#include "main.h"

#define FMOD(x,y) (fmod(x,y) < 0 ? fmod(x,y) + y : fmod(x,y))
#define ANGLE_DIFF(x,y) (FMOD((x)-(y), 2*M_PI))
#define ANGLE_IN_INTERVAL(a,b,x) (ANGLE_DIFF(x,a) < ANGLE_DIFF(b,a))
#define FLIP(x,y) do {double tmp = x; x = y; y = tmp;} while(0)

// level 0: helper functions

int isInsideBB(DrawingContext *ctx, point_t p)
{
	cairo_user_to_device(ctx->cairo, &p.x, &p.y);
	return -p.x < ctx->dim->width && p.x < 3*ctx->dim->width && -p.y < ctx->dim->height && p.y < 3*ctx->dim->height;
}

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(gsl_matrix *m, vector_t x)
{
	vector_t out;

	LOOP(i) out.x[i] = 0.0;
	LOOP(i) LOOP(j) out.x[i] += gsl_matrix_get(m, i, j) * x.x[j];

	return out;
}

vector_t apply_transpose(gsl_matrix *m, vector_t x)
{
	vector_t out;

	LOOP(i) out.x[i] = 0.0;
	LOOP(i) LOOP(j) out.x[i] += gsl_matrix_get(m, j, i) * x.x[j];

	return out;
}

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, 6);

	initializeTriangleGeneratorsCurrent(gen, ctx);

	gsl_matrix_set_identity(tmp);
	for(int i = 0; i < strlen(word); i++) {
		if(word[i] >= 'a' && word[i] <= 'c')
			multiply_right(tmp, gen[word[i]-'a'], ctx->ws);
		else if(word[i] >= 'A' && word[i] <= 'C')
			multiply_right(tmp, gen[word[i]-'A'+3], 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, 8);

	return count;
}

int wordEigenvalues(DrawingContext *ctx, const char *word, double *out)
{
	gsl_matrix *tmp = getTempMatrix(ctx->ws);
	gsl_vector *ev = getTempVector(ctx->ws);
	gsl_matrix **gen = getTempMatrices(ctx->ws, 6);

	initializeTriangleGeneratorsCurrent(gen, ctx);

	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_eigenvalues(tmp, ev, ctx->ws);

	LOOP(i) out[i] = gsl_vector_get(ev, i);

	releaseTempMatrices(ctx->ws, 7);
	releaseTempVectors(ctx->ws, 1);

	return count;
}

// level 1: the elementary drawing functions, drawPoint, drawSegment2d

void drawPoint(DrawingContext *ctx, point_t p)
{
	cairo_t *C = ctx->cairo;

	cairo_save(C);
	cairo_arc(C, p.x, p.y, 3.0/ctx->dim->scalefactor, 0, 2*M_PI);
	cairo_close_path(C);
	cairo_fill(C);
	cairo_restore(C);

	/*
	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

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));
}

void drawSegmentWith(DrawingContext *ctx, vector_t a, vector_t b, vector_t line, int contains)
{
	point_t a_ = vectorToPoint(ctx,a);
	point_t b_ = vectorToPoint(ctx,b);
	double x[3];
	double cofactor;
	double r, tline, tminus, tplus;
	double coeff0, coeff1, coeff2;
	point_t m, xminus, xplus;

	// multiply line with inverse of cob to get it as implicit line x in chart
	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 * line.x[j];
	}

	// t = parameter on segment of intersection with line, s(t) = a + (b-a)*t
	tline = -(a_.x*x[0] + a_.y*x[1] + x[2])/((b_.x - a_.x)*x[0] + (b_.y - a_.y)*x[1]);

	/*
	printf("tline: %f\n", tline);

	point_t s;
	s.x = a_.x - (b_.x-a_.x)*tline;
	s.y = a_.y - (b_.y-a_.y)*tline;
	drawPoint(ctx, s);
	*/

	if((tline < 0 || tline > 1) != contains) {
		drawSegment2d(ctx, a_, b_);
	} else { // need to draw complementary segment
		// find t so that s(t) is at radius r from center, |s(t)-m| = r
		m.x = ctx->dim->center_x;
		m.y = ctx->dim->center_y;
		r = ctx->dim->radius;
		// equation is coeff2 t^2 + 2 coeff1 t + coeff0 = 0
		coeff0 = (a_.x - m.x)*(a_.x - m.x) + (a_.y - m.y)*(a_.y - m.y) - r*r;
		coeff1 = (a_.x - m.x)*(b_.x - a_.x) + (a_.y - m.y)*(b_.y - a_.y);
		coeff2 = (b_.x - a_.x)*(b_.x - a_.x) + (b_.y - a_.y)*(b_.y - a_.y);
		if(coeff1*coeff1 - coeff0*coeff2 <= 0)
			return;
		tplus  = (- coeff1 + sqrt(coeff1*coeff1 - coeff0*coeff2))/coeff2;
		tminus = (- coeff1 - sqrt(coeff1*coeff1 - coeff0*coeff2))/coeff2;
		xplus.x = a_.x + tplus * (b_.x - a_.x);
		xplus.y = a_.y + tplus * (b_.y - a_.y);
		xminus.x = a_.x + tminus * (b_.x - a_.x);
		xminus.y = a_.y + tminus * (b_.y - a_.y);
		if(tplus > 1)
			drawSegment2d(ctx, b_, xplus);
		if(tminus < 0)
			drawSegment2d(ctx, a_, xminus);
	}
}

// level 3: boxes and polygons

void drawPolygon(DrawingContext *ctx, int segments, 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);
		if(segments)
			drawSegment(ctx, prev, current);
		else
			drawCovector(ctx, cross(prev, current));
	}
	if(segments)
		drawSegment(ctx, current, first);
	else
		drawCovector(ctx, cross(current, first));

	va_end(args);
}

void drawTriangle(DrawingContext *ctx, const char *word)
{
	vector_t p[3];

	fixedPoints(ctx, word, p);
	drawPolygon(ctx, 1, 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, 1, 4, p[0][0], i[0], p[1][0], i[1]);
}

void drawBoxLines(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, 0, 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);
}

void drawRotationOrbitFrame(DrawingContext *ctx, gsl_matrix *frame, vector_t start)
{
	vector_t v[3], w;
	point_t p;
	double parameter, startangle;
	int iterations = 2000;
	gsl_matrix *inverse = getTempMatrix(ctx->ws);
	gsl_vector *start_v = getTempVector(ctx->ws);
	gsl_vector *start_in_frame = getTempVector(ctx->ws);
	cairo_t *C = ctx->cairo;

