle(DrawingContext *ctx, const char *word)
{
point_t p[3];
fixedPoints(word, p);
drawPolygon(ctx, 3, p[0], p[1], p[2]);
}
void drawBox(DrawingContext *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(DrawingContext *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;
LOOP(i) word1[len+i] = (base-'A'+6+i+1)%3+'a';
LOOP(i) word2[len+i] = (base-'A'+6-i-1)%3+'a';
// printf("Words: %s %s\n", word1, word2);
drawBox(ctx, word1, word2);
}
int compareAngle(const void *x, const void *y)
{
return ((double*)x)[2] > ((double*)y)[2] ? 1 : -1;
}
int computeLimitCurve()
{
int p = 5, q = 5, r = 5;
int k = 2, l = 2, m = 2;
int column = use_repelling ? 2 : 0;
generate_triangle_group(group, n_group_elements, p, q, r);
// do first in the Fuchsian case to get the angles
cartanMatrix(cartan, M_PI/p, M_PI/q, M_PI/r, 1.0);
initializeTriangleGenerators(gen, cartan);
gsl_matrix_set_identity(matrices[0]);
for(int i = 1; i < n_group_elements; i++)
multiply(matrices[group[i].parent->id], gen[group[i].letter], matrices[i]);
diagonalize_symmetric_form(cartan, cob, ws);
multiply_many(ws, coxeter, 3, gen[0], gen[1], gen[2]);
int ev_count_fuchsian = real_eigenvectors(coxeter, coxeter_fixedpoints, ws);
if(ev_count_fuchsian != 3)
return 0;
for(int i = 0; i < n_group_elements; i++) {
multiply_many(ws, fixedpoints, 3, cob, matrices[i], coxeter_fixedpoints);
limit_curve[3*i+2] = atan2(
gsl_matrix_get(fixedpoints, 0, column)/gsl_matrix_get(fixedpoints, 2, column),
gsl_matrix_get(fixedpoints, 1, column)/gsl_matrix_get(fixedpoints, 2, column));
}
// now to it again to calculate x and y coordinates
cartanMatrix(cartan, M_PI*k/p, M_PI*l/q, M_PI*m/r, parameter);
initializeTriangleGenerators(gen, cartan);
gsl_matrix_set_identity(matrices[0]);
for(int i = 1; i < n_group_elements; i++)
multiply(matrices[group[i].parent->id], gen[group[i].letter], matrices[i]);
gsl_matrix_memcpy(cob, cartan); // is this a good choice of basis
// gsl_matrix_set_identity(cob);
multiply_many(ws, coxeter, 3, gen[0], gen[1], gen[2]); multiply_many(ws, coxeter, 3, gen[0], gen[1], gen[2]);
int ev_count = real_eigenvectors(coxeter, coxeter_fixedpoints, ws); int ev_count = real_eigenvectors(coxeter, coxeter_fixedpoints, ws);
if(ev_count == 1) if(ev_count == 1)
column = 0; column = 0;
if(ev_count == 0) if(ev_count == 0)
return 0; goto error_out;
for(int i = 0; i < n_group_elements; i++) { for(int i = 0; i < ctx->n_group_elements; i++) {
multiply_many(ws, fixedpoints, 3, cob, matrices[i], coxeter_fixedpoints); multiply_many(ws, fixedpoints, 3, ctx->cob, elements[i], coxeter_fixedpoints);
limit_curve[3*i] = gsl_matrix_get(fixedpoints, 0, column)/gsl_matrix_get(fixedpoints, 2, column); ctx->limit_curve[3*i ] = gsl_matrix_get(fixedpoints, 0, column)/gsl_matrix_get(fixedpoints, 2, column);
limit_curve[3*i+1] = gsl_matrix_get(fixedpoints, 1, column)/gsl_matrix_get(fixedpoints, 2, column); ctx->limit_curve[3*i+1] = gsl_matrix_get(fixedpoints, 1, column)/gsl_matrix_get(fixedpoints, 2, column);
} }
qsort(limit_curve, n_group_elements, 3*sizeof(double), compareAngle); qsort(ctx->limit_curve, ctx->n_group_elements, 3*sizeof(double), compareAngle);
return 1; ctx->limit_curve_valid = 1;
}
success = 1;
void drawBoxes(DrawingContext *ctx)
{ error_out:
cairo_t *C = ctx->cairo; releaseTempMatrices(ctx, 11+ctx->n_group_elements);
cairo_set_source_rgb(C, 1, 0, 0); return success;
drawTriangle(ctx, "abc");
cairo_set_source_rgb(C, 0, 0, 1);
drawTriangle(ctx, "aca abc aca");
drawTriangle(ctx, "acac abc caca");
drawTriangle(ctx, "acaca abc acaca");
cairo_set_source_rgb(C, 0, 0.8, 0);
drawTriangle(ctx, "cac abc cac");
drawTriangle(ctx, "caca abc acac");
drawTriangle(ctx, "cacac abc cacac");
/*
cairo_set_source_rgb(C, 1, 0, 0);
drawBoxStd(ctx, "c", 'C');
drawBoxStd(ctx, "", 'B');
drawBoxStd(ctx, "a", 'A');
drawBoxStd(ctx, "", 'C');
drawBoxStd(ctx, "b", 'B');
cairo_set_source_rgb(C, 0, 0, 0);
drawBoxStd(ctx, "ca", 'A');
drawBoxStd(ctx, "cac", 'C');
drawBoxStd(ctx, "caca", 'A');
drawBoxStd(ctx, "acac", 'C');
drawBoxStd(ctx, "aca", 'A');
drawBoxStd(ctx, "ac", 'C');
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');
drawBoxStd(ctx, "caca cb", 'B');
drawBoxStd(ctx, "caca cbc", 'C');
drawBoxStd(ctx, "caca cbcb", 'B');
drawBoxStd(ctx, "caca bcbc", 'C');
drawBoxStd(ctx, "caca bcb", 'B');
drawBoxStd(ctx, "caca bc", 'C');
cairo_set_source_rgb(C, 1, 0, 1);
drawBoxStd(ctx, "ca bc", 'C');
drawBoxStd(ctx, "ca bcb", 'B');
drawBoxStd(ctx, "ca bcbc", 'C');
drawBoxStd(ctx, "ca cbcb", 'B');
drawBoxStd(ctx, "ca cbc", 'C');
drawBoxStd(ctx, "ca cb", 'B');
cairo_set_source_rgb(C, 0, 1, 0);
// drawBoxStd(ctx, "ca bc", 'C');
drawBoxStd(ctx, "cabc ba", 'A');
drawBoxStd(ctx, "cabc bab", 'B');
drawBoxStd(ctx, "cabc baba", 'A');
drawBoxStd(ctx, "cabc abab", 'B');
drawBoxStd(ctx, "cabc aba", 'A');
drawBoxStd(ctx, "cabc ab", 'B');
*/
}
void drawReflectors(DrawingContext *ctx)
{
gsl_matrix *tmp = ws->stack[10];
gsl_matrix *tmp2 = ws->stack[11];
point_t p[3];
// points
cairo_set_source_rgb(ctx->cairo, 0, 0, 0);
LOOP(i) p[i].x = gsl_matrix_get(cob, 0, i) / gsl_matrix_get(cob, 2, i);
LOOP(i) p[i].y = gsl_matrix_get(cob, 1, i) / gsl_matrix_get(cob, 2, i);
LOOP(i) drawPoint(ctx, p[i]);
// lines
invert(cob, tmp2, ws);
multiply(cartan, tmp2, tmp);
LOOP(i) drawImplicitLine(ctx, gsl_matrix_get(tmp, i, 0), gsl_matrix_get(tmp, i, 1), gsl_matrix_get(tmp, i, 2));
}
void drawAttractors(DrawingContext *ctx)
{
point_t p[3][3];
fixedPoints("abc", p[0]);
fixedPoints("bca", p[1]);
fixedPoints("cab", p[2]);
double color[3][3] = {{1,0,0},{0,0.7,0},{0,0,1}};
LOOP(i) LOOP(j) {
cairo_set_source_rgb(ctx->cairo, color[i][0], color[i][1], color[i][2]);
drawPoint(ctx, p[i][j]);
}
LOOP(i) LOOP(j) {
cairo_set_source_rgb(ctx->cairo, color[i][0], color[i][1], color[i][2]);
drawLine(ctx, p[i][j], p[i][(j+1)%3]);
}
}
void draw(DrawingContext *ctx)
{
cairo_t *C = ctx->cairo;
cairo_set_source_rgb(C, 1, 1, 1);
cairo_paint(C);
cairo_set_matrix(C, &ctx->matrix);
// defaults; use save/restore whenever these are changed
cairo_set_line_width(C, 1.0/ctx->scalefactor);
cairo_set_font_size(C, 16);
cairo_set_line_join(C, CAIRO_LINE_JOIN_BEVEL);
cairo_set_line_cap(C, CAIRO_LINE_CAP_ROUND);
if(limit_curve_valid) {
if(show_limit) {
cairo_save(C);
int previous_inside = 0;
for(int i = 0; i < n_group_elements; i++) {
double x = limit_curve[3*i];
double y = limit_curve[3*i+1];
cairo_user_to_device(C, &x, &y);
if(-x < ctx->width && x < 3*ctx->width && -y < ctx->height && y < 3*ctx->height) {
if(limit_with_lines) {
