kugel: Reorganize figures directory, add tikz spherical coordinates and flux

8 files changed, 0 insertions, 853 deletions

diff --git a/buch/papers/kugel/images/Makefile b/buch/papers/kugel/images/Makefile
deleted file mode 100644
index 4226dab..0000000
--- a/buch/papers/kugel/images/Makefile
+++ /dev/null
@@ -1,30 +0,0 @@
-#
-# Makefile -- build images
-#
-# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-#
-all: curvature.jpg spherecurve.jpg
-
-curvature.inc:	curvgraph.m
-	octave curvgraph.m
-
-curvature.png:	curvature.pov curvature.inc
-	povray +A0.1 +W1920 +H1080 +Ocurvature.png curvature.pov
-
-curvature.jpg:	curvature.png
-	convert curvature.png -density 300 -units PixelsPerInch curvature.jpg
-
-spherecurve2.inc:	spherecurve.m
-	octave spherecurve.m
-
-spherecurve.png:	spherecurve.pov spherecurve.inc
-	povray +A0.1 +W1080 +H1080 +Ospherecurve.png spherecurve.pov
-
-spherecurve.jpg:	spherecurve.png
-	convert spherecurve.png -density 300 -units PixelsPerInch spherecurve.jpg
-
-spherecurve:	spherecurve.cpp
-	g++ -o spherecurve -g -Wall -O spherecurve.cpp
-
-spherecurve.inc:	spherecurve
-	./spherecurve
diff --git a/buch/papers/kugel/images/curvature.maxima b/buch/papers/kugel/images/curvature.maxima
deleted file mode 100644
index 6313642..0000000
--- a/buch/papers/kugel/images/curvature.maxima
+++ /dev/null
@@ -1,6 +0,0 @@
-
-f: exp(-r^2/sigma^2)/sigma;
-laplacef: ratsimp(diff(r * diff(f,r), r) / r);
-f: exp(-r^2/(2*sigma^2))/(sqrt(2)*sigma);
-laplacef: ratsimp(diff(r * diff(f,r), r) / r);
-
diff --git a/buch/papers/kugel/images/curvature.pov b/buch/papers/kugel/images/curvature.pov
deleted file mode 100644
index 3b15d77..0000000
--- a/buch/papers/kugel/images/curvature.pov
+++ /dev/null
@@ -1,139 +0,0 @@
-//
-// curvature.pov
-//
-// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-//
-
-#version 3.7;
-#include "colors.inc"
-
-global_settings {
-	assumed_gamma 1
-}
-
-#declare imagescale = 0.09;
-
-camera {
-	location <10, 10, -40>
-	look_at <0, 0, 0>
-	right 16/9 * x * imagescale
-	up y * imagescale
-}
-
-light_source {
-	<-10, 10, -40> color White
-	area_light <1,0,0> <0,0,1>, 10, 10
-	adaptive 1
-	jitter
-}
-
-sky_sphere {
-	pigment {
-		color rgb<1,1,1>
-	}
-}
-
-//
-// draw an arrow from <from> to <to> with thickness <arrowthickness> with
-// color <c>
-//
-#macro arrow(from, to, arrowthickness, c)
-#declare arrowdirection = vnormalize(to - from);
-#declare arrowlength = vlength(to - from);
-union {
-	sphere {
-		from, 1.1 * arrowthickness
-	}
-	cylinder {
-		from,
-		from + (arrowlength - 5 * arrowthickness) * arrowdirection,
-		arrowthickness
-	}
-	cone {
-		from + (arrowlength - 5 * arrowthickness) * arrowdirection,
-		2 * arrowthickness,
-		to,
-		0
-	}
-	pigment {
-		color c
-	}
-	finish {
-		specular 0.9
-		metallic
-	}
-}
-#end
-
-arrow(<-3.1,0,0>, <3.1,0,0>, 0.01, White)
-arrow(<0,-1,0>, <0,1,0>, 0.01, White)
-arrow(<0,0,-2.1>, <0,0,2.1>, 0.01, White)
-
-#include "curvature.inc"
-
-#declare sigma = 1;
-#declare s = 1.4;
-#declare N0 = 0.4;
-#declare funktion = function(r) {
-	(exp(-r*r/(sigma*sigma)) / sigma
-	-
-	exp(-r*r/(2*sigma*sigma)) / (sqrt(2)*sigma)) / N0
-};
-#declare hypot = function(xx, yy) { sqrt(xx*xx+yy*yy) };
