just used the program a bit

draw.c

@@ -65,6 +65,30 @@ int fixedPoints(DrawingContext *ctx, const char *word, vector_t *out)
 	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)
@@ -98,7 +122,7 @@ void drawSegment2d(DrawingContext *ctx, point_t a, point_t b)
 
 // level 2: drawVector, drawCovector, drawSegment
 
-static point_t vectorToPoint(DrawingContext *ctx, vector_t in)
+point_t vectorToPoint(DrawingContext *ctx, vector_t in)
 {
 	double x[3];
 	point_t out;
@@ -155,6 +179,53 @@ 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 semgent
+		// 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, ...)
@@ -244,19 +315,18 @@ void drawBoxStd(DrawingContext *ctx, const char *word, char base)
 	drawBox(ctx, word1, word2);
 }
 
-void drawRotationOrbit(DrawingContext *ctx, const char *word, vector_t start)
+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 *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);
+//	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]);
@@ -284,10 +354,20 @@ void drawRotationOrbit(DrawingContext *ctx, const char *word, vector_t start)
 
 	cairo_stroke(C);
 
-	releaseTempMatrices(ctx->ws, 2);
+	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;
@@ -333,10 +413,10 @@ void drawDualRotationOrbit(DrawingContext *ctx, const char *word, vector_t start
 	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)
+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;
+	vector_t v[3], w, w_;
-	point_t p;
+	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);
@@ -418,6 +498,16 @@ void drawArc(DrawingContext *ctx, const char *word, vector_t start, vector_type_
 		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);
 
@@ -434,6 +524,16 @@ void drawArc(DrawingContext *ctx, const char *word, vector_t start, vector_type_
 				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);
 
@@ -441,6 +541,11 @@ void drawArc(DrawingContext *ctx, const char *word, vector_t start, vector_type_
 	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)
@@ -506,10 +611,12 @@ char *conjugate_word(const char *word, int modifier, const char *conj, char *buf
 	return buffer;
 }
 
-void drawCurvedBox(DrawingContext *ctx, int base, const char *conj)
+void drawCurvedBox(DrawingContext *ctx, int base, const char *conj, int style)
 {
-	vector_t p[6][3];
+	vector_t p[10][3];
 	vector_t l[2][3];
+	vector_t corner1, corner2;
+	vector_t tmp1, tmp2;
 	char word[100];
 	int modifier = base - 'A';
 
@@ -525,21 +632,64 @@ void drawCurvedBox(DrawingContext *ctx, int base, const char *conj)
 	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("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]);
 
+	// main conic
 	conjugate_word("ab", modifier, conj, word);
-	drawArc(ctx, word, p[0][0], VT_POINT, p[2][0], VT_POINT, p[1][0], 0);
+	drawArcWithOutput(ctx, word, p[0][0], VT_POINT, p[2][0], VT_POINT, p[1][0], 0, &tmp1, &tmp2, style != 1);
-	conjugate_word("bcab", modifier, conj, word);
+	if(style == 2)
-	drawArc(ctx, word, p[2][0], VT_POINT, l[1][0], VT_LINE, p[4][0], 1);
+		drawSegment(ctx, tmp1, tmp2);
-	conjugate_word("ab", modifier, conj, word);
+	if(style == 3) {
-	drawArc(ctx, word, p[1][0], VT_POINT, p[3][0], VT_POINT, p[0][0], 0);
+		drawVector(ctx, tmp1);
-	conjugate_word("abcaba", modifier, conj, word);
+		drawVector(ctx, tmp2);
-	drawArc(ctx, word, p[3][0], VT_POINT, l[0][0], VT_LINE, p[5][0], 1);
+	}
 
-	drawCovector(ctx, l[0][0]);
+	conjugate_word("ab", modifier, conj, word);
-	drawCovector(ctx, l[1][0]);
+	drawArcWithOutput(ctx, word, p[1][0], VT_POINT, p[3][0], VT_POINT, p[0][0], 0, &tmp1, &tmp2, style != 1);
+	if(style == 2)
+		drawSegment(ctx, tmp1, tmp2);
+	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)
+		drawSegment(ctx, tmp1, tmp2);
+
+	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)
+		drawSegment(ctx, tmp1, tmp2);
+	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);
+	}
 }
 
 
@@ -547,18 +697,119 @@ 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]);
 