if(!previous_inside)
cairo_move_to(C, limit_curve[3*i], limit_curve[3*i+1]);
else
cairo_line_to(C, limit_curve[3*i], limit_curve[3*i+1]);
} else {
cairo_move_to(C, limit_curve[3*i], limit_curve[3*i+1]);
cairo_close_path(C);
}
previous_inside = 1;
} else {
previous_inside = 0;
}
}
if(!limit_with_lines) { // draw dots instead of lines
cairo_set_line_cap(C, CAIRO_LINE_CAP_ROUND);
cairo_set_line_width(C, 3.0/ctx->scalefactor);
}
cairo_set_source_rgb(C, 0, 0, 0);
cairo_stroke(C);
cairo_restore(C);
}
if(show_boxes)
drawBoxes(ctx);
if(show_attractors)
drawAttractors(ctx);
if(show_reflectors)
drawReflectors(ctx);
}
cairo_identity_matrix(C);
cairo_move_to(C, 15, 30);
cairo_set_source_rgb(C, 0, 0, 0);
char buf[100];
sprintf(buf, "t = exp(%.8f) = %.8f", log(parameter), parameter);
cairo_show_text(C, buf);
cairo_surface_flush(cairo_get_target(C));
}
void setup()
{
n_group_elements = 50000;
limit_curve = malloc(3*n_group_elements*sizeof(double));
group = malloc(n_group_elements*sizeof(groupelement_t));
ws = workspace_alloc(3);
LOOP(i) gen[i] = gsl_matrix_alloc(3, 3);
matrices = malloc(n_group_elements*sizeof(gsl_matrix*));
for(int i = 0; i < n_group_elements; i++)
matrices[i] = gsl_matrix_alloc(3, 3);
cartan = gsl_matrix_alloc(3, 3);
cob = gsl_matrix_alloc(3, 3);
coxeter = gsl_matrix_alloc(3, 3);
coxeter_fixedpoints = gsl_matrix_alloc(3, 3);
fixedpoints = gsl_matrix_alloc(3, 3);
}
void destroy()
{
free(limit_curve);
free(group);
workspace_free(ws);
LOOP(i) gsl_matrix_free(gen[i]);
for(int i = 0; i < n_group_elements; i++)
gsl_matrix_free(matrices[i]);
free(matrices);
gsl_matrix_free(cartan);
gsl_matrix_free(cob);
gsl_matrix_free(coxeter);
gsl_matrix_free(coxeter_fixedpoints);
gsl_matrix_free(fixedpoints);
}
void print(DrawingContext *screen)
{
DrawingContext file;
cairo_surface_t *surface;
char filename[100];
time_t t = time(NULL);
strftime(filename, sizeof(filename), "screenshot_%Y%m%d_%H%M%S.pdf", localtime(&t));
file.width = screen->width;
file.height = screen->width / sqrt(2.0);
file.matrix = screen->matrix;
file.matrix.y0 += ((double)file.height - (double)screen->height) / 2.0; // recenter vertically
updateDimensions(&file);
surface = cairo_pdf_surface_create(filename, (double)file.width, (double)file.height);
file.cairo = cairo_create(surface);
draw(&file);
cairo_destroy(file.cairo);
cairo_surface_destroy(surface);
printf("Wrote sceenshot to file: %s\n", filename);
}
int processEvent(GraphicsInfo *info, XEvent *ev)
{
int state;
unsigned long key;
switch(ev->type) {
case KeyPress:
state = ev->xkey.state & (ShiftMask | LockMask | ControlMask);
key = XkbKeycodeToKeysym(ev->xkey.display, ev->xkey.keycode, 0, !!(state & ShiftMask));
printf("Key pressed: %ld\n", key);
switch(key) {
case XK_Down:
parameter /= exp(0.002);
limit_curve_valid = computeLimitCurve();
break;
case XK_Up:
parameter *= exp(0.002);
limit_curve_valid = computeLimitCurve();
break;
case XK_Left:
parameter /= exp(0.0001);
limit_curve_valid = computeLimitCurve();
break;
case XK_Right:
parameter *= exp(0.0001);
limit_curve_valid = computeLimitCurve();
break;
case XK_Page_Down:
parameter /= exp(0.2);
limit_curve_valid = computeLimitCurve();
break;
case XK_Page_Up:
parameter *= exp(0.2);
limit_curve_valid = computeLimitCurve();
