893 lines
25 KiB
C
893 lines
25 KiB
C
#include "main.h"
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#define FMOD(x,y) (fmod(x,y) < 0 ? fmod(x,y) + y : fmod(x,y))
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#define ANGLE_DIFF(x,y) (FMOD((x)-(y), 2*M_PI))
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#define ANGLE_IN_INTERVAL(a,b,x) (ANGLE_DIFF(x,a) < ANGLE_DIFF(b,a))
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#define FLIP(x,y) do {double tmp = x; x = y; y = tmp;} while(0)
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// level 0: helper functions
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int isInsideBB(DrawingContext *ctx, point_t p)
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{
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cairo_user_to_device(ctx->cairo, &p.x, &p.y);
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return -p.x < ctx->dim->width && p.x < 3*ctx->dim->width && -p.y < ctx->dim->height && p.y < 3*ctx->dim->height;
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}
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vector_t cross(vector_t a, vector_t b)
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{
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vector_t result;
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result.x[0] = a.x[1]*b.x[2] - a.x[2]*b.x[1];
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result.x[1] = a.x[2]*b.x[0] - a.x[0]*b.x[2];
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result.x[2] = a.x[0]*b.x[1] - a.x[1]*b.x[0];
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return result;
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}
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vector_t apply(gsl_matrix *m, vector_t x)
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{
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vector_t out;
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LOOP(i) out.x[i] = 0.0;
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LOOP(i) LOOP(j) out.x[i] += gsl_matrix_get(m, i, j) * x.x[j];
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return out;
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}
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vector_t apply_transpose(gsl_matrix *m, vector_t x)
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{
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vector_t out;
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LOOP(i) out.x[i] = 0.0;
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LOOP(i) LOOP(j) out.x[i] += gsl_matrix_get(m, j, i) * x.x[j];
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return out;
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}
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int fixedPoints(DrawingContext *ctx, const char *word, vector_t *out)
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{
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gsl_matrix *tmp = getTempMatrix(ctx->ws);
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gsl_matrix *ev = getTempMatrix(ctx->ws);
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gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
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initializeTriangleGenerators(gen, ctx->cartan);
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gsl_matrix_set_identity(tmp);
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for(int i = 0; i < strlen(word); i++) {
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if(word[i] == ' ')
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continue;
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multiply_right(tmp, gen[word[i]-'a'], ctx->ws);
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}
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int count = real_eigenvectors(tmp, ev, ctx->ws);
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LOOP(i) LOOP(j) out[i].x[j] = gsl_matrix_get(ev, j, i);
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releaseTempMatrices(ctx->ws, 5);
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return count;
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}
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// level 1: the elementary drawing functions, drawPoint, drawSegment2d
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void drawPoint(DrawingContext *ctx, point_t p)
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{
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cairo_t *C = ctx->cairo;
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cairo_save(C);
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cairo_arc(C, p.x, p.y, 5.0/ctx->dim->scalefactor, 0, 2*M_PI);
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cairo_close_path(C);
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cairo_fill(C);
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cairo_restore(C);
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/*
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cairo_save(C);
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cairo_move_to(C, p.x, p.y);
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cairo_close_path(C);
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cairo_set_line_cap(C, CAIRO_LINE_CAP_ROUND);
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cairo_set_line_width(C, 10.0/ctx->dim->scalefactor);
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cairo_stroke(C);
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cairo_restore(C);
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*/
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}
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void drawSegment2d(DrawingContext *ctx, point_t a, point_t b)
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{
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cairo_t *C = ctx->cairo;
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cairo_move_to(C, a.x, a.y);
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cairo_line_to(C, b.x, b.y);
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cairo_stroke(C);
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}
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// level 2: drawVector, drawCovector, drawSegment
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static point_t vectorToPoint(DrawingContext *ctx, vector_t in)
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{
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double x[3];
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point_t out;
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LOOP(i) x[i] = 0.0;
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LOOP(i) LOOP(j) x[i] += gsl_matrix_get(ctx->cob, i, j) * in.x[j];
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out.x = x[0] / x[2];
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out.y = x[1] / x[2];
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return out;
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}
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void drawVector(DrawingContext *ctx, vector_t v)
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{
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drawPoint(ctx, vectorToPoint(ctx, v));
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}
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static void drawImplicitLine(DrawingContext *ctx, double a, double b, double c)
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{
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double norm, lambda;
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point_t m, s, xminus, xplus;
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m.x = ctx->dim->center_x;
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m.y = ctx->dim->center_y;
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lambda = (a*m.x + b*m.y + c)/(a*a + b*b);
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s.x = m.x - lambda*a;
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s.y = m.y - lambda*b;
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norm = sqrt(a*a + b*b);
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xminus.x = s.x - ctx->dim->radius * b / norm;
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xminus.y = s.y + ctx->dim->radius * a / norm;
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xplus.x = s.x + ctx->dim->radius * b / norm;
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xplus.y = s.y - ctx->dim->radius * a / norm;
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drawSegment2d(ctx, xminus, xplus);
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}
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void drawCovector(DrawingContext *ctx, vector_t v)
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{
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double x[3];
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double cofactor;
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LOOP(i) x[i] = 0.0;
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LOOP(i) LOOP(j) {
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cofactor = gsl_matrix_get(ctx->cob, (i+1)%3, (j+1)%3) * gsl_matrix_get(ctx->cob, (i+2)%3, (j+2)%3)
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- gsl_matrix_get(ctx->cob, (i+1)%3, (j+2)%3) * gsl_matrix_get(ctx->cob, (i+2)%3, (j+1)%3);
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x[i] += cofactor * v.x[j];
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}
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drawImplicitLine(ctx, x[0], x[1], x[2]);
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}
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void drawSegment(DrawingContext *ctx, vector_t a, vector_t b)
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{
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drawSegment2d(ctx, vectorToPoint(ctx, a), vectorToPoint(ctx, b));
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}
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// level 3: boxes and polygons
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void drawPolygon(DrawingContext *ctx, int segments, int sides, ...)
