triangle_group_limit_set/draw.c

#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->ws);
	gsl_vector *tmp2 = getTempVector(ctx->ws);
	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->ws, 2);
}

int fixedPoints(DrawingContext *ctx, const char *word, vector_t *out)
{
	gsl_matrix *tmp = getTempMatrix(ctx->ws);
	gsl_matrix *ev = getTempMatrix(ctx->ws);
	gsl_matrix **gen = getTempMatrices(ctx->ws, 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->ws, 5);

	return count;
}

void transformFrameStd(DrawingContext *ctx, vector_t *x, gsl_matrix *out)
{
	gsl_matrix *tmp = getTempMatrix(ctx->ws);
	gsl_vector *fourth = getTempVector(ctx->ws);
	gsl_vector *lambda = getTempVector(ctx->ws);
	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->ws, 1);
	releaseTempVectors(ctx->ws, 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 drawBoxes2(DrawingContext *ctx)
{
	/*
	cairo_set_source_rgb(ctx->cairo, 1, 0.5, 0);
	drawBoxStd(ctx, "a", 'A');
	drawBoxStd(ctx, "ca", 'A');
	drawBoxStd(ctx, "aca", 'A');
	drawBoxStd(ctx, "caca", 'A');
	drawBoxStd(ctx, "acaca", 'A');
	cairo_set_source_rgb(ctx->cairo, 0, 0.5, 1);
	drawBoxStd(ctx, "acac", 'A');
	drawBoxStd(ctx, "cac", 'A');
	drawBoxStd(ctx, "ac", 'A');
	drawBoxStd(ctx, "c", 'A');
	drawBoxStd(ctx, "", 'A');
	*/

	/*
	cairo_set_source_rgb(ctx->cairo, 0, 0.5, 1);
	drawBox(ctx, "abc", "cab");
//	drawBox(ctx, "ba abc ab", "ba cab ab");
	drawBox(ctx, "baba abc abab", "baba cab abab");
	drawBox(ctx, "abab abc baba", "abab cab baba");
	drawBox(ctx, "ab abc ba", "ab cab ba");

	cairo_set_source_rgb(ctx->cairo, 1, 0.5, 0);
	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, "aba abc aba", "aba cab aba");
//	drawBox(ctx, "a abc a", "a cab a");

	cairo_set_source_rgb(ctx->cairo, 0, 0.5, 1);
	drawBox(ctx, "bca", "abc");
//	drawBox(ctx, "cb bca bc", "cb abc bc");
	drawBox(ctx, "cbcb bca bcbc", "cbcb abc bcbc");
	drawBox(ctx, "bcbc bca cbcb", "bcbc abc cbcb");
	drawBox(ctx, "bc bca cb", "bc abc cb");

	cairo_set_source_rgb(ctx->cairo, 1, 0.5, 0);
	drawBox(ctx, "c bca c", "c abc c");
	drawBox(ctx, "cbc bca cbc", "cbc abc cbc");
	drawBox(ctx, "cbcbc bca cbcbc", "cbcbc abc cbcbc");
	drawBox(ctx, "bcb bca bcb", "bcb abc bcb");
//	drawBox(ctx, "b bca b", "b abc b");
*/

	cairo_set_source_rgb(ctx->cairo, 0, 0, 0);
	drawBox(ctx, "abc", "cab");

	cairo_set_source_rgb(ctx->cairo, 0, 0.5, 1);
//	drawBox(ctx, "cab", "bca");
//	drawBox(ctx, "ac cab ca", "ac bca ca");
//	drawBox(ctx, "acac cab caca", "acac bca caca");
	drawBox(ctx, "caca cab acac", "caca bca acac");
	drawBox(ctx, "ca cab ac", "ca bca ac");

	cairo_set_source_rgb(ctx->cairo, 1, 0.5, 0);
	drawBox(ctx, "a cab a", "a bca a");
	drawBox(ctx, "aca cab aca", "aca bca aca");
//	drawBox(ctx, "acaca cab acaca", "acaca bca acaca");
//	drawBox(ctx, "cac cab cac", "cac bca cac");
//	drawBox(ctx, "c cab c", "c bca c");

}

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_boxes2)
			drawBoxes2(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));
}