-	fixedPoints(ctx, "abc", p[3]);
+	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) {
+	cairo_set_source_rgb(C, 0.6, 0.6, 1);
+	drawRotationOrbit(ctx, "bcabcb", p[1][0]); // bcC
+	drawRotationOrbit(ctx, "abcabcba", p[0][0]); // abcC
+	drawRotationOrbit(ctx, "bcabcabacb", p[1][0]); // bcabC''
+	drawRotationOrbit(ctx, "bacabcacab", p[3][0]); // bacaC'
+	drawRotationOrbit(ctx, "bcacabcacacb", p[4][0]); // bcacaC' bcacabacb
+	}
+
+	cairo_set_source_rgb(C, 1, 0, 1);
+//	drawRotationOrbit(ctx, "bacabcacab", p[3][0]); // ababcba
+	cairo_set_source_rgb(C, 0, 0, 0);
+	fixedPoints(ctx, "abababcbaba", p[3]);
+//	drawRotationOrbit(ctx, "abababcabcbababa", p[3][0]); //  bab abc bab
+
+	cairo_set_source_rgb(C, 0, 0, 1);
+//	fixedPoints(ctx, "cab", p[3]);
+//	drawRotationOrbit(ctx, "cabc", p[3][0]);
+//	fixedPoints(ctx, "bca", p[3]);
+//	drawRotationOrbit(ctx, "bcabcb", p[3][0]);
+//	fixedPoints(ctx, "bc abc cb", p[3]);
+//	drawRotationOrbit(ctx, "bcabcb", p[3][0]);
+
+	fixedPoints(ctx, "bc bca cb", p[3]);
+//	drawRotationOrbit(ctx, "bcbcacbc", p[3][0]);
+
+	/*
+	cairo_set_source_rgb(C, 0, 0, 0);
+	strncpy(word,"abc",100);
+	for(int i = 0; i < 9; i++) {
+		conjugate_word(word, 0, "ab", word2);
+		strncpy(word, word2, 100);
+		fixedPoints(ctx, word, ptmp);
+		drawVector(ctx, ptmp[0]);
+//		drawVector(ctx, ptmp[2]);
+	}
+
+	strncpy(word,"bca",100);
+	for(int i = 0; i < 9; i++) {
+		conjugate_word(word, 0, "ab", word2);
+		strncpy(word, word2, 100);
+		fixedPoints(ctx, word, ptmp);
+		drawVector(ctx, ptmp[0]);
+//		drawVector(ctx, ptmp[2]);
+	}
+
+
+	strncpy(word,"abc",100);
+	for(int i = 0; i < 9; i++) {
+		conjugate_word(word, 0, "bc", word2);
+		strncpy(word, word2, 100);
+		fixedPoints(ctx, word, ptmp);
+		drawVector(ctx, ptmp[0]);
+	}
+
+	strncpy(word,"cab",100);
+	for(int i = 0; i < 9; i++) {
+		conjugate_word(word, 0, "bc", word2);
+		strncpy(word, word2, 100);
+		fixedPoints(ctx, word, ptmp);
+		drawVector(ctx, ptmp[0]);
+	}
+
+	strncpy(word,"cab",100);
+	for(int i = 0; i < 9; i++) {
+		conjugate_word(word, 0, "ca", word2);
+		strncpy(word, word2, 100);
+		fixedPoints(ctx, word, ptmp);
+		drawVector(ctx, ptmp[0]);
+	}
+
+	strncpy(word,"abc",100);
+	for(int i = 0; i < 9; i++) {
+		conjugate_word(word, 0, "ca", word2);
+		strncpy(word, word2, 100);
+		fixedPoints(ctx, word, ptmp);
+		drawVector(ctx, ptmp[0]);
+		}
+	*/
+
+	/*
+	cairo_set_source_rgb(C, 1, 0, 0);
+	drawVector(ctx, p[0][0]);
+	cairo_set_source_rgb(C, 0, 0.6, 0);
+	drawVector(ctx, p[1][0]);
+	cairo_set_source_rgb(C, 0, 0, 1);
+	drawVector(ctx, p[2][0]);
+	*/
+
+	/*
 	fixedPoints(ctx, "ab abc ba", p[4]);
 	fixedPoints(ctx, "abab abc baba", p[5]);
 	fixedPoints(ctx, "ababab abc bababa", p[6]);
@@ -567,7 +818,6 @@ void drawBoxes(DrawingContext *ctx)
 	fixedPoints(ctx, "bababa abc ababab", p[9]);
 	fixedPoints(ctx, "baba abc abab", p[10]);
 	fixedPoints(ctx, "ba abc ab", p[11]);
-
 	fixedPoints(ctx, "bca", p[12]);
 	fixedPoints(ctx, "b abc b", p[13]);
 	fixedPoints(ctx, "bab abc bab", p[14]);
@@ -577,43 +827,50 @@ void drawBoxes(DrawingContext *ctx)
 	fixedPoints(ctx, "ababab bca bababa", p[18]);
 	fixedPoints(ctx, "abab bca baba", p[19]);
 	fixedPoints(ctx, "ab bca ba", p[20]);
+	*/
 