//	computeRotationMatrixFrame(ctx, frame, word);
	LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);

	LOOP(i) gsl_vector_set(start_v, i, start.x[i]);
	solve(frame, start_v, start_in_frame, ctx->ws);
	parameter = gsl_vector_get(start_in_frame, 2);
	parameter /= sqrt(gsl_vector_get(start_in_frame, 0)*gsl_vector_get(start_in_frame, 0) +
	                  gsl_vector_get(start_in_frame, 1)*gsl_vector_get(start_in_frame, 1));
	startangle = atan2(gsl_vector_get(start_in_frame, 1), gsl_vector_get(start_in_frame, 0));

	int previous_inside = 0;
	for(int k = 0; k <= iterations; k++) {
		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];
		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, 1);
	releaseTempVectors(ctx->ws, 2);
}

void drawRotationOrbit(DrawingContext *ctx, const char *word, vector_t start)
{
	gsl_matrix *frame = getTempMatrix(ctx->ws);

	computeRotationMatrixFrame(ctx, frame, word);
	drawRotationOrbitFrame(ctx, frame, start);

	releaseTempMatrices(ctx->ws, 1);
}

void drawDualRotationOrbit(DrawingContext *ctx, const char *word, vector_t start)
{
	vector_t v[3], w;
	point_t p;
	double parameter, startangle;
	int iterations = 200;
	gsl_matrix *frame = getTempMatrix(ctx->ws);
	gsl_matrix *inverse = getTempMatrix(ctx->ws);
	gsl_vector *start_v = getTempVector(ctx->ws);
	gsl_vector *start_in_frame = getTempVector(ctx->ws);
	cairo_t *C = ctx->cairo;

	computeRotationMatrixFrame(ctx, frame, word);
	LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);

	LOOP(i) gsl_vector_set(start_v, i, start.x[i]);
//	solve(frame, start_v, start_in_frame, ctx->ws);
	gsl_blas_dgemv(CblasTrans, 1.0, frame, start_v, 0.0, start_in_frame);
	parameter = sqrt(gsl_vector_get(start_in_frame, 0)*gsl_vector_get(start_in_frame, 0) +
	                  gsl_vector_get(start_in_frame, 1)*gsl_vector_get(start_in_frame, 1));
	parameter /= gsl_vector_get(start_in_frame, 2);
	startangle = atan2(gsl_vector_get(start_in_frame, 1), gsl_vector_get(start_in_frame, 0));

	int previous_inside = 0;
	for(int k = 0; k <= iterations; k++) {
		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];
		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);
}

void drawArcWithOutput(DrawingContext *ctx, const char *word, vector_t start, vector_type_t starttype, vector_t end, vector_type_t endtype, vector_t third, int contain, vector_t *start_vector_out, vector_t *end_vector_out, int dontdraw)
{
	vector_t v[3], w, w_;
	point_t p, p_;
	double radius, angle_start, angle_end, angle_third, angle, angle_end_delta, sign, angle_start_final, angle_end_final, angle_end_other;
	int iterations = 200;
	gsl_matrix *frame = getTempMatrix(ctx->ws);
	gsl_matrix *inverse = getTempMatrix(ctx->ws);
	gsl_vector *vector = getTempVector(ctx->ws);
	gsl_vector *vector_in_frame = getTempVector(ctx->ws);
	cairo_t *C = ctx->cairo;

	computeRotationMatrixFrame(ctx, frame, word);
	LOOP(i) LOOP(j) v[i].x[j] = gsl_matrix_get(frame, j, i);

	LOOP(i) gsl_vector_set(vector, i, start.x[i]);
	if(starttype == VT_POINT) {
		solve(frame, vector, vector_in_frame, ctx->ws);
		radius = sqrt(gsl_vector_get(vector_in_frame, 0)*gsl_vector_get(vector_in_frame, 0) +
		                 gsl_vector_get(vector_in_frame, 1)*gsl_vector_get(vector_in_frame, 1));
		radius /= fabs(gsl_vector_get(vector_in_frame, 2));
		angle_start = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
		                    gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
	} else {
		gsl_blas_dgemv(CblasTrans, 1.0, frame, vector, 0.0, vector_in_frame);
		radius = fabs(gsl_vector_get(vector_in_frame, 2));
		radius /= sqrt(gsl_vector_get(vector_in_frame, 0)*gsl_vector_get(vector_in_frame, 0) +
		               gsl_vector_get(vector_in_frame, 1)*gsl_vector_get(vector_in_frame, 1));

		angle_start = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
		                    gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
	}

	LOOP(i) gsl_vector_set(vector, i, third.x[i]);
	solve(frame, vector, vector_in_frame, ctx->ws);
	angle_third = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
	                    gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));

	LOOP(i) gsl_vector_set(vector, i, end.x[i]);
	if(endtype == VT_POINT) {
		solve(frame, vector, vector_in_frame, ctx->ws);
		angle_end = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
		                  gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));
	} else {
		gsl_blas_dgemv(CblasTrans, 1.0, frame, vector, 0.0, vector_in_frame);

