#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, 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;
}

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

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

	releaseTempMatrices(ctx->ws, 4);
	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);
}

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]);

	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 = 200;
	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;

//	computeRotationMatrix(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);

	computeRotationMatrix(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;

	computeRotationMatrix(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;

	computeRotationMatrix(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, "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]);
	}
}

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]);


	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);
	}
}


void drawBoxes(DrawingContext *ctx)
{
	gsl_matrix *rot = getTempMatrix(ctx->ws);
	gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
	gsl_matrix *frame = getTempMatrix(ctx->ws);
	cairo_t *C = ctx->cairo;
	cairo_save(C);

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

	fixedPoints(ctx, "abc", p[0]);
	fixedPoints(ctx, "bca", p[1]);
	fixedPoints(ctx, "cab", p[2]);
	fixedPoints(ctx, "bacabab", p[3]);
	fixedPoints(ctx, "bcacabacb", p[4]);

	cairo_set_line_width(C, 2.0/ctx->dim->scalefactor);
	cairo_set_source_rgb(C, 0.6, 0.6, 0.6);

	drawRotationOrbit(ctx, "ab", p[0][0]);
	drawRotationOrbit(ctx, "bc", p[0][0]);
	drawRotationOrbit(ctx, "ca", p[0][0]);

	if(ctx->mode >= 2) {
		drawRotationOrbit(ctx, "bcabcb", p[1][0]); // bcC
		drawRotationOrbit(ctx, "abcabcba", p[0][0]); // abcC
	}

	cairo_set_source_rgb(C, 0, 0, 0);
	fixedPoints(ctx, "abababcbaba", p[3]);

	cairo_set_source_rgb(C, 0, 0, 1);
	fixedPoints(ctx, "bc bca cb", p[3]);

	cairo_restore(C);
	releaseTempMatrices(ctx->ws, 5);
}

void drawBoxes2(DrawingContext *ctx)
{
	gsl_matrix *rot = getTempMatrix(ctx->ws);
	gsl_matrix **gen = getTempMatrices(ctx->ws, 3);
	cairo_t *C = ctx->cairo;
	cairo_save(C);
	initializeTriangleGenerators(gen, ctx->cartan);

	vector_t p[4][3];

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

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

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

	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);
	}

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

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

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

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

	    cairo_restore(C);
	    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, 0.5, 0.5, 1);

	int n = 18;
	vector_t p[n][3];
	vector_t l[n][3];
	vector_t ptmp[3], ltmp[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]);
}*/

	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, 3);
	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);
	initializeTriangleGenerators(gen, ctx->cartan);

	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]);

	initializeTriangleGenerators(gen, ctx->cartan);
	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, 5 + 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, marking = (%.5f, %.5f)", log(ctx->parameter), ctx->parameter, 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));
}