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{
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va_list args;
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vector_t first, prev, current;
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va_start(args, sides);
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first = va_arg(args, vector_t);
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current = first;
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for(int i = 0; i < sides-1; i++) {
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prev = current;
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current = va_arg(args, vector_t);
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if(segments)
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drawSegment(ctx, prev, current);
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else
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drawCovector(ctx, cross(prev, current));
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}
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if(segments)
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drawSegment(ctx, current, first);
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else
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drawCovector(ctx, cross(current, first));
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va_end(args);
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}
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void drawTriangle(DrawingContext *ctx, const char *word)
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{
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vector_t p[3];
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fixedPoints(ctx, word, p);
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drawPolygon(ctx, 1, 3, p[0], p[1], p[2]);
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}
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void drawBox(DrawingContext *ctx, const char *word1, const char *word2)
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{
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vector_t p[2][3],i[2];
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fixedPoints(ctx, word1, p[0]);
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fixedPoints(ctx, word2, p[1]);
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// intersect attracting line with neutral line of the other element
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for(int j = 0; j < 2; j++)
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i[j] = cross(cross(p[j%2][0],p[j%2][1]),cross(p[(j+1)%2][0],p[(j+1)%2][2]));
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drawPolygon(ctx, 1, 4, p[0][0], i[0], p[1][0], i[1]);
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}
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void drawBoxLines(DrawingContext *ctx, const char *word1, const char *word2)
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{
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vector_t p[2][3],i[2];
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fixedPoints(ctx, word1, p[0]);
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fixedPoints(ctx, word2, p[1]);
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// intersect attracting line with neutral line of the other element
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for(int j = 0; j < 2; j++)
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i[j] = cross(cross(p[j%2][0],p[j%2][1]),cross(p[(j+1)%2][0],p[(j+1)%2][2]));
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drawPolygon(ctx, 0, 4, p[0][0], i[0], p[1][0], i[1]);
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}
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void drawBoxStd(DrawingContext *ctx, const char *word, char base)
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{
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char word1[100];
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char word2[100];
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int len = strlen(word);
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if(len*2 + 4 > 100)
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return;
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for(int i = 0; i < len; i++) {
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word1[i] = word1[2*len+2-i] = word[i];
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word2[i] = word2[2*len+2-i] = word[i];
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}
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word1[2*len+3] = 0;