		// this is only the average angle
		angle_end = atan2(gsl_vector_get(vector_in_frame, 1)/gsl_vector_get(vector_in_frame, 2),
		                  gsl_vector_get(vector_in_frame, 0)/gsl_vector_get(vector_in_frame, 2));

		angle_end_delta = acos(-fabs(gsl_vector_get(vector_in_frame, 2))/radius/
		                       sqrt(gsl_vector_get(vector_in_frame, 0)*gsl_vector_get(vector_in_frame, 0) +
		                            gsl_vector_get(vector_in_frame, 1)*gsl_vector_get(vector_in_frame, 1)));
	}

	int previous_inside = 0;

	for(int i = 0; i < 4; i++) {
		angle_start_final = angle_start;

		if(endtype == VT_POINT) {
			angle_end_final = angle_end;
		} else {
			if(i >= 2) {
				angle_end_final = angle_end - angle_end_delta;
				angle_end_other = angle_end + angle_end_delta;
			} else {
				angle_end_final = angle_end + angle_end_delta;
				angle_end_other = angle_end - angle_end_delta;
			}
		}

		if(i%2)
			FLIP(angle_start_final, angle_end_final);

		if(endtype == VT_LINE && ANGLE_IN_INTERVAL(angle_start_final, angle_end_final, angle_end_other))
			continue;
		if(contain && !ANGLE_IN_INTERVAL(angle_start_final, angle_end_final, angle_third))
			continue;
		if(!contain && ANGLE_IN_INTERVAL(angle_start_final, angle_end_final, angle_third))
			continue;

		break;
	}

	// output the start end end point
	/*
	LOOP(i) w.x[i] = v[2].x[i] / radius + cos(angle_start_final) * v[0].x[i] + sin(angle_start_final) * v[1].x[i];
	p = vectorToPoint(ctx, w);
	LOOP(i) w.x[i] = v[2].x[i] / radius + cos(angle_end_final) * v[0].x[i] + sin(angle_end_final) * v[1].x[i];
	p_ = vectorToPoint(ctx, w);
	printf("\\draw (%f,%f) -- (%f,%f);\n", p.x, p.y, p_.x, p_.y);
	*/

	if(!dontdraw) {
		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;
			}
		}
	}

	if(start_vector_out)
		LOOP(i) start_vector_out->x[i] = v[2].x[i] / radius +
			cos(angle_start_final) * v[0].x[i] +
			sin(angle_start_final) * v[1].x[i];
	if(end_vector_out)
		LOOP(i) end_vector_out->x[i] = v[2].x[i] / radius +
			cos(angle_end_final) * v[0].x[i] +
			sin(angle_end_final) * v[1].x[i];

	cairo_stroke(C);

	releaseTempMatrices(ctx->ws, 2);
	releaseTempVectors(ctx->ws, 2);
}

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)
{
	drawArcWithOutput(ctx, word, start, starttype, end, endtype, third, contain, 0, 0, 0);
}

// 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, "cba", p[0]);
	fixedPoints(ctx, "bac", p[1]);
	fixedPoints(ctx, "acb", 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]);
	}
}

char *conjugate_word(const char *word, int modifier, const char *conj, char *buffer)
{
	int wordlen = strlen(word);
	int conjlen = strlen(conj);

	for(int i = 0; i < conjlen; i++) {
		buffer[i] = conj[i];
		buffer[2*conjlen+wordlen-1-i] = conj[i];
	}

	for(int i = 0; i < wordlen; i++) {
		if(word[i] == ' ')
			buffer[conjlen+i] = word[i];
		else
			buffer[conjlen+i] = (word[i]+modifier-'a')%3 + 'a';
	}

	buffer[2*conjlen + wordlen] = 0;

	return buffer;
}

void drawCurvedBox(DrawingContext *ctx, int base, const char *conj, int style)
{
	vector_t p[11][3];
	vector_t l[2][3];
	vector_t corner1, corner2;
	vector_t tmp1, tmp2;
	char word[100];
	int modifier = base - 'A';

	conjugate_word("abc", modifier, conj, word);
	fixedPoints(ctx, word, p[0]);
	conjugate_word("bca", modifier, conj, word);
	fixedPoints(ctx, word, p[1]);
	conjugate_word("b abc b", modifier, conj, word);
	fixedPoints(ctx, word, p[2]);
	conjugate_word("ab abc ba", modifier, conj, word);
	fixedPoints(ctx, word, p[3]);
	conjugate_word("baca cab acab", modifier, conj, word);
	fixedPoints(ctx, word, p[4]);
	conjugate_word("abaca cab acaba", modifier, conj, word);
	fixedPoints(ctx, word, p[5]);
	conjugate_word("bca cab acb", modifier, conj, word);
	fixedPoints(ctx, word, p[6]);
	conjugate_word("abca cab acba", modifier, conj, word);
	fixedPoints(ctx, word, p[7]);
	conjugate_word("abacababa", modifier, conj, word);
	fixedPoints(ctx, word, p[8]);
	conjugate_word("bacabab", modifier, conj, word);
	fixedPoints(ctx, word, p[9]);
	conjugate_word("cab", modifier, conj, word);
	fixedPoints(ctx, word, p[10]);


//	conjugate_word("bca b abc b acb", modifier, conj, word);
//	fixedPoints(ctx, word, p[6]);
//	conjugate_word("bca baca cab acab acb", modifier, conj, word);
//	fixedPoints(ctx, word, p[7]);


	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]);
	LOOP(j) l[10][j] = cross(p[10][(3-j)%3], p[10][(4-j)%3]);

	// main conic
	conjugate_word("ab", modifier, conj, word);
	drawArcWithOutput(ctx, word, p[0][0], VT_POINT, p[2][0], VT_POINT, p[1][0], 0, &tmp1, &tmp2, style != 1);
	if(style == 2)
		drawSegmentWith(ctx, tmp1, tmp2, l[10][0], 0);
	if(style == 3) {
		drawVector(ctx, tmp1);
		drawVector(ctx, tmp2);
	}

	conjugate_word("ab", modifier, conj, word);
	drawArcWithOutput(ctx, word, p[1][0], VT_POINT, p[3][0], VT_POINT, p[0][0], 0, &tmp1, &tmp2, style != 1);
	if(style == 2)
		drawSegmentWith(ctx, tmp1, tmp2, l[10][0], 0);
	if(style == 3) {
		drawVector(ctx, tmp1);
		drawVector(ctx, tmp2);
	}

	conjugate_word("bcabcb", modifier, conj, word);
	drawArcWithOutput(ctx, word, p[2][0], VT_POINT, l[1][0], VT_LINE, p[6][0], 1, &tmp1, &tmp2, style != 1);  // only 1st cutoff
	if(style == 2)
		drawSegmentWith(ctx, tmp1, tmp2, l[10][0], 0);

	corner1 = tmp2;

