simplify image generation

complex_anosov.c

@@ -161,10 +161,17 @@ int main(int argc, char *argv[])
 
 	if(mode == MODE_HELP) {
 		fprintf(stderr, "Usage: %s <help|evs|summary|trace_ids> [arguments]\n", argv[0]);
-		fprintf(stderr, "%s help                           display this page\n", argv[0]);
+		fprintf(stderr, "%s help                                          display this page\n", argv[0]);
-		fprintf(stderr, "%s evs <n> <q1> <q2> <q3> <treal> <timag>        enumerate group and output unique (log) eigenvalue triples\n", argv[0]);
+		fprintf(stderr, "%s evs       <n> <q1> <q2> <q3> <treal> <timag>  enumerate group and output unique (log) eigenvalue triples\n", argv[0]);
-		fprintf(stderr, "%s summary <n> <q1> <q2> <q3> <treal> <timag>    only output max slope etc.\n", argv[0]);
+		fprintf(stderr, "%s summary   <n> <q1> <q2> <q3> <treal> <timag>  only output max slope etc.\n", argv[0]);
 		fprintf(stderr, "%s trace_ids <n> <q1> <q2> <q3> <treal> <timag>  list of ids of unique traces\n", argv[0]);
+		fprintf(stderr, "\n");
+		fprintf(stderr, "This program computes the traces and inverse traces of the first n elements of a SL(3,C) representation of the\n");
+		fprintf(stderr, "triangle reflection group with corner orders (5,5,5). The representation is given by the parameters q1,q2,q3,\n");
+		fprintf(stderr, "treal, and timag. q1,q2,q3 can each be 1 or 2 and determine the connected component. (1,1,1) is Hitchin and\n");
+		fprintf(stderr, "(2,2,2) is Barbot. treal and timag are the components of the complex parameter and have to be given as rational\n");
+		fprintf(stderr, "numbers. If the environment variable IDLIST is set to a filename, a list of elements can be read from this file.\n");
+		fprintf(stderr, "Such a list can be precomputed with the \"trace_ids\" subcommand and speeds up the computation considerably.\n");
 		return 0;
 	}
 

make_picture.py

@@ -3,65 +3,43 @@
 import sys
 import math
 
-def sharpen(x):
-	alpha = 1
-	y = abs(2*x-1)**alpha # between 0 and 1
-	if x > 0.499 and x < 0.501:
-		return 0.5
-	elif x > 0.5:
-		return (y+1)/2
-	else:
-		return (1-y)/2
-
 f = open(sys.argv[1])
 lines = [x.split() for x in f]
 f.close()
 
-res1 = int(sys.argv[2]) # 400 pixel per unit
+res = int(sys.argv[2]) # pixel per unit
-res2 = int(sys.argv[3]) # 50 pixel in picture (acutally one quadrant)
 
-data = {(round(float(l[0])*res1), round(float(l[1])*res1)) : float(l[5]) for l in lines}
+data = {(round(float(l[0])*res), round(float(l[1])*res)) : float(l[5]) for l in lines}
 data[(0,0)] = 2.0
 
+xmin = min([p[0] for p in data.keys()])
+xmax = max([p[0] for p in data.keys()])
+ymin = min([p[1] for p in data.keys()])
+ymax = max([p[1] for p in data.keys()])
+yrange=max([-ymin,ymax])
+
 print("P3")
-print("1000 1000")
+print("{dx:d} {dy:d}".format(dx=xmax-xmin+1, dy=2*yrange+1))
 print("255")
 
-for i in range (-500,500):
+for i in range(-yrange,yrange+1):
-	for j in range(-500,500):
+	for j in range(xmin,xmax+1):
-		x = j/500*res2
+		x = j
-		y = i/500*res2
+		y = i if i >= ymin and i <= ymax else -i
 
-		if y < 0:
+		if not (x,y) in data:
-			y = -y
-
-		x0 = math.floor(x)
-		y0 = math.floor(y)
-		x1 = math.ceil(x)
-		y1 = math.ceil(y)
-		tx = sharpen(x-x0)
-		ty = sharpen(y-y0)
-
-		if not (x0,y0) in data or not (x0,y1) in data or not (x1,y0) in data or not (x1,y1) in data:
 			value = 0
 		else:
-			value = 0.0
+			value = data[(x,y)]-1
-			value += data[(x0,y0)]*(1-tx)*(1-ty)
-			value += data[(x0,y1)]*(1-tx)*ty
-			value += data[(x1,y0)]*tx*(1-ty)
-			value += data[(x1,y1)]*tx*ty
-			value -= 1
 
 		value = 0 if value < 0 else 1 if value > 1 else value
 
-		r = round(255*math.sqrt(value))
+		r = round(255*value**0.5)
 		g = round(255*(value)**3)
-		b = round(255*math.sin(2*math.pi*(value)))
+		b = round(255*(math.sin(2*math.pi*value)))
 
 		r = 0 if r < 0 else 255 if r > 255 else r
 		g = 0 if g < 0 else 255 if g > 255 else g
 		b = 0 if b < 0 else 255 if b > 255 else b
 
 		print("%d %d %d" % (r,g,b))
-
-#print(data)

qext.c

@@ -37,16 +37,6 @@ static void qext_init_type(struct qext_type *type)
 	}
 }
 
-struct qext_type *qext_newtype(int rank, const int *coeffs)
-{
-	struct qext_type *type = malloc(sizeof(struct qext_type));
-	type->rank = rank;
-	type->integer_coeffs = coeffs;
-	qext_init_type(type);
-
-	return type;
-}
-
 void qext_init(qext_number x, struct qext_type *type)
 {
 	if(type->coeffs == NULL) // uninitialized default type

qext.h

@@ -20,7 +20,6 @@ extern struct qext_type *QT_TRIVIAL;
 extern struct qext_type *QT_SQRT5;
 extern struct qext_type *QT_GAUSS_SQRT5;
 
-struct qext_type *qext_newtype(int rank, const int *coeffs);
 void qext_init(qext_number x, struct qext_type *type);
 void qext_clear(qext_number x);
 void qext_set(qext_number x, qext_number y);