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word2[2*len+3] = 0;
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LOOP(i) word1[len+i] = (base-'A'+6+i+1)%3+'a';
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LOOP(i) word2[len+i] = (base-'A'+6-i-1)%3+'a';
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// printf("Words: %s %s\n", word1, word2);
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drawBox(ctx, word1, word2);
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}
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void drawRotationOrbit(DrawingContext *ctx, const char *word, vector_t start)
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{
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vector_t v[3], w;
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point_t p;
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double parameter, startangle;
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int iterations = 200;
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gsl_matrix *frame = getTempMatrix(ctx->ws);
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gsl_matrix *inverse = getTempMatrix(ctx->ws);
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gsl_vector *start_v = getTempVector(ctx->ws);
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gsl_vector *start_in_frame = getTempVector(ctx->ws);
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cairo_t *C = ctx->cairo;
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computeRotationMatrix(ctx, frame, word);
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LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);
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LOOP(i) gsl_vector_set(start_v, i, start.x[i]);
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solve(frame, start_v, start_in_frame, ctx->ws);
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parameter = gsl_vector_get(start_in_frame, 2);
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parameter /= sqrt(gsl_vector_get(start_in_frame, 0)*gsl_vector_get(start_in_frame, 0) +
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gsl_vector_get(start_in_frame, 1)*gsl_vector_get(start_in_frame, 1));
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startangle = atan2(gsl_vector_get(start_in_frame, 1), gsl_vector_get(start_in_frame, 0));
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int previous_inside = 0;
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for(int k = 0; k <= iterations; k++) {
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LOOP(i) w.x[i] = parameter * v[2].x[i] + cos(2*k*M_PI/iterations) * v[0].x[i] + sin(2*k*M_PI/iterations) * v[1].x[i];
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p = vectorToPoint(ctx, w);
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if(isInsideBB(ctx, p)) {
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if(!previous_inside)
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cairo_move_to(C, p.x, p.y);
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else
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cairo_line_to(C, p.x, p.y);
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previous_inside = 1;
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} else {
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previous_inside = 0;
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}
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}
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cairo_stroke(C);
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releaseTempMatrices(ctx->ws, 2);
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releaseTempVectors(ctx->ws, 2);
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}
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void drawDualRotationOrbit(DrawingContext *ctx, const char *word, vector_t start)
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{
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vector_t v[3], w;
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point_t p;
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double parameter, startangle;
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int iterations = 200;
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gsl_matrix *frame = getTempMatrix(ctx->ws);
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gsl_matrix *inverse = getTempMatrix(ctx->ws);
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gsl_vector *start_v = getTempVector(ctx->ws);
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gsl_vector *start_in_frame = getTempVector(ctx->ws);