	conjugate_word("abcabcba", modifier, conj, word);
	drawArcWithOutput(ctx, word, p[3][0], VT_POINT, l[0][0], VT_LINE, p[7][0], 1, &tmp1, &tmp2, style != 1);  // only 1st cutoff
	if(style == 2)
		drawSegmentWith(ctx, tmp1, tmp2, l[10][0], 0);
	corner2 = tmp2;

	if(style == 1 || style == 2) {
		drawSegmentWith(ctx, p[0][0], corner2, l[1][1], 0);
		drawSegmentWith(ctx, p[1][0], corner1, l[0][1], 0);
	} else if(style == 3)
	{
		drawVector(ctx, corner1);
		drawVector(ctx, corner2);
	}
}

groupelement_t *left(const char *word, groupelement_t *g)
{
	int n = strlen(word);

	for(int i = n-1; i >= 0; i--) {
		if(word[i] == ' ')
			continue;

		g = g->adj[word[i]-'a'];

		if(!g)
			break;
	}

	return g;
}

void drawBoxes(DrawingContext *ctx)
{
	gsl_matrix *tmp = getTempMatrix(ctx->ws);
	gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
	gsl_matrix *frame = getTempMatrix(ctx->ws);
	gsl_matrix *frame2 = getTempMatrix(ctx->ws);
	gsl_vector *startpoint_drawbasis = getTempVector(ctx->ws);
	gsl_vector *startpoint_globalbasis = getTempVector(ctx->ws);
	gsl_matrix **elements = getTempMatrices(ctx->ws, ctx->n_group_elements);

	cairo_t *C = ctx->cairo;
	cairo_save(C);
	cairo_set_line_width(C, 2.0/ctx->dim->scalefactor);
	cairo_set_source_rgb(C, 0.6, 0.6, 0.6);

	vector_t p[22][3];
	vector_t fp[3];
	vector_t l[22][3];
	vector_t alpha[6];
	vector_t ptmp[3];
	vector_t start;
	vector_t start2;
	char word[100], word2[100];

	fixedPoints(ctx, "cba", p[0]);
	fixedPoints(ctx, "acb", p[1]);
	fixedPoints(ctx, "bac", p[2]);

	initializeTriangleGeneratorsCurrent(gen, ctx);
	gsl_matrix_set_identity(elements[0]);
	for(int i = 1; i < ctx->n_group_elements; i++) {
		if(ctx->group[i].length % 2)
			continue;
		int letter = ROTATION_LETTER(ctx->group[i].letter, ctx->group[i].parent->letter);
		multiply(gen[letter], elements[ctx->group[i].parent->parent->id], elements[i]);
	}

	gsl_vector_set(startpoint_drawbasis, 0, ctx->marking.x);
	gsl_vector_set(startpoint_drawbasis, 1, ctx->marking.y);
	gsl_vector_set(startpoint_drawbasis, 2, 1);
	solve(ctx->cob, startpoint_drawbasis, startpoint_globalbasis, ctx->ws);
	LOOP(i) start.x[i] = gsl_vector_get(startpoint_globalbasis, i);

	/*
	fixedPoints(ctx, "ABAB", fp);
	drawCovector(ctx, cross(fp[0], fp[2]));
	drawVector(ctx, fp[1]);
	computeRotationMatrixFrame(ctx, frame, "c");
	drawRotationOrbit(ctx, "c", start); // ba cb ab ac = C A c B
	drawVector(ctx, start);

	computeMatrix(ctx, tmp, "ABABc");
	start2 = apply(tmp, start);
	computeRotationMatrixFrame(ctx, frame, "c");
	multiply(tmp, frame, frame2);
	drawVector(ctx, start2);
	drawRotationOrbitFrame(ctx, frame2, apply(tmp, start));

	computeMatrix(ctx, tmp, "ABABcABABC");
	start2 = apply(tmp, start);
	computeRotationMatrixFrame(ctx, frame, "c");
	multiply(tmp, frame, frame2);
	drawVector(ctx, start2);
	drawRotationOrbitFrame(ctx, frame2, apply(tmp, start));
	*/

	for(groupelement_t *cur = &ctx->group[180]; cur->parent; cur = cur->parent)
		fputc('a'+cur->letter, stdout);
	fputc('\n', stdout);

	queue_t queue;
	queue_init(&queue);
	queue_put(&queue, 0);
	int current;
	groupelement_t *cur, *next;

	for(int i = 0; i < ctx->n_group_elements_combinatorial; i++)
		ctx->group[i].visited = 0;

	cur = &ctx->group[0];

	computeRotationMatrixFrame(ctx, frame, "c");

	for(int i = 0; i < 1000; i++) {
		if(ctx->group[i].length % 2 != 0)
			continue;

		multiply(elements[i], frame, frame2);
		drawRotationOrbitFrame(ctx, frame2, apply(elements[i], start));
	}

	/*
	while((current = queue_get(&queue)) != -1) {
		cur = &ctx->group[current];

		if(cur->visited > 4)
			continue;

		if(cur->id < ctx->n_group_elements) {
			multiply(elements[cur->id], frame, frame2);
			drawRotationOrbitFrame(ctx, frame2, apply(elements[cur->id], start));
		}

	next = left("ab ab", cur);
	if(next && next->visited == 0) {
		queue_put(&queue, next->id);
		next->visited = cur->visited+1;
	}
	next = left("cbac cbac", cur);
	if(next && next->visited == 0) {
		queue_put(&queue, next->id);
		next->visited = cur->visited+1;
	}
	next = left("cacbca cacbca", cur);
	if(next && next->visited == 0) {
		queue_put(&queue, next->id);
		next->visited = cur->visited+1;
	}
	next = left("cabcacbcac cabcacbcac", cur);
	if(next && next->visited == 0) {
		queue_put(&queue, next->id);
		next->visited = cur->visited+1;
	}
	next = left("acbcacba acbcacba", cur);
	if(next && next->visited == 0) {
		queue_put(&queue, next->id);
		next->visited = cur->visited+1;
	}
	next = left("bcacbc bcacbc", cur);
	if(next && next->visited == 0) {
		queue_put(&queue, next->id);
		next->visited = cur->visited+1;
	}
	}
	*/