+//	initializeTriangleGenerators(gen, ctx->cartan);
 
-	initializeTriangleGenerators(gen, ctx->cartan);
+//	for(int i = 0; i < 22; i++) LOOP(j) l[i][j] = cross(p[i][(3-j)%3], p[i][(4-j)%3]);
-
-	for(int i = 0; i < 22; 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_line_width(C, 2.0/ctx->dim->scalefactor);
+	/*
+	gsl_matrix_set(frame, 0, 0, 2.0);
+	gsl_matrix_set(frame, 0, 1, 0.0);
+	gsl_matrix_set(frame, 0, 2, 1.0);
+	gsl_matrix_set(frame, 1, 0, -1.0);
+	gsl_matrix_set(frame, 1, 1, sqrt(3));
+	gsl_matrix_set(frame, 1, 2, 1.0);
+	gsl_matrix_set(frame, 2, 0, -1.0);
+	gsl_matrix_set(frame, 2, 1, -sqrt(3));
+	gsl_matrix_set(frame, 2, 2, 1.0);*/
+//	drawRotationOrbitFrame(ctx, frame, p[0][0]);
 
-	cairo_set_source_rgb(C, 0, 0, 0);
-	drawRotationOrbit(ctx, "ab", p[0][0]);
 //	drawRotationOrbit(ctx, "bc", p[0][0]);
 
-	cairo_set_source_rgb(C, 0.5, 0.5, 1);
 //	drawRotationOrbit(ctx, "ca", p[0][0]);
 
+/*
 	for(int i = 0; i < 18; i++) {
 		if(i == 0)
 			cairo_set_source_rgb(C, 1, 0, 0);
-		else if(i == 8 || i == 10)
+		else if(i == 8)
 			cairo_set_source_rgb(C, 0, 0, 1);
 		else if(i == 9)
 			cairo_set_source_rgb(C, 0, 0.6, 0);
 		else
 			cairo_set_source_rgb(C, 0, 0, 0);
 		drawVector(ctx, p[3+i][0]);
-		drawCovector(ctx, l[3+i][0]);
+//		drawCovector(ctx, l[3+i][0]);
 }
-
+*/
-	cairo_set_source_rgb(C, 0, 0, 1.0);
 
 //	drawRotationOrbit(ctx, "ab", cross(l[0][0], l[2][1]));
 
 //	drawRotationOrbit(ctx, "abca", p[0][0]);
 
 	cairo_restore(C);
-	releaseTempMatrices(ctx->ws, 4);
+	releaseTempMatrices(ctx->ws, 5);
 }
 
 void drawBoxes2(DrawingContext *ctx)
@@ -624,6 +881,216 @@ void drawBoxes2(DrawingContext *ctx)
 	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, 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);
+
+	cairo_set_source_rgb(C, 0, 0.8, 0.5);
+//	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 >= 4) {
+		drawCurvedBox(ctx, 'C', "b", 2);
+		drawCurvedBox(ctx, 'C', "bab", 2);
+		drawCurvedBox(ctx, 'C', "babab", 2);
+	}
+
+	if(ctx->mode >= 5) {
+	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', "abababca", 2);
+	drawCurvedBox(ctx, 'B', "abababcaca", 2);
+	drawCurvedBox(ctx, 'B', "abababa", 2);
+	drawCurvedBox(ctx, 'B', "abababaca", 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);
+	drawCurvedBox(ctx, 'B', "bababca", 2);
+	drawCurvedBox(ctx, 'B', "bababcaca", 2);
+	drawCurvedBox(ctx, 'B', "bababa", 2);
+	drawCurvedBox(ctx, 'B', "bababaca", 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];
@@ -680,6 +1147,7 @@ void drawBoxes2(DrawingContext *ctx)
 