-
-#declare Funktion = function(x,y) { funktion(hypot(x+s,y)) - funktion(hypot(x-s,y)) };
-#macro punkt(xx,yy)
-	<xx, Funktion(xx, yy), yy>
-#end
-
-#declare griddiameter = 0.006;
-union {
-	#declare xmin = -3;
-	#declare xmax = 3;
-	#declare ymin = -2;
-	#declare ymax = 2;
-
-
-	#declare xstep = 0.2;
-	#declare ystep = 0.02;
-	#declare xx = xmin;
-	#while (xx < xmax + xstep/2)
-		#declare yy = ymin;
-		#declare P = punkt(xx, yy);
-		#while (yy < ymax - ystep/2)
-			#declare yy = yy + ystep;
-			#declare Q = punkt(xx, yy);
-			sphere { P, griddiameter }
-			cylinder { P, Q, griddiameter }
-			#declare P = Q;
-		#end
-		sphere { P, griddiameter }
-		#declare xx = xx + xstep;
-	#end
-
-	#declare xstep = 0.02;
-	#declare ystep = 0.2;
-	#declare yy = ymin;
-	#while (yy < ymax + ystep/2)
-		#declare xx = xmin;
-		#declare P = punkt(xx, yy);
-		#while (xx < xmax - xstep/2)
-			#declare xx = xx + xstep;
-			#declare Q = punkt(xx, yy);
-			sphere { P, griddiameter }
-			cylinder { P, Q, griddiameter }
-			#declare P = Q;
-		#end
-		sphere { P, griddiameter }
-		#declare yy = yy + ystep;
-	#end
-
-	pigment {
-		color rgb<0.8,0.8,0.8>
-	}
-	finish {
-		metallic
-		specular 0.8
-	}
-}
-
diff --git a/buch/papers/kugel/images/curvgraph.m b/buch/papers/kugel/images/curvgraph.m
deleted file mode 100644
index 75effd6..0000000
--- a/buch/papers/kugel/images/curvgraph.m
+++ /dev/null
@@ -1,140 +0,0 @@
-#
-# curvature.m
-#
-# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-#
-
-global N;
-N = 10;
-
-global sigma2;
-sigma2 = 1;
-
-global s;
-s = 1.4;
-
-global cmax;
-cmax = 0.9;
-global cmin;
-cmin = -0.9;
-
-global Cmax;
-global Cmin;
-Cmax = 0;
-Cmin = 0;
-
-xmin = -3;
-xmax = 3;
-xsteps = 200;
-hx = (xmax - xmin) / xsteps;
-
-ymin = -2;
-ymax = 2;
-ysteps = 200;
-hy = (ymax - ymin) / ysteps;
-
-function retval = f0(r)
-	global sigma2;
-	retval = exp(-r^2/sigma2)/sqrt(sigma2) - exp(-r^2/(2*sigma2))/(sqrt(2*sigma2));
-end
-
-global N0;
-N0 = f0(0)
-N0 = 0.4;
-
-function retval = f1(x,y)
-	global N0;
-	retval = f0(hypot(x, y)) / N0;
-endfunction
-
-function retval = f(x, y)
-	global s;
-	retval = f1(x+s, y) - f1(x-s, y);
-endfunction
-
-function retval = curvature0(r)
-	global sigma2;
-	retval = (
-		-4*(sigma2-r^2)*exp(-r^2/sigma2)
-		+
-		(2*sigma2-r^2)*exp(-r^2/(2*sigma2))
-	) / (sigma2^(5/2));
-endfunction
-
-function retval = curvature1(x, y)
-	retval = curvature0(hypot(x, y));
-endfunction
-
-function retval = curvature(x, y)
-	global s;
-	retval = curvature1(x+s, y) - curvature1(x-s, y);
-endfunction
-
-function retval = farbe(x, y)
-	global Cmax;
-	global Cmin;
-	global cmax;
-	global cmin;
-	c = curvature(x, y);
-	if (c < Cmin) 
-		Cmin = c
-	endif
-	if (c > Cmax) 
-		Cmax = c
-	endif
-	u = (c - cmin) / (cmax - cmin);
-	if (u > 1)
-		u = 1;
-	endif
-	if (u < 0)
-		u = 0;
-	endif
-	color = [ u, 0.5, 1-u ];
-	color = color/max(color);
-	color(1,4) = c/2;
-	retval = color;
-endfunction
-
-function dreieck(fn, A, B, C)
-	fprintf(fn, "\ttriangle {\n");
-	fprintf(fn, "\t    <%.4f,%.4f,%.4f>,\n", A(1,1), A(1,3), A(1,2));
-	fprintf(fn, "\t    <%.4f,%.4f,%.4f>,\n", B(1,1), B(1,3), B(1,2));
-	fprintf(fn, "\t    <%.4f,%.4f,%.4f>\n",  C(1,1), C(1,3), C(1,2));