//	drawRotationOrbit(ctx, "a", p[1][0]);
//	drawRotationOrbit(ctx, "b", p[2][0]);

	cairo_restore(C);
	releaseTempMatrices(ctx->ws, 9 + ctx->n_group_elements);
	releaseTempVectors(ctx->ws, 2);
}

void drawBoxes2(DrawingContext *ctx)
{
	gsl_matrix *rot = getTempMatrix(ctx->ws);
	gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
	cairo_t *C = ctx->cairo;
	cairo_save(C);
	initializeTriangleGeneratorsCurrent(gen, ctx);

	vector_t p[4][3];

	fixedPoints(ctx, "cba", p[0]);
	fixedPoints(ctx, "acb", p[1]);
	fixedPoints(ctx, "bac", p[2]);

	cairo_set_line_width(C, 2.5/ctx->dim->scalefactor);

	/*
	cairo_set_source_rgb(C, 0, 1, 1);
	fixedPoints(ctx, "abc", p[0]);
	drawRotationOrbit(ctx, "bc", p[0][0]); // (r^{-1}a)^2 C / cbr
	fixedPoints(ctx, "bca", p[0]);
	drawRotationOrbit(ctx, "abca", p[0][0]); // (r^{-1}a)^2 C / cbr

	cairo_set_source_rgb(C, 1, 1, 0);
	fixedPoints(ctx, "abc", p[0]);
	drawRotationOrbit(ctx, "cbcabc", p[0][0]); // (r^{-1}a)^4 C / cbac r-
	fixedPoints(ctx, "bca", p[0]);
	drawRotationOrbit(ctx, "acbcabca", p[0][0]); // (r^{-1}a)^4 C / cbac r-

	cairo_set_source_rgb(C, 1, 0, 1);
	fixedPoints(ctx, "abc", p[0]);
	drawRotationOrbit(ctx, "cbacabcabc", p[0][0]); // (r^{-1}a)^6 C / cbacba
	fixedPoints(ctx, "bca", p[0]);
	drawRotationOrbit(ctx, "acbacabcabca", p[0][0]); // (r^{-1}a)^6 C / cbacba
	*/

	/*
	cairo_set_source_rgb(C, 1, 0, 0);
	fixedPoints(ctx, "bca", p[3]);
	drawRotationOrbit(ctx, "bcabcb", p[3][0]); // cb c a bc
	fixedPoints(ctx, "abc", p[3]);
	drawRotationOrbit(ctx, "abcabcba", p[3][0]); // cb c a bc

	cairo_set_source_rgb(C, 0, 1, 0);
	fixedPoints(ctx, "ababcba", p[3]);
	drawRotationOrbit(ctx, "ababcababa", p[3][0]); // cb c a bc
	fixedPoints(ctx, "abc", p[3]);
	drawRotationOrbit(ctx, "abcabcabacba", p[3][0]); // cb c a bc
	*/

//	drawRotationOrbit(ctx, "bc", p[3][0]);

	cairo_set_source_rgb(C, 0, 0, 0);
	drawCurvedBox(ctx, 'A', "", 2);

	cairo_set_source_rgb(C, 0, 0, 1);
//	drawCurvedBox(ctx, 'C', "ab", 2);

//	drawCurvedBox(ctx, 'C', "ab", 2);
//	drawCurvedBox(ctx, 'B', "bca", 2);
//	drawCurvedBox(ctx, 'B', "ba", 2);
//	drawCurvedBox(ctx, 'B', "bca", 2);
//	drawCurvedBox(ctx, 'B', "abca", 2);
//	drawCurvedBox(ctx, 'C', "abab", 2);
//	drawCurvedBox(ctx, 'C', "ababab", 2);

	if(ctx->mode >= 3 && ctx->mode != 4) {
		cairo_set_source_rgb(C, 0, 0, 0);
		drawCurvedBox(ctx, 'B', "", 2);
		drawCurvedBox(ctx, 'C', "", 2);
	}

	if(ctx->mode == 4 || ctx->mode == 5) {
		cairo_set_source_rgb(C, 0, 0.8, 0.5);
		drawCurvedBox(ctx, 'A', "", 2);
		drawCurvedBox(ctx, 'A', "bc", 2);
		drawCurvedBox(ctx, 'A', "bcbc", 2);
		drawCurvedBox(ctx, 'A', "bcbcbc", 2);
		drawCurvedBox(ctx, 'A', "bcbcbcbc", 2);
		drawCurvedBox(ctx, 'A', "bcbcbcbcbc", 2);
		drawCurvedBox(ctx, 'A', "bcbcbcbcbcbc", 2);
//		drawCurvedBox(ctx, 'A', "b", 2);
//		drawCurvedBox(ctx, 'A', "bcb", 2);
//		drawCurvedBox(ctx, 'A', "bcbcb", 2);
//		drawCurvedBox(ctx, 'A', "bcbcbcb", 2);
//		drawCurvedBox(ctx, 'A', "bcbcbcbcb", 2);
	}

	if(ctx->mode == 6) {
		cairo_set_source_rgb(C, 0, 0.8, 0.5);
		drawCurvedBox(ctx, 'C', "abababab", 2);
		drawCurvedBox(ctx, 'C', "ababababab", 2);
	}

	if(ctx->mode >= 6) {
		cairo_set_source_rgb(C, 0, 0.8, 0.5);
		drawCurvedBox(ctx, 'C', "ab", 2);
		drawCurvedBox(ctx, 'C', "abab", 2);
		drawCurvedBox(ctx, 'C', "ababab", 2);
	}

	if(ctx->mode >= 8) {
		cairo_set_source_rgb(C, 0, 0.8, 0.5);
		drawCurvedBox(ctx, 'C', "b", 2);
		drawCurvedBox(ctx, 'C', "bab", 2);
		drawCurvedBox(ctx, 'C', "babab", 2);
	}

	if(ctx->mode >= 9) {
	cairo_set_source_rgb(C, 0.8, 0, 0.5);
	drawCurvedBox(ctx, 'B', "abca", 2);
	drawCurvedBox(ctx, 'B', "abcaca", 2);
	drawCurvedBox(ctx, 'B', "abcacaca", 2);
	drawCurvedBox(ctx, 'B', "aba", 2);
	drawCurvedBox(ctx, 'B', "abaca", 2);
	drawCurvedBox(ctx, 'B', "abacaca", 2);