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cairo_t *C = ctx->cairo;
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computeRotationMatrix(ctx, frame, word);
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LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);
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LOOP(i) gsl_vector_set(start_v, i, start.x[i]);
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// solve(frame, start_v, start_in_frame, ctx->ws);
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gsl_blas_dgemv(CblasTrans, 1.0, frame, start_v, 0.0, start_in_frame);
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parameter = sqrt(gsl_vector_get(start_in_frame, 0)*gsl_vector_get(start_in_frame, 0) +
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gsl_vector_get(start_in_frame, 1)*gsl_vector_get(start_in_frame, 1));
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parameter /= gsl_vector_get(start_in_frame, 2);
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startangle = atan2(gsl_vector_get(start_in_frame, 1), gsl_vector_get(start_in_frame, 0));
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int previous_inside = 0;
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for(int k = 0; k <= iterations; k++) {
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LOOP(i) w.x[i] = parameter * v[2].x[i] + cos(2*k*M_PI/iterations) * v[0].x[i] + sin(2*k*M_PI/iterations) * v[1].x[i];
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p = vectorToPoint(ctx, w);
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if(isInsideBB(ctx, p)) {
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if(!previous_inside)
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cairo_move_to(C, p.x, p.y);
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else
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cairo_line_to(C, p.x, p.y);
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previous_inside = 1;
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} else {
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previous_inside = 0;
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}
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}
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cairo_stroke(C);
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releaseTempMatrices(ctx->ws, 2);
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releaseTempVectors(ctx->ws, 2);
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}
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void drawArc(DrawingContext *ctx, const char *word, vector_t start, vector_type_t starttype, vector_t end, vector_type_t endtype, vector_t third, int contain)
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{
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vector_t v[3], w;
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point_t p;
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double radius, angle_start, angle_end, angle_third, angle, angle_end_delta, sign, angle_start_final, angle_end_final, angle_end_other;
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int iterations = 200;
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gsl_matrix *frame = getTempMatrix(ctx->ws);
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gsl_matrix *inverse = getTempMatrix(ctx->ws);
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gsl_vector *vector = getTempVector(ctx->ws);
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gsl_vector *vector_in_frame = getTempVector(ctx->ws);
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cairo_t *C = ctx->cairo;
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computeRotationMatrix(ctx, frame, word);
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LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);
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LOOP(i) gsl_vector_set(vector, i, start.x[i]);
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if(starttype == VT_POINT) {
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solve(frame, vector, vector_in_frame, ctx->ws);
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radius = sqrt(gsl_vector_get(vector_in_frame, 0)*gsl_vector_get(vector_in_frame, 0) +
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gsl_vector_get(vector_in_frame, 1)*gsl_vector_get(vector_in_frame, 1));
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radius /= fabs(gsl_vector_get(vector_in_frame, 2));
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angle_start = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
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gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