-	fprintf(fn, "\t}\n");
-endfunction
-
-function viereck(fn, punkte)
-	color = farbe(mean(punkte(:,1)), mean(punkte(:,2)));
-	fprintf(fn, "    mesh {\n");
-	dreieck(fn, punkte(1,:), punkte(2,:), punkte(3,:));
-	dreieck(fn, punkte(2,:), punkte(3,:), punkte(4,:));
-	fprintf(fn, "\tpigment { color rgb<%.4f,%.4f,%.4f> } // %.4f\n",
-		color(1,1), color(1,2), color(1,3), color(1,4));
-	fprintf(fn, "    }\n");
-endfunction
-
-fn = fopen("curvature.inc", "w");
-punkte = zeros(4,3);
-for ix = (0:xsteps-1)
-	x = xmin + ix * hx;
-	punkte(1,1) = x;      
-	punkte(2,1) = x;
-	punkte(3,1) = x + hx;
-	punkte(4,1) = x + hx;
-	for iy = (0:ysteps-1)
-		y = ymin + iy * hy;
-		punkte(1,2) = y;
-		punkte(2,2) = y + hy;
-		punkte(3,2) = y;
-		punkte(4,2) = y + hy;
-		for i = (1:4)
-			punkte(i,3) = f(punkte(i,1), punkte(i,2));
-		endfor
-		viereck(fn, punkte);
-	end
-end
-#fprintf(fn, "    finish { metallic specular 0.5 }\n");
-fclose(fn);
-
-printf("Cmax = %.4f\n", Cmax);
-printf("Cmin = %.4f\n", Cmin);
diff --git a/buch/papers/kugel/images/spherecurve.cpp b/buch/papers/kugel/images/spherecurve.cpp
deleted file mode 100644
index 8ddf5e5..0000000
--- a/buch/papers/kugel/images/spherecurve.cpp
+++ /dev/null
@@ -1,292 +0,0 @@
-/*
- * spherecurve.cpp
- *
- * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
- */
-#include <cstdio>
-#include <cstdlib>
-#include <cmath>
-#include <string>
-#include <iostream>
-
-inline double	sqr(double x) { return x * x; }
-
-/**
- * \brief Class for 3d vectors (also used as colors)
- */
-class vector {
-	double	X[3];
-public:
-	vector() { X[0] = X[1] = X[2] = 0; }
-	vector(double a) { X[0] = X[1] = X[2] = a; }
-	vector(double x, double y, double z) {
-		X[0] = x; X[1] = y; X[2] = z;
-	}
-	vector(double theta, double phi) {
-		double	s = sin(theta);
-		X[0] = cos(phi) * s;
-		X[1] = sin(phi) * s;
-		X[2] = cos(theta);
-	}
-	vector(const vector& other) {
-		for (int i = 0; i < 3; i++) {
-			X[i] = other.X[i];
-		}
-	}
-	vector	operator+(const vector& other) const {
-		return vector(X[0] + other.X[0],
-				X[1] + other.X[1],
-				X[2] + other.X[2]);
-	}
-	vector	operator*(double l) const {
-		return vector(X[0] * l, X[1] * l, X[2] * l);
-	}
-	double	operator*(const vector& other) const {
-		double	s = 0;
-		for (int i = 0; i < 3; i++) {
-			s += X[i] * other.X[i];
-		}
-		return s;
-	}
-	double	norm() const {
-		double	s = 0;
-		for (int i = 0; i < 3; i++) {
-			s += sqr(X[i]);
-		}
-		return sqrt(s);
-	}
-	vector	normalize() const {
-		double	l = norm();
-		return vector(X[0]/l, X[1]/l, X[2]/l);
-	}
-	double	max() const {
-		return std::max(X[0], std::max(X[1], X[2]));
-	}
-	double	l0norm() const {
-		double	l = 0;
-		for (int i = 0; i < 3; i++) {
-			if (fabs(X[i]) > l) {
-				l = fabs(X[i]);
-			}
-		}
-		return l;
-	}
-	vector	l0normalize() const {
-		double	l = l0norm();
-		vector	result(X[0]/l, X[1]/l, X[2]/l);
-		return result;
-	}
-	const double&	operator[](int i) const { return X[i]; }
-	double&	operator[](int i) { return X[i]; }
-};
-
-/**
- * \brief Derived 3d vector class implementing color
- *
- * The constructor in this class converts a single value into a
- * color on a suitable gradient.