	drawCurvedBox(ctx, 'B', "ababca", 2);
	drawCurvedBox(ctx, 'B', "ababcaca", 2);
	drawCurvedBox(ctx, 'B', "ababcacaca", 2);
	drawCurvedBox(ctx, 'B', "ababa", 2);
	drawCurvedBox(ctx, 'B', "ababaca", 2);
	drawCurvedBox(ctx, 'B', "ababacaca", 2);

	drawCurvedBox(ctx, 'B', "abababca", 2);
	drawCurvedBox(ctx, 'B', "abababcaca", 2);
	drawCurvedBox(ctx, 'B', "abababcacaca", 2);
	drawCurvedBox(ctx, 'B', "abababa", 2);
	drawCurvedBox(ctx, 'B', "abababaca", 2);
	drawCurvedBox(ctx, 'B', "abababacaca", 2);

	drawCurvedBox(ctx, 'B', "bca", 2);
	drawCurvedBox(ctx, 'B', "bcaca", 2);
	drawCurvedBox(ctx, 'B', "bcacaca", 2);
	drawCurvedBox(ctx, 'B', "ba", 2);
	drawCurvedBox(ctx, 'B', "baca", 2);
	drawCurvedBox(ctx, 'B', "bacaca", 2);

	drawCurvedBox(ctx, 'B', "babca", 2);
	drawCurvedBox(ctx, 'B', "babcaca", 2);
	drawCurvedBox(ctx, 'B', "babcacaca", 2);
	drawCurvedBox(ctx, 'B', "baba", 2);
	drawCurvedBox(ctx, 'B', "babaca", 2);
	drawCurvedBox(ctx, 'B', "babacaca", 2);

	drawCurvedBox(ctx, 'B', "bababca", 2);
	drawCurvedBox(ctx, 'B', "bababcaca", 2);
	drawCurvedBox(ctx, 'B', "bababcacaca", 2);
	drawCurvedBox(ctx, 'B', "bababa", 2);
	drawCurvedBox(ctx, 'B', "bababaca", 2);
	drawCurvedBox(ctx, 'B', "bababacaca", 2);
	}

//	drawCurvedBox(ctx, 'B', "abab", 2);
//	drawCurvedBox(ctx, 'B', "ababab", 2);



//	drawCurvedBox(ctx, 'C', "b", 1);

//	drawCurvedBox(ctx, 'C', "ababab");
//	drawCurvedBox(ctx, 'C', "abababab");
//	drawCurvedBox(ctx, 'C', "b");
//	drawCurvedBox(ctx, 'C', "bab");
//	drawCurvedBox(ctx, 'C', "babab");

//	drawCurvedBox(ctx, 'C', "abababab");
//	drawCurvedBox(ctx, 'C', "ababababab");
//	drawCurvedBox(ctx, 'C', "abababababab");


	cairo_set_source_rgb(C, 0, 0, 1);
//	drawCurvedBox(ctx, 'B', "abca", 1);
//	drawCurvedBox(ctx, 'B', "aba", 1);
//	drawCurvedBox(ctx, 'B', "bca", 1);
//	drawCurvedBox(ctx, 'B', "ba", 1);
//	drawCurvedBox(ctx, 'B', "abaca");
//	drawCurvedBox(ctx, 'B', "abcaca");
//	drawCurvedBox(ctx, 'B', "abaca");
//	drawCurvedBox(ctx, 'B', "aba");
//	drawCurvedBox(ctx, 'B', "ababca");
//	drawCurvedBox(ctx, 'B', "ababa");
//	drawCurvedBox(ctx, 'B', "abababca");
//	drawCurvedBox(ctx, 'B', "abababa");
//	drawCurvedBox(ctx, 'B', "bca");
//	drawCurvedBox(ctx, 'B', "ba");
//	drawCurvedBox(ctx, 'B', "babca");
//	drawCurvedBox(ctx, 'B', "baba");
//	drawCurvedBox(ctx, 'B', "bababca");
//	drawCurvedBox(ctx, 'B', "bababa");

	cairo_set_source_rgb(C, 1, 0, 1);
//	drawCurvedBox(ctx, 'A', "abcac");
//	drawCurvedBox(ctx, 'A', "bcac");
//	drawCurvedBox(ctx, 'A', "abcacbc");
//	drawCurvedBox(ctx, 'A', "abcac");
//	drawCurvedBox(ctx, 'A', "abcacbc");

//	drawCurvedBox(ctx, 'A', "ababc");
//	drawCurvedBox(ctx, 'A', "ababcbc");
/*	drawCurvedBox(ctx, 'A', "abcac");
	drawCurvedBox(ctx, 'A', "ababc");
	drawCurvedBox(ctx, 'A', "abac");

	drawCurvedBox(ctx, 'A', "ababcabc");
	drawCurvedBox(ctx, 'A', "ababcac");
	drawCurvedBox(ctx, 'A', "abababc");
	drawCurvedBox(ctx, 'A', "ababac");

	drawCurvedBox(ctx, 'A', "abababcabc");
	drawCurvedBox(ctx, 'A', "abababcac");
	drawCurvedBox(ctx, 'A', "ababababc");
	drawCurvedBox(ctx, 'A', "abababac");

	drawCurvedBox(ctx, 'A', "bcabc");
	drawCurvedBox(ctx, 'A', "bcac");
	drawCurvedBox(ctx, 'A', "babc");
	drawCurvedBox(ctx, 'A', "bac");

	drawCurvedBox(ctx, 'A', "babcabc");
	drawCurvedBox(ctx, 'A', "babcac");
	drawCurvedBox(ctx, 'A', "bababc");
	drawCurvedBox(ctx, 'A', "babac");

	drawCurvedBox(ctx, 'A', "bababcabc");
	drawCurvedBox(ctx, 'A', "bababcac");
	drawCurvedBox(ctx, 'A', "babababc");
	drawCurvedBox(ctx, 'A', "bababac");
	*/

//	drawCurvedBox(ctx, 'A', "ababc");

	cairo_set_source_rgb(C, 1, 0.5, 0);
//	drawCurvedBox(ctx, 'C', "abcabcab");