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} else {
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gsl_blas_dgemv(CblasTrans, 1.0, frame, vector, 0.0, vector_in_frame);
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radius = fabs(gsl_vector_get(vector_in_frame, 2));
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radius /= sqrt(gsl_vector_get(vector_in_frame, 0)*gsl_vector_get(vector_in_frame, 0) +
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gsl_vector_get(vector_in_frame, 1)*gsl_vector_get(vector_in_frame, 1));
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angle_start = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
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gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
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}
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LOOP(i) gsl_vector_set(vector, i, third.x[i]);
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solve(frame, vector, vector_in_frame, ctx->ws);
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angle_third = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
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gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
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LOOP(i) gsl_vector_set(vector, i, end.x[i]);
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if(endtype == VT_POINT) {
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solve(frame, vector, vector_in_frame, ctx->ws);
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angle_end = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
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gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
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} else {
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gsl_blas_dgemv(CblasTrans, 1.0, frame, vector, 0.0, vector_in_frame);
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// this is only the average angle
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angle_end = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
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gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
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angle_end_delta = acos(-fabs(gsl_vector_get(vector_in_frame, 2))/radius/
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sqrt(gsl_vector_get(vector_in_frame, 0)*gsl_vector_get(vector_in_frame, 0) +
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gsl_vector_get(vector_in_frame, 1)*gsl_vector_get(vector_in_frame, 1)));
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printf("angle_end_delta: %f\n", angle_end_delta);
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}
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int previous_inside = 0;
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for(int i = 0; i < 4; i++) {
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angle_start_final = angle_start;
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if(endtype == VT_POINT) {
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angle_end_final = angle_end;
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} else {
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if(i >= 2) {
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angle_end_final = angle_end - angle_end_delta;
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angle_end_other = angle_end + angle_end_delta;
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} else {
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angle_end_final = angle_end + angle_end_delta;
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angle_end_other = angle_end - angle_end_delta;
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}
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}
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if(i%2)
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FLIP(angle_start_final, angle_end_final);
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printf("start: %f, end: %f, other: %f, third: %f\n", angle_start_final, angle_end_final, angle_end_other, angle_third);
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printf("interval1: %d, interval2: %d, diff: %f %f %f\n", ANGLE_IN_INTERVAL(angle_start, angle_end_final, angle_end_other), ANGLE_IN_INTERVAL(angle_start_final, angle_end_final, angle_third), ANGLE_DIFF(angle_end_final, angle_start_final), ANGLE_DIFF(angle_end_other, angle_start_final), ANGLE_DIFF(angle_third, angle_start_final));