 	cairo_set_source_rgb(C, 0, 0, 0);
 	drawCovector(ctx, rotation_line);
+*/
 
 //	for(int j = 0; j < 5; j++)
 //		drawCovector(ctx, reflection_line[j]);
@@ -773,12 +1241,12 @@ void drawDualLimitCurve(DrawingContext *ctx)
 	cairo_t *C = ctx->cairo;
 
 	cairo_save(C);
-	cairo_set_source_rgb(C, 0, 0, 0);
+	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]);
@@ -800,7 +1268,6 @@ void drawDualLimitCurve(DrawingContext *ctx)
 	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]);
@@ -830,25 +1297,43 @@ void drawDualLimitCurve(DrawingContext *ctx)
 	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]);
+//		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, 0.0, 0.0, 0.0);
+//	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];
@@ -873,7 +1358,7 @@ void drawLimitCurve(DrawingContext *ctx)
 			p.y = ctx->limit_curve[3*i+1];
 
 			if(isInsideBB(ctx, p)) {
-				cairo_arc(C, p.x, p.y, 0.5/ctx->dim->scalefactor, 0, 2*M_PI);
+				cairo_arc(C, p.x, p.y, 2.0/ctx->dim->scalefactor, 0, 2*M_PI);
 				cairo_close_path(C);
 				cairo_fill(C);
 			}
@@ -883,12 +1368,81 @@ void drawLimitCurve(DrawingContext *ctx)
 	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);
+	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, 1, 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]);
+
+	//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);
+
+	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 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);
+	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", log(ctx->parameter), ctx->parameter);
+	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);
 }
 
@@ -931,6 +1485,14 @@ void draw(DrawingContext *ctx)
 		if(ctx->show_boxes2)
 			drawBoxes2(ctx);
 
+		if(ctx->show_marking)
+		{
+			cairo_set_source_rgb(C, 1, 0, 1);
+			drawPoint(ctx, ctx->marking);
+		}
+
+		if(ctx->show_coxeter_orbit)
+			drawCoxeterOrbit(ctx);
 	}
 
 	cairo_identity_matrix(C); // text is in screen coordinates

limit_set.c

@@ -44,6 +44,7 @@ int computeLimitCurve(DrawingContext *ctx)
 	int success = 0;
 
 	int column = ctx->use_repelling ? 2 : 0;
+	double x,y;
 //	int column = 1;
 	ctx->limit_curve_count = -1;
 
@@ -52,7 +53,7 @@ int computeLimitCurve(DrawingContext *ctx)
 	initializeTriangleGenerators(gen, cartan_pos);
 	gsl_matrix_set_identity(elements[0]);
 	for(int i = 1; i < ctx->n_group_elements; i++)
-		multiply(elements[group[i].parent->id], gen[group[i].letter], elements[i]);
+		multiply(gen[group[i].letter], elements[group[i].parent->id], elements[i]);
 	diagonalize_symmetric_form(cartan_pos, cob_pos, ws);
 	multiply_many(ws, coxeter_pos, 3, gen[0], gen[1], gen[2]);
 	int ev_count_pos = real_eigenvectors(coxeter_pos, coxeter_fixedpoints_pos, ws);
@@ -71,7 +72,7 @@ int computeLimitCurve(DrawingContext *ctx)
 	initializeTriangleGenerators(gen, ctx->cartan);
 	gsl_matrix_set_identity(elements[0]);
 	for(int i = 1; i < ctx->n_group_elements; i++)
-		multiply(elements[group[i].parent->id], gen[group[i].letter], elements[i]);
+		multiply(gen[group[i].letter], elements[group[i].parent->id], elements[i]);
 
 	multiply_many(ws, coxeter, 3, gen[0], gen[1], gen[2]);
 	int ev_count = real_eigenvectors(coxeter, coxeter_fixedpoints, ws);
@@ -84,8 +85,19 @@ int computeLimitCurve(DrawingContext *ctx)
 	for(int i = 0; i < ctx->n_group_elements; i++) {
 		multiply_many(ws, fixedpoints, 3, ctx->cob, elements[i], coxeter_fixedpoints);
 