//	drawCurvedBox(ctx, 'B', "bca");
//	drawCurvedBox(ctx, 'B', "abcacaca");
//	drawCurvedBox(ctx, 'B', "abaca");
//	drawCurvedBox(ctx, 'B', "aba");
//	drawCurvedBox(ctx, 'B', "aba");
//	drawCurvedBox(ctx, 'B', "abcaca");
//	drawCurvedBox(ctx, 'B', "aba");
//	drawCurvedBox(ctx, 'B', "abaca");

	cairo_set_source_rgb(C, 0, 0, 1);
//	drawCurvedBox(ctx, 'A', "abcabc");
//	drawCurvedBox(ctx, 'A', "abcabcbc");
//	drawCurvedBox(ctx, 'A', "abcacbc");
//	drawCurvedBox(ctx, 'A', "abcac");

//	drawCurvedBox(ctx, 'A', "bcabc");
//	drawCurvedBox(ctx, 'A', "bcabcbc");
//	drawCurvedBox(ctx, 'A', "bcacbc");
//	drawCurvedBox(ctx, 'A', "bcac");

//	drawCurvedBox(ctx, 'A', "abcac");
//	drawCurvedBox(ctx, 'A', "abcac");
//	drawCurvedBox(ctx, 'A', "abcacbc");

//	drawCurvedBox(ctx, 'B', "abacaca");
//	drawCurvedBox(ctx, 'B', "abacacaca");


	cairo_set_source_rgb(C, 0, 1, 1);
	fixedPoints(ctx, "ababcba", p[0]);
//	drawRotationOrbit(ctx, "abcaba", p[0][0]);

/*
	int p = 9;

	vector_t fp[3][3],neutral_line[3],reflection_line[p],star[2*p],outer[2];
	vector_t rotation_line = {0,0,1};

	cairo_set_line_width(C, 1.5/ctx->dim->scalefactor);
	cairo_set_source_rgb(C, 1, 0, 0);

	multiply(gen[0], gen[1], rot);

	fixedPoints(ctx, "abc", fp[0]);
	fixedPoints(ctx, "bca", fp[1]);
	fixedPoints(ctx, "cab", fp[2]);

	LOOP(i) neutral_line[i] = cross(fp[i][0], fp[i][2]);
	LOOP(j) reflection_line[0].x[j] = gsl_matrix_get(ctx->cartan, 0, j);
	star[0] = cross(neutral_line[0],reflection_line[0]);
	star[p] = cross(neutral_line[2],reflection_line[0]);

	for(int j = 1; j < p; j++) {
		reflection_line[j] = apply_transpose(rot, reflection_line[j-1]);
		star[j] = apply(rot, star[j-1]);
		star[j+p] = apply(rot, star[j+p-1]);
	}

	outer[0] = cross(neutral_line[0],reflection_line[5]);
	outer[1] = cross(neutral_line[2],reflection_line[5]);

	for(int j = 0; j < 8; j++) {
		drawVector(ctx, star[j]);
		drawVector(ctx, star[p+j]);
	}

	for(int j = 0; j < 7; j++) {
//		if(j == 3)
//			continue;
		drawSegment(ctx, star[j%p], star[(j+1)%p+p]);
		drawSegment(ctx, star[(j+1)%p+p], star[(j+1)%p]);
		drawSegment(ctx, star[(j+1)%p], star[j%p+p]);
		drawSegment(ctx, star[j%p+p], star[j%p]);
	}

	cairo_set_source_rgb(C, 0, 0, 1);
	drawVector(ctx,outer[0]);
	drawVector(ctx,outer[1]);

//	drawCovector(ctx, neutral_line[0]);
//	drawCovector(ctx, neutral_line[2]);

	drawSegment(ctx, star[0], star[p]);
	drawSegment(ctx, star[p], outer[1]);
	drawSegment(ctx, outer[1], outer[0]);
	drawSegment(ctx, outer[0], star[0]);

	cairo_set_source_rgb(C, 0, 0, 0);
	drawCovector(ctx, rotation_line);
*/

//	for(int j = 0; j < 5; j++)
//		drawCovector(ctx, reflection_line[j]);

	// 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, 1, 4, p[0][0], i[0], p[1][0], i[1]);

	// 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_line_width(C, 1.5/ctx->dim->scalefactor);
	cairo_set_source_rgb(C, 1, 0, 0);
//	drawBox(ctx, "bca", "abc");

	drawCurvedBox(ctx, 'A', "");
*/
		/*
	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");
	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, "babababab abc babababab", "babababab cab babababab");
*/

	cairo_restore(C);
	releaseTempMatrices(ctx->ws, 7);
}

void drawRotatedReflectors(DrawingContext *ctx)
{
	gsl_matrix *rot = getTempMatrix(ctx->ws);
	gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
	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);

	initializeTriangleGeneratorsCurrent(gen, ctx);

	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, 7);
}

void drawDualLimitCurve(DrawingContext *ctx)
{
	cairo_t *C = ctx->cairo;

	cairo_save(C);
	cairo_set_source_rgb(C, 0.5, 0.5, 1);

	gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
	gsl_matrix **elements = getTempMatrices(ctx->ws, ctx->n_group_elements);

//	wordEigenvalues(ctx, "abc", ev);
//	LOOP(i) LOOP(j) gsl_matrix_set(coxeter_fixedpoints, j, i, cox[0][i].x[j]);

	initializeTriangleGeneratorsCurrent(gen, ctx);
	gsl_matrix_set_identity(elements[0]);
	for(int i = 1; i < ctx->n_group_elements; i++)
		multiply(gen[ctx->group[i].letter], elements[ctx->group[i].parent->id], elements[i]);

	vector_t p[3], l[3], v;

	fixedPoints(ctx, "cba", p);
	drawVector(ctx, p[0]);
	drawVector(ctx, p[1]);
	drawVector(ctx, p[2]);

	LOOP(i) l[i] = cross(p[(i+1)%3], p[(i+2)%3]);

	for(int i = 0; i < ctx->n_group_elements; i++) {
		v = apply_transpose(elements[i], l[0]);
		drawCovector(ctx, v);
	}

	releaseTempMatrices(ctx->ws, 3 + ctx->n_group_elements);
//	releaseTempVectors(ctx->ws, 4);