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if(endtype == VT_LINE && ANGLE_IN_INTERVAL(angle_start_final, angle_end_final, angle_end_other))
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continue;
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if(contain && !ANGLE_IN_INTERVAL(angle_start_final, angle_end_final, angle_third))
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continue;
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if(!contain && ANGLE_IN_INTERVAL(angle_start_final, angle_end_final, angle_third))
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continue;
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break;
|
|
}
|
|
|
|
|
|
// printf("angle_start: %f, angle_end: %f, angle_third: %f\n", angle_start, angle_end, angle_third);
|
|
|
|
for(int k = 0; k <= iterations; k++) {
|
|
angle = angle_start_final + (double)k/(double)iterations * ANGLE_DIFF(angle_end_final, angle_start_final);
|
|
|
|
LOOP(i) w.x[i] = v[2].x[i] / radius + cos(angle) * v[0].x[i] + sin(angle) * v[1].x[i];
|
|
p = vectorToPoint(ctx, w);
|
|
|
|
if(isInsideBB(ctx, p)) {
|
|
if(!previous_inside)
|
|
cairo_move_to(C, p.x, p.y);
|
|
else
|
|
cairo_line_to(C, p.x, p.y);
|
|
previous_inside = 1;
|
|
} else {
|
|
previous_inside = 0;
|
|
}
|
|
}
|
|
|
|
cairo_stroke(C);
|
|
|
|
releaseTempMatrices(ctx->ws, 2);
|
|
releaseTempVectors(ctx->ws, 2);
|
|
}
|
|
|
|
// 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)
|
|
{
|
|
int n = 3;
|
|
vector_t p[6][3];
|
|
vector_t l[6][3];
|
|
|
|
fixedPoints(ctx, "abc", p[0]);
|
|
fixedPoints(ctx, "bca", p[1]);
|
|
fixedPoints(ctx, "cab", p[2]);
|
|
fixedPoints(ctx, "a cab a", p[3]);
|
|
fixedPoints(ctx, "b abc b", p[4]);
|
|
fixedPoints(ctx, "c bca c", p[5]);
|
|
|
|
double color[6][3] = {{1,0,0},{0,0.7,0},{0,0,1},{0,1,1},{0,1,1},{0,1,1}};
|
|
|
|
for(int i = 0; i < n; i++) LOOP(j) l[i][j] = cross(p[i][(3-j)%3], p[i][(4-j)%3]);
|
|
|
|
for(int i = 0; i < n; i++) LOOP(j) {
|
|
cairo_set_source_rgb(ctx->cairo, color[i][0], color[i][1], color[i][2]);
|
|
drawVector(ctx, p[i][j]);
|
|
}
|
|
|
|
for(int i = 0; i < n; i++) LOOP(j) {
|
|
cairo_set_source_rgb(ctx->cairo, color[i][0], color[i][1], color[i][2]);
|
|
drawCovector(ctx, l[i][j]);
|
|
}
|
|
}
|
|
|
|
void drawCurvedBox(DrawingContext *ctx)
|
|
{
|
|
vector_t p[6][3];
|
|
vector_t l[2][3];
|
|
|
|
fixedPoints(ctx, "abc", p[0]);
|
|
fixedPoints(ctx, "bca", p[1]);
|
|
fixedPoints(ctx, "babcb", p[2]);
|
|
fixedPoints(ctx, "ababcba", p[3]);
|
|
fixedPoints(ctx, "bacac abc cacab", p[4]);
|
|
fixedPoints(ctx, "abacac abc cacaba", p[5]);
|
|
|
|
LOOP(j) l[0][j] = cross(p[0][(3-j)%3], p[0][(4-j)%3]);
|
|
LOOP(j) l[1][j] = cross(p[1][(3-j)%3], p[1][(4-j)%3]);
|
|
|
|
drawArc(ctx, "ab", p[0][0], VT_POINT, p[2][0], VT_POINT, p[1][0], 0);
|
|
drawArc(ctx, "bcab", p[2][0], VT_POINT, l[1][0], VT_LINE, p[4][0], 1);
|
|
drawArc(ctx, "ab", p[1][0], VT_POINT, p[3][0], VT_POINT, p[0][0], 0);
|
|
drawArc(ctx, "abcaba", p[3][0], VT_POINT, l[0][0], VT_LINE, p[5][0], 1);
|
|
|
|
drawCovector(ctx, l[0][0]);
|
|
drawCovector(ctx, l[1][0]);
|
|
}
|
|
|
|
|
|
void drawBoxes(DrawingContext *ctx)
|
|
{
|
|
gsl_matrix *rot = getTempMatrix(ctx->ws);
|
|
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
|
|
cairo_t *C = ctx->cairo;
|
|
|
|
vector_t p[6][3];
|
|
vector_t l[6][3];
|
|
vector_t alpha[6];
|
|
|
|
fixedPoints(ctx, "abc", p[0]);
|
|
fixedPoints(ctx, "bca", p[1]);
|
|
fixedPoints(ctx, "cab", p[2]);
|
|
|
|
initializeTriangleGenerators(gen, ctx->cartan);
|
|
|
|
for(int i = 0; i < 6; i++) LOOP(j) l[i][j] = cross(p[i][(3-j)%3], p[i][(4-j)%3]);
|
|
LOOP(i) LOOP(j) alpha[i].x[j] = gsl_matrix_get(ctx->cartan, i, j);
|
|
|
|
cairo_set_source_rgb(C, 0.5, 0.5, 0.5);
|
|
|
|
drawCurvedBox(ctx);
|
|
|
|
/*
|
|
drawRotationOrbit(ctx, "ca", p[0][0]);
|
|
drawRotationOrbit(ctx, "ab", p[1][0]);
|
|
drawRotationOrbit(ctx, "bc", p[2][0]);
|
|
drawRotationOrbit(ctx, "cbac", p[4][0]);
|
|
drawRotationOrbit(ctx, "abca", p[5][0]);
|
|
*/
|
|
|
|
/*
|
|
cairo_set_source_rgb(C, 0.0, 0.0, 1.0);
|
|
drawDualRotationOrbit(ctx, "ca", l[0][2]);
|
|
drawDualRotationOrbit(ctx, "ab", l[1][2]);
|
|
drawDualRotationOrbit(ctx, "bc", l[2][2]);
|
|
drawDualRotationOrbit(ctx, "bacb", l[3][2]);
|
|
drawDualRotationOrbit(ctx, "cbac", l[4][2]);
|
|
drawDualRotationOrbit(ctx, "abca", l[5][2]);
|
|
*/
|
|
|
|
/*
|
|
cairo_set_source_rgb(C, 0, 0, 1);
|
|
fixedPoints(ctx, "abc", p[0]); //
|
|
fixedPoints(ctx, "ababcba", p[1]);
|
|
drawRotationOrbit(ctx, "abcaba", p[0][0]); // abcaba a rar- r-ar a rar- a
|
|
drawRotationOrbit(ctx, "ab", p[0][0]); // ab a rar- a rar- rar- a
|
|
drawRotationOrbit(ctx, "abcabcba", p[0][0]); // abc abc ba
|
|
drawCovector(ctx, cross(p[0][0],p[0][1]));
|
|
drawCovector(ctx, cross(p[1][0],p[1][1]));