-		ctx->limit_curve[3*i  ] = gsl_matrix_get(fixedpoints, 0, column)/gsl_matrix_get(fixedpoints, 2, column);
+		x = ctx->limit_curve[3*i  ] = gsl_matrix_get(fixedpoints, 0, column)/gsl_matrix_get(fixedpoints, 2, column);
-		ctx->limit_curve[3*i+1] = gsl_matrix_get(fixedpoints, 1, column)/gsl_matrix_get(fixedpoints, 2, column);
+		y = ctx->limit_curve[3*i+1] = gsl_matrix_get(fixedpoints, 1, column)/gsl_matrix_get(fixedpoints, 2, column);
+
+		if((x - ctx->marking.x)*(x - ctx->marking.x) + (y - ctx->marking.y)*(y - ctx->marking.y) < 25e-10)
+		{
+			printf("limit point %d is close: length %d, ", i, group[i].length);
+			for(groupelement_t *cur = &group[i]; cur->parent; cur = cur->parent)
+				fputc('a' + cur->letter, stdout); // bcbcbca, bacbcacab, bc bca cb
+			fputc('\n',stdout);
+		}
+
+		// bca abc acb = abc
+
 	}
 
 	qsort(ctx->limit_curve, ctx->n_group_elements, 3*sizeof(double), compareAngle);

linalg.c

@@ -242,6 +242,30 @@ eigenvectors_out:
 	return success;
 }
 
+int real_eigenvalues(gsl_matrix *g, gsl_vector *eval_real, workspace_t *ws)
+{
+	gsl_matrix *g_ = getTempMatrix(ws);
+
+	gsl_matrix_memcpy(g_, g);
+	gsl_eigen_nonsymmv_params(0, ws->work_nonsymmv);
+	int r = gsl_eigen_nonsymmv(g_, ws->eval_complex, ws->evec_complex, ws->work_nonsymmv);
+	ERROR(r, "gsl_eigen_nonsymmv failed!\n");
+
+	gsl_eigen_nonsymmv_sort(ws->eval_complex, ws->evec_complex, GSL_EIGEN_SORT_ABS_DESC);
+
+	int real = 0;
+
+	for(int i = 0; i < ws->n; i++) {
+		if(FCMP(GSL_IMAG(gsl_vector_complex_get(ws->eval_complex, i)), 0) == 0) {// real
+			gsl_vector_set(eval_real, real, GSL_REAL(gsl_vector_complex_get(ws->eval_complex, i)));
+			real++;
+		}
+	}
+
+	releaseTempMatrices(ws, 1);
+	return real;
+}
+
 // only fills in the real eigenvectors and returns their count
 int real_eigenvectors(gsl_matrix *g, gsl_matrix *evec_real, workspace_t *ws)
 {

linalg.h

@@ -50,6 +50,7 @@ double trace(gsl_matrix *g);
 double determinant(gsl_matrix *g, workspace_t *ws);
 int eigenvectors(gsl_matrix *g, gsl_matrix *evec, workspace_t *ws);
 int real_eigenvectors(gsl_matrix *g, gsl_matrix *evec, workspace_t *ws);
+int real_eigenvalues(gsl_matrix *g, gsl_vector *evec, workspace_t *ws);
 void eigenvectors_symm(gsl_matrix *g, gsl_vector *eval, gsl_matrix *evec, workspace_t *ws);
 int diagonalize_symmetric_form(gsl_matrix *A, gsl_matrix *cob, workspace_t *ws);
 void projective_frame(gsl_vector **vertices, gsl_matrix *result, workspace_t *ws);

main.c

@@ -15,16 +15,19 @@
 DrawingContext *screen_context;
 