/*
	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]);
}*/

	/*
	fixedPoints(ctx, "abc", ptmp);
	drawCovector(ctx, cross(ptmp[0], ptmp[1]));
	fixedPoints(ctx, "bca", ptmp);
	drawCovector(ctx, cross(ptmp[0], ptmp[1]));
	fixedPoints(ctx, "cab", ptmp);
	drawCovector(ctx, cross(ptmp[0], ptmp[1]));
	fixedPoints(ctx, "babcb", ptmp);
	drawCovector(ctx, cross(ptmp[0], ptmp[1]));
	fixedPoints(ctx, "cbcac", ptmp);
	drawCovector(ctx, cross(ptmp[0], ptmp[1]));
	fixedPoints(ctx, "acaba", ptmp);
	drawCovector(ctx, cross(ptmp[0], ptmp[1]));
	*/

	cairo_restore(C);
}

void drawLimitCurve(DrawingContext *ctx)
{
	int close_points = 0;
	cairo_t *C = ctx->cairo;

	cairo_save(C);

//	cairo_set_source_rgb(C, 0.6, 0.6, 0.6);
	cairo_set_source_rgb(C, 0, 0, 0);

	if(ctx->limit_with_lines) {
		int previous_inside = 0;
		cairo_new_path(C);

		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 drawCoxeterOrbit(DrawingContext *ctx)
{
	gsl_matrix *rot = getTempMatrix(ctx->ws);
	gsl_matrix **gen = getTempMatrices(ctx->ws, 6);
	gsl_vector *eval = getTempVector(ctx->ws);
	gsl_matrix *coxeter_fixedpoints = getTempMatrix(ctx->ws);
	gsl_vector *startpoint_coxeterbasis = getTempVector(ctx->ws);
	gsl_vector *startpoint_globalbasis = getTempVector(ctx->ws);
	gsl_vector *startpoint_drawbasis = getTempVector(ctx->ws);
	gsl_matrix **elements = getTempMatrices(ctx->ws, ctx->n_group_elements);

	cairo_t *C = ctx->cairo;
	vector_t cox[3][3];
	vector_t abcb[3];
	double ev[3];
	vector_t v, start;
	point_t p;
	int first = 1;

	cairo_save(C);
	initializeTriangleGeneratorsCurrent(gen, ctx);

	cairo_set_source_rgb(C, 0, 0, 1);

	fixedPoints(ctx, "abc", cox[0]);
	fixedPoints(ctx, "bca", cox[1]);
	fixedPoints(ctx, "cab", cox[2]);
//	fixedPoints(ctx, "babc", abcb);
	wordEigenvalues(ctx, "abc", ev);
	LOOP(i) LOOP(j) gsl_matrix_set(coxeter_fixedpoints, j, i, cox[0][i].x[j]);

	initializeTriangleGeneratorsCurrent(gen, ctx);
	gsl_matrix_set_identity(elements[0]);
	for(int i = 1; i < ctx->n_group_elements; i++)
		multiply(gen[ctx->group[i].letter], elements[ctx->group[i].parent->id], elements[i]);

	//printf("coxeter eigenvalues: %f %f %f\n", ev[0], ev[1], ev[2]);

//	LOOP(i) gsl_vector_set(startpoint_globalbasis, i, cox[1][0].x[i]);

	gsl_vector_set(startpoint_drawbasis, 0, ctx->marking.x);
	gsl_vector_set(startpoint_drawbasis, 1, ctx->marking.y);
	gsl_vector_set(startpoint_drawbasis, 2, 1);
	solve(ctx->cob, startpoint_drawbasis, startpoint_globalbasis, ctx->ws);

//	solve(coxeter_fixedpoints, startpoint_globalbasis, startpoint_coxeterbasis, ctx->ws);
//	LOOP(i) start.x[i] = gsl_vector_get(startpoint_coxeterbasis, i);

	LOOP(i) start.x[i] = gsl_vector_get(startpoint_globalbasis, i);

	/*
	for(int t = -1000; t < 1000; t++) {
		LOOP(i) v.x[i] = 0;
		LOOP(i) LOOP(j) v.x[j] += pow(fabs(ev[i]),t*0.01)*start.x[i]*cox[0][i].x[j];
		p = vectorToPoint(ctx, v);

		if(first) {
			cairo_move_to(C, p.x, p.y);
			first = 0;
		} else {
			cairo_line_to(C, p.x, p.y);
		}
	}
	cairo_stroke(C);
	*/

	for(int i = 0; i < ctx->n_group_elements; i++) {
		v = apply(elements[i], start);
		drawVector(ctx, v);
//		ctx->limit_curve[3*i+2] = atan2(
//			gsl_matrix_get(fixedpoints_pos, 2, column)/gsl_matrix_get(fixedpoints_pos, 0, column),
//			gsl_matrix_get(fixedpoints_pos, 1, column)/gsl_matrix_get(fixedpoints_pos, 0, column));
	}


/*	for(int t = -20; t < 20; t++) {
		LOOP(i) v.x[i] = 0;
		LOOP(i) LOOP(j) v.x[j] += (ev[i]<0&&t%2?-1:1)*pow(fabs(ev[i]),t/3.0)*start.x[i]*cox[0][i].x[j];
		drawVector(ctx, v);
		}*/

	cairo_set_source_rgb(C, 0, 0, 0);
//	LOOP(i) drawVector(ctx, abcb[i]);

	cairo_restore(C);
	releaseTempMatrices(ctx->ws, 8 + ctx->n_group_elements);
	releaseTempVectors(ctx->ws, 4);
}

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, s = exp(%.8f) = %.8f, marking = (%.5f, %.5f)", log(ctx->parameter), ctx->parameter, log(ctx->parameter2), ctx->parameter2, ctx->marking.x, ctx->marking.y);
	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);

		if(ctx->show_marking)
		{
			cairo_set_source_rgb(C, 0, 0, 1);
			drawPoint(ctx, ctx->marking);
		}

		if(ctx->show_coxeter_orbit)
			drawCoxeterOrbit(ctx);
	}

	cairo_identity_matrix(C); // text is in screen coordinates

	if(ctx->show_text)
		drawText(ctx);

	cairo_surface_flush(cairo_get_target(C));
}