break;
case ' ':
parameter = 2.890053638;
limit_curve_valid = computeLimitCurve();
break;
case XK_Return:
parameter = 2.76375163;
limit_curve_valid = computeLimitCurve();
break;
case 'm':
printf("info->context->matrix.xx = %f;\n", info->context->matrix.xx);
printf("info->context->matrix.xy = %f;\n", info->context->matrix.xy);
printf("info->context->matrix.x0 = %f;\n", info->context->matrix.x0);
printf("info->context->matrix.yx = %f;\n", info->context->matrix.yx);
printf("info->context->matrix.yy = %f;\n", info->context->matrix.yy);
printf("info->context->matrix.y0 = %f;\n", info->context->matrix.y0);
break;
case 'b':
show_boxes = !show_boxes;
break;
case 'a':
show_attractors = !show_attractors;
break;
case 'r':
show_reflectors = !show_reflectors;
break;
case 'L':
limit_with_lines = !limit_with_lines;
break;
case 'l':
show_limit = !show_limit;
break;
case 'p':
print(info->context);
break;
case 'f':
use_repelling = !use_repelling;
limit_curve_valid = computeLimitCurve();
}
return STATUS_REDRAW;
}
return STATUS_NOTHING;
}
int main()
{
GraphicsInfo *info;
parameter = 3.0;
setup();
limit_curve_valid = computeLimitCurve();
info = initCairo(0, KeyPressMask, 200, 200, "Triangle group");
if(!info)
return 1;
DrawingContext *ctx = info->context;
ctx->matrix.xx = 837.930824;
ctx->matrix.xy = -712.651341;
ctx->matrix.x0 = 180.427716;
ctx->matrix.yx = 712.651341;
ctx->matrix.yy = 837.930824;
ctx->matrix.y0 = 1412.553240;
/*
info->context->matrix.xx = 1636.583641;
info->context->matrix.xy = -1391.897150;
info->context->matrix.x0 = 975.772883;
info->context->matrix.yx = 1391.897150;
info->context->matrix.yy = 1636.583641;
info->context->matrix.y0 = 2446.174297;
*/
updateDimensions(ctx);
startTimer(info);
while(1) {
int result = checkEvents(info, processEvent, NULL);
if(result == STATUS_QUIT)
return 0;
else if(result == STATUS_REDRAW) {
struct timeval current_time;
double start_time, intermediate_time, end_time;
gettimeofday(&current_time, 0);
start_time = current_time.tv_sec + current_time.tv_usec*1e-6;
updateDimensions(info->context);
draw(info->context);
gettimeofday(&current_time, 0);
intermediate_time = current_time.tv_sec + current_time.tv_usec*1e-6;
cairo_set_source_surface(info->front_context, info->buffer_surface, 0, 0);
cairo_paint(info->front_context);
gettimeofday(&current_time, 0);
end_time = current_time.tv_sec + current_time.tv_usec*1e-6;
printf("drawing finished in %.2f milliseconds, of which %.2f milliseconds were buffer switching\n", (end_time - start_time) * 1000, (end_time - intermediate_time) * 1000);
}
waitUpdateTimer(info);
}
destroyCairo(info);
destroy();
return 0;
} }

289
main.c Normal file
View File

@ -0,0 +1,289 @@
#include <math.h>
#include <stdio.h>
#include <time.h>
#include <sys/time.h>
#include <cairo/cairo-pdf.h>
#include <X11/XKBlib.h>
#include "main.h"
#include "initcairo.h"
#include "triangle.h"
#include "linalg.h"
#define TOGGLE(a) do { (a) = !(a); } while(0)
DrawingContext *screen_context;
// setup everything except cairo and dim, which will be provided by the graphics system
void setupContext(DrawingContext *ctx)
{
ctx->n_group_elements = NUM_GROUP_ELEMENTS;
ctx->p[0] = 5;
ctx->p[1] = 5;
ctx->p[2] = 5;
ctx->k[0] = 2;
ctx->k[1] = 2;
ctx->k[2] = 2;