|
|
|
|
cairo_set_source_rgb(C, 0, 0.7, 0);
|
|
fixedPoints(ctx, "ab abc ba", p[0]); //
|
|
fixedPoints(ctx, "ab ababcba ba", p[1]);
|
|
drawRotationOrbit(ctx, "ababcababa", p[0][0]); // abcaba a rar- r-ar a rar- a
|
|
drawRotationOrbit(ctx, "ab", p[0][0]); // ab a rar- a rar- rar- a
|
|
drawRotationOrbit(ctx, "ababcabcbaba", p[0][0]); // abc abc ba
|
|
drawCovector(ctx, cross(p[0][0],p[0][1]));
|
|
drawCovector(ctx, cross(p[1][0],p[1][1]));
|
|
*/
|
|
|
|
cairo_set_source_rgb(C, 0, 0, 1.0);
|
|
// drawRotationOrbit(ctx, "bcab", p[3][0]);
|
|
// drawRotationOrbit(ctx, "abca", p[5][0]);
|
|
// drawRotationOrbit(ctx, "bacb", p[3][0]);
|
|
|
|
// LOOP(i) drawVector(ctx, p[i+3][0]);
|
|
|
|
cairo_set_source_rgb(C, 0.5, 0.5, 0.5);
|
|
// drawCovector(ctx, alpha[1]);
|
|
// drawCovector(ctx, alpha[2]);
|
|
/*
|
|
alpha[3] = apply_transpose(gen[1], alpha[0]);
|
|
drawCovector(ctx, alpha[3]);
|
|
*/
|
|
releaseTempMatrices(ctx->ws, 4);
|
|
}
|
|
|
|
void drawBoxes2(DrawingContext *ctx)
|
|
{
|
|
gsl_matrix *tmp = getTempMatrix(ctx->ws);
|
|
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
|
|
cairo_t *C = ctx->cairo;
|
|
initializeTriangleGenerators(gen, ctx->cartan);
|
|
|
|
// abc, ababcba, abababcbaba, ..., cab
|
|
// bca, acaba, abacababa, ..., babcb
|
|
|
|
vector_t v[4][3];
|
|
vector_t i[4];
|
|
|
|
fixedPoints(ctx, "abc", v[0]);
|
|
fixedPoints(ctx, "bca", v[1]);
|
|
fixedPoints(ctx, "cab", v[2]);
|
|
fixedPoints(ctx, "acaba", v[3]);
|
|
i[0] = cross(cross(v[0][1],v[0][2]),cross(v[2][0],v[2][2]));
|
|
i[1] = cross(cross(v[1][1],v[1][2]),cross(v[3][0],v[3][2]));
|
|
i[2] = cross(cross(v[2][0],v[2][2]),cross(v[3][0],v[3][2]));
|
|
i[3] = cross(cross(v[0][0],v[0][2]),cross(v[1][0],v[1][2]));
|
|
|
|
cairo_set_source_rgb(C, 0, 0, 1);
|
|
// drawPolygon(ctx, 1, 6, v[2][2], v[1][1], v[0][1], v[3][2], v[3][1], v[2][1]);
|
|
// drawPolygon(ctx, 1, 6, v[1][2], i[1], i[2], i[0], v[0][2], i[3]);
|
|
|
|
/*
|
|
cairo_set_source_rgb(C, 1, 0, 0);
|
|
drawBox(ctx, "cab", "bca");
|
|
cairo_set_source_rgb(C, 1, 0.5, 0);
|
|
drawBox(ctx, "bc bca cb", "bc abc cb");
|
|
drawBox(ctx, "bcbc bca cbcb", "bcbc abc cbcb");
|
|
drawBox(ctx, "bcbcbc bca cbcbcb", "bcbcbc abc cbcbcb");
|
|
drawBox(ctx, "bcbcbcbc bca cbcbcbcb", "bcbcbcbc abc cbcbcbcb");
|
|
drawBox(ctx, "bcbcbcbcbc bca cbcbcbcbcb", "bcbcbcbcbc abc cbcbcbcbcb");
|
|
*/
|
|
|
|
cairo_set_source_rgb(C, 1, 0, 0);
|
|
drawBox(ctx, "bca", "abc");
|
|
cairo_set_source_rgb(C, 1, 0.5, 0);
|
|
drawBox(ctx, "ab abc ba", "ab cab ba");
|
|
drawBox(ctx, "abab abc baba", "abab cab baba");
|
|
drawBox(ctx, "ababab abc bababa", "ababab cab bababa");
|
|
drawBox(ctx, "abababab abc babababa", "abababab cab babababa");
|
|
drawBox(ctx, "ababababab abc bababababa", "ababababab cab bababababa");
|
|
|
|
cairo_set_source_rgb(C, 1, 0, 0);
|
|
drawBox(ctx, "ab ca cab ac ba", "ab ca bca ac ba");
|
|
drawBox(ctx, "ab caca cab acac ba", "ab caca bca acac ba");
|
|
drawBox(ctx, "ab cacaca cab acacac ba", "ab cacaca bca acacac ba");
|
|
drawBox(ctx, "ab cacacaca cab acacacac ba", "ab cacacaca bca acacacac ba");
|
|
drawBox(ctx, "ab cacacacaca cab acacacacac ba", "ab cacacacaca bca acacacacac ba");
|
|
/*
|
|
drawBox(ctx, "ab abc ba", "ab cab ba");
|
|
drawBox(ctx, "abab abc baba", "abab cab baba");
|
|
drawBox(ctx, "ababab abc bababa", "ababab cab bababa");
|
|
drawBox(ctx, "abababab abc babababa", "abababab cab babababa");
|
|
drawBox(ctx, "ababababab abc bababababa", "ababababab cab bababababa");
|
|
*/
|
|
|
|
// abc -> arar abc r-ar-a = (ar)³
|
|
// bca -> (ar)² (ra)³ (ar)-² -> a rarr a rar- r-ar rar- a = ababcba
|
|
// a rar- r-ar a r-ar a rar- a r-ar ra-r a = abcacabacba
|
|
|
|
// drawBox(ctx, "ab ca cab ac ba", "ab ca bca ac ba");
|
|
// drawBox(ctx, "ab ca bc bca cb ac ba", "ab ca bc abc cb ac ba");
|
|
// drawBox(ctx, "ab ca bc ab abc ba cb ac ba", "ab ca bc ab cab ba cb ac ba");
|
|
|
|
// these are the right boxes
|
|
/*
|
|
cairo_set_source_rgb(C, 1, 0.5, 0);
|
|
drawBox(ctx, "abababab abc babababa", "abababab cab babababa");
|
|
drawBox(ctx, "ababab abc bababa", "ababab cab bababa");
|
|
drawBox(ctx, "abab abc baba", "abab cab baba");
|
|
drawBox(ctx, "ab abc ba", "ab cab ba");
|
|
drawBox(ctx, "b abc b", "b cab b");
|
|
drawBox(ctx, "bab abc bab", "bab cab bab");
|
|
drawBox(ctx, "babab abc babab", "babab cab babab");
|
|
drawBox(ctx, "bababab abc bababab", "bababab cab bababab");
|
|
*/
|
|
|
|
|
|
// drawBox(ctx, "ab a cab a ba", "ab a bca a ba");
|
|
// drawBox(ctx, "ab ca cab ac ba", "ab ca bca ac ba");
|
|
|
|
// drawBox(ctx, "cab", "bca");
|
|
// drawBox(ctx, "ca cab ac", "ca bca ac");
|
|
|
|
releaseTempMatrices(ctx->ws, 4);
|
|
}
|
|
|
|