 // setup everything except cairo and dim, which will be provided by the graphics system
-void setupContext(DrawingContext *ctx)
+void setupContext(DrawingContext *ctx, int argc, char *argv[])
 {
 	ctx->n_group_elements = NUM_GROUP_ELEMENTS;
-	ctx->p[0] = 9;
+	ctx->p[0] = atoi(argv[1]);
-	ctx->p[1] = 9;
+	ctx->p[1] = atoi(argv[2]);
-	ctx->p[2] = 9;
+	ctx->p[2] = atoi(argv[3]);
-	ctx->k[0] = 4;
+	ctx->k[0] = atoi(argv[4]);
-	ctx->k[1] = 4;
+	ctx->k[1] = atoi(argv[5]);
-	ctx->k[2] = 4;
+	ctx->k[2] = atoi(argv[6]);
-	ctx->parameter = 5.35;
+	if(argc > 7)
+		ctx->parameter = atof(argv[7]);
+	else
+		ctx->parameter = 1.0;
 //	ctx->parameter = 2.77;
 //	ctx->parameter = 0.1;
 	ctx->show_boxes = 0;
@@ -35,9 +38,14 @@ void setupContext(DrawingContext *ctx)
 	ctx->show_limit= 1;
 	ctx->show_dual_limit= 0;
 	ctx->show_text = 1;
+	ctx->mode = 0;
 	ctx->use_rotation_basis = 0;
-	ctx->limit_with_lines = 1;
+	ctx->limit_with_lines = 0;
 	ctx->use_repelling = 0;
+	ctx->show_marking = 1;
+	ctx->marking.x = -0.73679;
+	ctx->marking.y = -0.01873;
+	ctx->show_coxeter_orbit = 0;
 
 	ctx->limit_curve = malloc(3*ctx->n_group_elements*sizeof(double));
 	ctx->limit_curve_count = -1;
@@ -137,21 +145,7 @@ void updateMatrices(DrawingContext *ctx)
 
 	gsl_matrix *tmp = getTempMatrix(ctx->ws);
 
-	if(ctx->use_rotation_basis % 4 == 0) {
+	if(ctx->use_rotation_basis % 5 == 0) {
-		gsl_matrix_memcpy(ctx->cob, ctx->cartan); // is this a good choice of basis for any reason?
-
-		gsl_matrix_set(tmp, 0, 0, 1.0);
-		gsl_matrix_set(tmp, 0, 1, -1.0);
-		gsl_matrix_set(tmp, 0, 2, 0.0);
-		gsl_matrix_set(tmp, 1, 0, 1.0);
-		gsl_matrix_set(tmp, 1, 1, 1.0);
-		gsl_matrix_set(tmp, 1, 2, 1.0);
-		gsl_matrix_set(tmp, 2, 0, 0.0);
-		gsl_matrix_set(tmp, 2, 1, -1.0);
-		gsl_matrix_set(tmp, 2, 2, 1.0);
-		multiply_left(tmp, ctx->cob, ctx->ws);
-
-		/*
 		gsl_matrix_set(tmp, 0, 0, 0.0);
 		gsl_matrix_set(tmp, 0, 1, sqrt(3.0)/2.0);
 		gsl_matrix_set(tmp, 0, 2, -sqrt(3.0)/2.0);
@@ -162,13 +156,12 @@ void updateMatrices(DrawingContext *ctx)
 		gsl_matrix_set(tmp, 2, 1, 1.0);
 		gsl_matrix_set(tmp, 2, 2, 1.0);
 		gsl_matrix_memcpy(ctx->cob, tmp);
-		*/
+	} else if(ctx->use_rotation_basis % 5 == 1) {
-
+		gsl_matrix_memcpy(ctx->cob, ctx->cartan); // is this a good choice of basis for any reason?
-//		gsl_matrix_set_identity(ctx->cob); // is this a good choice of basis for any reason?
+	} else if(ctx->use_rotation_basis % 5 == 2) {
-	} else if(ctx->use_rotation_basis % 4 == 1) {
 		computeRotationMatrix(ctx, tmp, "ba");
 		invert(tmp, ctx->cob, ctx->ws);
-	} else if(ctx->use_rotation_basis % 4 == 2) {
+	} else if(ctx->use_rotation_basis % 5 == 3) {
 		computeBoxTransform(ctx, "bca", "abc", ctx->cob);
 //		computeBoxTransform(ctx, "cab", "bca", ctx->cob);
 //		computeBoxTransform(ctx, "acb", "cba", ctx->cob);
@@ -180,6 +173,21 @@ void updateMatrices(DrawingContext *ctx)
 	releaseTempMatrices(ctx->ws, 1);
 }
 