ctx->parameter = 3.0;
ctx->show_boxes = 0;
ctx->show_attractors = 0;
ctx->show_reflectors = 0;
ctx->show_limit= 1;
ctx->limit_with_lines = 1;
ctx->use_repelling = 0;
ctx->limit_curve = malloc(3*ctx->n_group_elements*sizeof(double));
ctx->limit_curve_valid = 0;
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]);
// the temporary stuff
ctx->cartan = gsl_matrix_alloc(3, 3);
ctx->cob = gsl_matrix_alloc(3, 3);
ctx->ws = workspace_alloc(3);
ctx->tmp = malloc(MAX_TEMP_MATRICES*sizeof(gsl_matrix*));
for(int i = 0; i < MAX_TEMP_MATRICES; i++)
ctx->tmp[i] = gsl_matrix_alloc(3, 3);
ctx->tmp_used = 0;
ctx->tmp_vec = malloc(MAX_TEMP_MATRICES*sizeof(gsl_vector*));
for(int i = 0; i < MAX_TEMP_MATRICES; i++)
ctx->tmp_vec[i] = gsl_vector_alloc(3);
ctx->tmp_vec_used = 0;
}
void destroyContext(DrawingContext *ctx)
{
free(ctx->limit_curve);
free(ctx->group);
gsl_matrix_free(ctx->cartan);
gsl_matrix_free(ctx->cob);
workspace_free(ctx->ws);
for(int i = 0; i < MAX_TEMP_MATRICES; i++)
gsl_matrix_free(ctx->tmp[i]);
free(ctx->tmp);
for(int i = 0; i < MAX_TEMP_VECTORS; i++)
gsl_vector_free(ctx->tmp_vec[i]);
free(ctx->tmp_vec);
}
void updateMatrices(DrawingContext *ctx)
{
double angle[3];
LOOP(i) angle[i] = M_PI*ctx->k[i]/ctx->p[i];
cartanMatrix(ctx->cartan, angle[0], angle[1], angle[2], ctx->parameter);
gsl_matrix_memcpy(ctx->cob, ctx->cartan); // is this a good choice of basis
}
void print(DrawingContext *screen)
{
DrawingContext file;
DimensionsInfo dim;
cairo_surface_t *surface;
char filename[100];
time_t t = time(NULL);
strftime(filename, sizeof(filename), "screenshot_%Y%m%d_%H%M%S.pdf", localtime(&t));
dim.width = screen->dim->width;
dim.height = screen->dim->width / sqrt(2.0);
dim.matrix = screen->dim->matrix;
dim.matrix.y0 += ((double)dim.height - (double)screen->dim->height) / 2.0; // recenter vertically
updateDimensions(&dim);
file.dim = &dim;
surface = cairo_pdf_surface_create(filename, (double)dim.width, (double)dim.height);
file.cairo = cairo_create(surface);
draw(&file);
cairo_destroy(file.cairo);
cairo_surface_destroy(surface);
printf("Wrote sceenshot to file: %s\n", filename);
}
int processEvent(GraphicsInfo *info, XEvent *ev)
{
int state;
unsigned long key;
switch(ev->type) {
case KeyPress:
state = ev->xkey.state & (ShiftMask | LockMask | ControlMask);
key = XkbKeycodeToKeysym(ev->xkey.display, ev->xkey.keycode, 0, !!(state & ShiftMask));
printf("Key pressed: %ld\n", key);
switch(key) {
case XK_Down:
screen_context->parameter /= exp(0.002);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Up:
screen_context->parameter *= exp(0.002);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Left:
screen_context->parameter /= exp(0.0001);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Right:
screen_context->parameter *= exp(0.0001);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Page_Down:
screen_context->parameter /= exp(0.2);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Page_Up:
screen_context->parameter *= exp(0.2);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case ' ':
screen_context->parameter = 2.890053638;
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case XK_Return:
screen_context->parameter = 2.76375163;
updateMatrices(screen_context);
computeLimitCurve(screen_context);