void drawRotatedReflectors(DrawingContext *ctx)
|
|
{
|
|
gsl_matrix *rot = getTempMatrix(ctx->ws);
|
|
gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
|
|
cairo_t *C = ctx->cairo;
|
|
vector_t fp[3], fp2[3];
|
|
vector_t w;
|
|
vector_t v[3];
|
|
|
|
cairo_set_source_rgb(C, 0.7, 0.7, 0.7);
|
|
|
|
initializeTriangleGenerators(gen, ctx->cartan);
|
|
|
|
LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(ctx->cartan, i, j);
|
|
multiply(gen[0], gen[1], rot);
|
|
|
|
for(int j = 0; j < ctx->p[2]; j++) {
|
|
drawCovector(ctx, v[0]);
|
|
v[0] = apply_transpose(rot, v[0]);
|
|
}
|
|
|
|
LOOP(i) LOOP(j) { v[i].x[j] = (i==j) ? 1.0 : 0.0; }
|
|
|
|
for(int j = 0; j < ctx->p[2]; j++) {
|
|
drawVector(ctx, v[0]);
|
|
v[0] = apply(rot, v[0]);
|
|
}
|
|
|
|
fixedPoints(ctx, "cab", fp);
|
|
fixedPoints(ctx, "cacabac", fp2);
|
|
drawRotationOrbit(ctx, "ac", fp[0]);
|
|
|
|
releaseTempMatrices(ctx->ws, 4);
|
|
}
|
|
|
|
void drawDualLimitCurve(DrawingContext *ctx)
|
|
{
|
|
cairo_t *C = ctx->cairo;
|
|
|
|
cairo_save(C);
|
|
cairo_set_source_rgb(C, 0, 0, 0);
|
|
|
|
int n = 18;
|
|
vector_t p[18][3];
|
|
vector_t l[n][3];
|
|
|
|
/*
|
|
fixedPoints(ctx, "abc", p[0]);
|
|
fixedPoints(ctx, "ab abc ba", p[1]);
|
|
fixedPoints(ctx, "abab abc baba", p[2]);
|
|
fixedPoints(ctx, "ababab abc bababa", p[3]);
|
|
fixedPoints(ctx, "abababab abc babababa", p[4]);
|
|
fixedPoints(ctx, "babababa abc abababab", p[5]);
|
|
fixedPoints(ctx, "bababa abc ababab", p[6]);
|
|
fixedPoints(ctx, "baba abc abab", p[7]);
|
|
fixedPoints(ctx, "ba abc ab", p[8]);
|
|
|
|
fixedPoints(ctx, "bca", p[9]);
|
|
fixedPoints(ctx, "ab bca ba", p[10]);
|
|
fixedPoints(ctx, "abab bca baba", p[11]);
|
|
fixedPoints(ctx, "ababab bca bababa", p[12]);
|
|
fixedPoints(ctx, "abababab bca babababa", p[13]);
|
|
fixedPoints(ctx, "babababa bca abababab", p[14]);
|
|
fixedPoints(ctx, "bababa bca ababab", p[15]);
|
|
fixedPoints(ctx, "baba bca abab", p[16]);
|
|
fixedPoints(ctx, "ba bca ab", p[17]);
|
|
*/
|
|
|
|
fixedPoints(ctx, "abc", p[0]);
|
|
fixedPoints(ctx, "ac abc ca", p[1]);
|
|
fixedPoints(ctx, "acac abc caca", p[2]);
|
|
fixedPoints(ctx, "acacac abc cacaca", p[3]);
|
|
fixedPoints(ctx, "acacacac abc cacacaca", p[4]);
|
|
fixedPoints(ctx, "cacacaca abc acacacac", p[5]);
|
|
fixedPoints(ctx, "cacaca abc acacac", p[6]);
|
|
fixedPoints(ctx, "caca abc acac", p[7]);
|
|
fixedPoints(ctx, "ca abc ac", p[8]);
|
|
|
|
fixedPoints(ctx, "bca", p[9]);
|
|
fixedPoints(ctx, "ac bca ca", p[10]);
|
|
fixedPoints(ctx, "acac bca caca", p[11]);
|
|
fixedPoints(ctx, "acacac bca cacaca", p[12]);
|
|
fixedPoints(ctx, "acacacac bca cacacaca", p[13]);
|
|
fixedPoints(ctx, "cacacaca bca acacacac", p[14]);
|
|
fixedPoints(ctx, "cacaca bca acacac", p[15]);
|
|
fixedPoints(ctx, "caca bca acac", p[16]);
|
|
fixedPoints(ctx, "ca bca ac", p[17]);
|
|
|
|
|
|
/*
|
|
fixedPoints(ctx, "cab", p[2]);
|
|
fixedPoints(ctx, "b abc b", p[3]);
|
|
fixedPoints(ctx, "c bca c", p[4]);
|
|
fixedPoints(ctx, "a cab a", p[5]);
|
|
*/
|
|
|
|
for(int i = 0; i < n; i++) {
|
|
LOOP(j) l[i][j] = cross(p[i][(3-j)%3], p[i][(4-j)%3]);
|
|
// drawCovector(ctx, l[i][0]);
|
|
drawCovector(ctx, l[i][2]);
|
|
}
|
|
|
|
cairo_restore(C);
|
|
}
|
|
|
|
void drawLimitCurve(DrawingContext *ctx)
|
|
{
|
|
cairo_t *C = ctx->cairo;
|
|
|
|
cairo_save(C);
|
|
|
|
cairo_set_source_rgb(C, 0, 0, 0);
|
|
|
|
if(ctx->limit_with_lines) {
|
|
int previous_inside = 0;
|
|
for(int i = 0; i < ctx->limit_curve_count; i++) {
|
|
point_t p;
|
|
p.x = ctx->limit_curve[3*i];
|
|
p.y = ctx->limit_curve[3*i+1];
|
|
|
|
if(isInsideBB(ctx, p)) {
|
|
if(!previous_inside)
|
|
cairo_move_to(C, p.x, p.y);
|
|
else
|
|
cairo_line_to(C, p.x, p.y);
|
|
previous_inside = 1;
|
|
} else {
|
|
previous_inside = 0;
|
|
}
|
|
}
|
|
|
|
cairo_stroke(C);
|
|
} else {
|
|
for(int i = 0; i < ctx->limit_curve_count; i++) {
|
|
point_t p;
|
|
p.x = ctx->limit_curve[3*i];
|
|
p.y = ctx->limit_curve[3*i+1];
|
|
|
|
if(isInsideBB(ctx, p)) {
|
|
cairo_arc(C, p.x, p.y, 2.0/ctx->dim->scalefactor, 0, 2*M_PI);
|
|
cairo_close_path(C);
|
|
cairo_fill(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_count >= 0) {
|
|
if(ctx->show_limit)
|
|
drawLimitCurve(ctx);
|
|
|
|
if(ctx->show_dual_limit)
|
|
drawDualLimitCurve(ctx);
|
|
|
|
if(ctx->show_attractors)
|
|
drawAttractors(ctx);
|
|
|
|
if(ctx->show_rotated_reflectors)
|
|
drawRotatedReflectors(ctx);
|
|
|
|
if(ctx->show_reflectors)
|
|
drawReflectors(ctx);
|
|
|
|
if(ctx->show_boxes)
|
|
drawBoxes(ctx);
|
|
|
|
if(ctx->show_boxes2)
|
|
drawBoxes2(ctx);
|
|
|
|
}
|
|
|
|
cairo_identity_matrix(C); // text is in screen coordinates
|
|
|
|
if(ctx->show_text)
|
|
drawText(ctx);
|
|
|
|
cairo_surface_flush(cairo_get_target(C));
|
|
}
|