+void output_info(DrawingContext *ctx)
+{
+	vector_t p[4][3];
+	point_t pt;
+
+	fixedPoints(ctx, "abc", p[0]);
+	fixedPoints(ctx, "bca", p[1]);
+	fixedPoints(ctx, "cab", p[2]);
+
+	pt = vectorToPoint(ctx, p[0][0]);
+	printf("(abc)-+ = (%f %f)\n", pt.x, pt.y);
+	pt = vectorToPoint(ctx, p[1][0]);
+	printf("(bca)-+ = (%f %f)\n", pt.x, pt.y);
+}
+
 void print(DrawingContext *screen)
 {
 	DrawingContext file;
@@ -216,7 +224,22 @@ int processEvent(GraphicsInfo *info, XEvent *ev)
 	unsigned long key;
 	char filename[100];
 
+//	fprintf(stderr, "Event: %d\n", ev->type);
+
 	switch(ev->type) {
+	case ButtonPress:
+		state = ev->xbutton.state & (ShiftMask | LockMask | ControlMask);
+
+		if(ev->xbutton.button == 1 && state & ShiftMask) {
+			screen_context->marking.x = (double)ev->xbutton.x;
+			screen_context->marking.y = (double)ev->xbutton.y;
+			printf("mouse button pressed: %f, %f\n", screen_context->marking.x, screen_context->marking.y);
+			cairo_set_matrix(screen_context->cairo, &screen_context->dim->matrix);
+			cairo_device_to_user(screen_context->cairo, &screen_context->marking.x, &screen_context->marking.y);
+			printf("mouse button pressed transformed: %f, %f\n", screen_context->marking.x, screen_context->marking.y);
+			return STATUS_REDRAW;
+		}
+		break;
 
 	case KeyPress:
 		state = ev->xkey.state & (ShiftMask | LockMask | ControlMask);
@@ -273,6 +296,9 @@ int processEvent(GraphicsInfo *info, XEvent *ev)
 			printf("matrix.yy = %f;\n", info->dim->matrix.yy);
 			printf("matrix.y0 = %f;\n", info->dim->matrix.y0);
 			break;
+		case 'i':
+			output_info(screen_context);
+			break;
 		case 'b':
 			TOGGLE(screen_context->show_boxes);
 			break;
@@ -348,6 +374,12 @@ int processEvent(GraphicsInfo *info, XEvent *ev)
 		case 't':
 			TOGGLE(screen_context->show_text);
 			break;
+		case 'c':
+			TOGGLE(screen_context->show_coxeter_orbit);
+			break;
+		case '1': case '2': case '3': case '4': case '5': case '6': case '7': case '8': case '9': case '0':
+			screen_context->mode = key - '0';
+			break;
 		}
 
 		return STATUS_REDRAW;
@@ -356,12 +388,12 @@ int processEvent(GraphicsInfo *info, XEvent *ev)
 	return STATUS_NOTHING;
 }
 
-int main()
+int main(int argc, char *argv[])
 {
 	GraphicsInfo *info;
 
 	screen_context = malloc(sizeof(DrawingContext));
-	setupContext(screen_context);
+	setupContext(screen_context, argc, argv);
 	updateMatrices(screen_context);
 	computeLimitCurve(screen_context);
 

main.h

@@ -39,8 +39,12 @@ typedef struct {
 	int show_limit;
 	int show_dual_limit;
 	int show_text;
+	int mode;
 	int use_rotation_basis;
 	int limit_with_lines;
+	int show_marking;
+	point_t marking;
+	int show_coxeter_orbit;
 	int use_repelling;
 	gsl_matrix *cartan, *cob;
 
@@ -70,6 +74,7 @@ vector_t cross(vector_t a, vector_t b);
 int fixedPoints(DrawingContext *ctx, const char *word, vector_t *out);
 void drawPoint(DrawingContext *ctx, point_t p);
 void drawSegment2d(DrawingContext *ctx, point_t a, point_t b);
+point_t vectorToPoint(DrawingContext *ctx, vector_t v);
 void drawVector(DrawingContext *ctx, vector_t v);
 void drawCovector(DrawingContext *ctx, vector_t v);
 void drawSegment(DrawingContext *ctx, vector_t a, vector_t b);
@@ -87,7 +92,7 @@ void drawText(DrawingContext *ctx);
 void draw(DrawingContext *ctx);
 
 // implemented in main.c
-void setupContext(DrawingContext *ctx);
+void setupContext(DrawingContext *ctx, int argc, char *argv[]);
 void destroyContext(DrawingContext *ctx);
 void print(DrawingContext *screen);
 int processEvent(GraphicsInfo *info, XEvent *ev);