break;
case 'm':
printf("matrix.xx = %f;\n", info->dim->matrix.xx);
printf("matrix.xy = %f;\n", info->dim->matrix.xy);
printf("matrix.x0 = %f;\n", info->dim->matrix.x0);
printf("matrix.yx = %f;\n", info->dim->matrix.yx);
printf("matrix.yy = %f;\n", info->dim->matrix.yy);
printf("matrix.y0 = %f;\n", info->dim->matrix.y0);
break;
case 'b':
TOGGLE(screen_context->show_boxes);
break;
case 'a':
TOGGLE(screen_context->show_attractors);
break;
case 'r':
TOGGLE(screen_context->show_reflectors);
break;
case 'L':
TOGGLE(screen_context->limit_with_lines);
break;
case 'l':
TOGGLE(screen_context->show_limit);
break;
case 'p':
print(screen_context);
break;
case 'f':
TOGGLE(screen_context->use_repelling);
computeLimitCurve(screen_context);
}
return STATUS_REDRAW;
}
return STATUS_NOTHING;
}
int main()
{
GraphicsInfo *info;
screen_context = malloc(sizeof(DrawingContext));
setupContext(screen_context);
updateMatrices(screen_context);
computeLimitCurve(screen_context);
// do stuff
/*
DrawingContext *ctx = screen_context;
gsl_matrix *tmp = getTempMatrix(ctx);
gsl_matrix *ev = getTempMatrix(ctx);
gsl_matrix *evinv = getTempMatrix(ctx);
gsl_matrix **gen = getTempMatrices(ctx, 3);
gsl_matrix *transform = getTempMatrix(ctx);
vector_t eigenvectors[3][3];
char words[3][4] = {"abc", "bca", "cab"};
initializeTriangleGenerators(gen, ctx->cartan);
gsl_matrix_set_identity(tmp);
for(int j = 0; j < strlen(words[0]); j++)
multiply_right(tmp, gen[words[0][j]-'a'], ctx->ws);
real_eigenvectors(tmp, ev, ctx->ws);
invert(ev, evinv, ctx->ws);
LOOP(i) {
gsl_matrix_set_identity(tmp);
for(int j = 0; j < strlen(words[i]); j++)
multiply_right(tmp, gen[words[i][j]-'a'], ctx->ws);
real_eigenvectors(tmp, ev, ctx->ws);
LOOP(j) LOOP(k) eigenvectors[i][j].x[k] = gsl_matrix_get(ev, k, j);
}
// solve the following: (x + y + z) (l) = lambda w
return 0;
*/
info = initCairo(0, KeyPressMask, 200, 200, "Triangle group");
if(!info)
return 1;
info->dim->matrix.xx = 837.930824;
info->dim->matrix.xy = -712.651341;
info->dim->matrix.x0 = 180.427716;
info->dim->matrix.yx = 712.651341;
info->dim->matrix.yy = 837.930824;
info->dim->matrix.y0 = 1412.553240;
updateDimensions(info->dim);
screen_context->dim = info->dim;
screen_context->cairo = info->buffer_context;
startTimer(info);
while(1) {
int result = checkEvents(info, processEvent, NULL);
if(result == STATUS_QUIT)
return 0;
else if(result == STATUS_REDRAW) {
struct timeval current_time;
double start_time, intermediate_time, end_time;
gettimeofday(&current_time, 0);
start_time = current_time.tv_sec + current_time.tv_usec*1e-6;
draw(screen_context);
gettimeofday(&current_time, 0);
intermediate_time = current_time.tv_sec + current_time.tv_usec*1e-6;
cairo_set_source_surface(info->front_context, info->buffer_surface, 0, 0);
cairo_paint(info->front_context);
gettimeofday(&current_time, 0);
end_time = current_time.tv_sec + current_time.tv_usec*1e-6;
printf("drawing finished in %.2f milliseconds, of which %.2f milliseconds were buffer switching\n", (end_time - start_time) * 1000, (end_time - intermediate_time) * 1000);
}
waitUpdateTimer(info);
}
free(screen_context);
destroyCairo(info);
destroyContext(screen_context);
return 0;
}

126
main.h Normal file
View File

@ -0,0 +1,126 @@
#ifndef TRIANGLE_GROUP_MAIN_H
#define TRIANGLE_GROUP_MAIN_H
#include "triangle.h"
#include "linalg.h"
#include "initcairo.h"
#undef ERROR
#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 MAX_TEMP_MATRICES 60000
#define MAX_TEMP_VECTORS 100
typedef struct {
double x[3];
} vector_t;
typedef struct {
double x;
double y;
} point_t;
typedef struct {
// infos about the screen to draw on
cairo_t *cairo;
DimensionsInfo *dim;
// a priori parameter
int p[3],k[3];
double parameter;
int n_group_elements;
int show_boxes;
int show_attractors;
int show_reflectors;
int show_limit;
int limit_with_lines;
int use_repelling;
gsl_matrix *cartan, *cob;
// precomputed and constant
groupelement_t *group;
// computed stuff
double *limit_curve; // x, y, angle triples
int limit_curve_valid;
// temporary; matrices can only be freed from the top, but that's enough for us
workspace_t *ws;
gsl_matrix **tmp;
int tmp_used;
gsl_vector **tmp_vec;
int tmp_vec_used;
} DrawingContext;
static gsl_matrix **getTempMatrices(DrawingContext *ctx, int n)
{
ERROR(ctx->tmp_used + n > MAX_TEMP_MATRICES, "Ran out of temporary matrices. Consider increasing MAX_TEMP_MATRICES\n");
int index = ctx->tmp_used;
ctx->tmp_used += n;
return ctx->tmp + index;
}
static gsl_matrix *getTempMatrix(DrawingContext *ctx)
{
return *getTempMatrices(ctx, 1);
}
static void releaseTempMatrices(DrawingContext *ctx, int n)
{
ERROR(ctx->tmp_used - n < 0, "Released more matrices then in use\n");
ctx->tmp_used -= n;
}
static gsl_vector **getTempVectors(DrawingContext *ctx, int n)
{
ERROR(ctx->tmp_vec_used + n > MAX_TEMP_VECTORS, "Ran out of temporary vectors. Consider increasing MAX_TEMP_VECTORS\n");
int index = ctx->tmp_vec_used;
ctx->tmp_vec_used += n;
return ctx->tmp_vec + index;
}
static gsl_vector *getTempVector(DrawingContext *ctx)
{
return *getTempVectors(ctx, 1);
}
static void releaseTempVectors(DrawingContext *ctx, int n)
{
ERROR(ctx->tmp_vec_used - n < 0, "Released more vectors then in use\n");
ctx->tmp_vec_used -= n;
}
// 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);
int computeLimitCurve(DrawingContext *ctx);
// implemented in draw.c
vector_t cross(vector_t a, vector_t b);
int fixedPoints(DrawingContext *ctx, const char *word, vector_t *out);
void drawPoint(DrawingContext *ctx, point_t p);
void drawSegment2d(DrawingContext *ctx, point_t a, point_t b);
void drawVector(DrawingContext *ctx, vector_t v);
void drawCovector(DrawingContext *ctx, vector_t v);
void drawSegment(DrawingContext *ctx, vector_t a, vector_t b);
void drawPolygon(DrawingContext *ctx, int sides, ...);
void drawTriangle(DrawingContext *ctx, const char *word);
void drawBox(DrawingContext *ctx, const char *word1, const char *word2);
void drawBoxStd(DrawingContext *ctx, const char *word, char base);
void drawReflectors(DrawingContext *ctx);
void drawAttractors(DrawingContext *ctx);
void drawBoxes(DrawingContext *ctx);
void drawLimitCurve(DrawingContext *ctx);
void drawText(DrawingContext *ctx);
void draw(DrawingContext *ctx);
// implemented in main.c
void setupContext(DrawingContext *ctx);
void destroyContext(DrawingContext *ctx);
void print(DrawingContext *screen);
int processEvent(GraphicsInfo *info, XEvent *ev);
void updateMatrices(DrawingContext *ctx);
#endif