- */
-class color : public vector {
-public:
-	static double	utop;
-	static double	ubottom;
-	static double	green;
-public:
-	color(double u) {
-		u = (u - ubottom) / (utop - ubottom);
-		if (u > 1) {
-			u = 1;
-		}
-		if (u < 0) {
-			u = 0;
-		}
-		u = pow(u,2);
-		(*this)[0] = u;
-		(*this)[1] = green * u * (1 - u);
-		(*this)[2] = 1-u;
-		double	l = l0norm();
-		for (int i = 0; i < 3; i++) {
-			(*this)[i] /= l;
-		}
-	}
-};
-
-double	color::utop = 12;
-double	color::ubottom = -31;
-double	color::green = 0.5;
-
-/**
- * \brief Surface model
- *
- * This class contains the definitions of the functions to plot
- * and the parameters to 
- */
-class surfacefunction {
-	static vector	axes[6];
-
-	double	_a;
-	double	_A;
-
-	double	_umin;
-	double	_umax;
-public:
-	double	a() const { return _a; }
-	double	A() const { return _A; }
-
-	double	umin() const { return _umin; }
-	double	umax() const { return _umax; }
-
-	surfacefunction(double a, double A) : _a(a), _A(A), _umin(0), _umax(0) {
-	}
-
-	double	f(double z) {
-		return A() * exp(a() * (sqr(z) - 1));
-	}
-
-	double	g(double z) {
-		return -f(z) * 2*a() * ((2*a()*sqr(z) + (3-2*a()))*sqr(z) - 1);
-	}
-
-	double	F(const vector& v) {
-		double	s = 0;
-		for (int i = 0; i < 6; i++) {
-			s += f(axes[i] * v);
-		}
-		return s / 6;
-	}
-
-	double	G(const vector& v) {
-		double	s = 0;
-		for (int i = 0; i < 6; i++) {
-			s += g(axes[i] * v);
-		}
-		return s / 6;
-	}
-protected:
-	color	farbe(const vector& v) {
-		double	u = G(v);
-		if (u < _umin) {
-			_umin = u;
-		}
-		if (u > _umax) {
-			_umax = u;
-		}
-		return color(u);
-	}
-};
-
-static double	phi = (1 + sqrt(5)) / 2;
-static double	sl = sqrt(sqr(phi) + 1);
-vector	surfacefunction::axes[6] = {
-	vector(   0.   , -1./sl, phi/sl ),
-	vector(   0.   ,  1./sl, phi/sl ),
-	vector(   1./sl, phi/sl,  0.    ),
-	vector(  -1./sl, phi/sl,  0.    ),
-	vector(  phi/sl,  0.   ,  1./sl ),
-	vector( -phi/sl,  0.   ,  1./sl )
-};
-
-/**
- * \brief Class to construct the plot
- */
-class surface : public surfacefunction {
-	FILE	*outfile;
-
-	int	_phisteps;
-	int	_thetasteps;
-	double	_hphi;
-	double	_htheta;
-public:
-	int	phisteps() const { return _phisteps; }
-	int	thetasteps() const { return _thetasteps; }
-	double	hphi() const { return _hphi; }
-	double	htheta() const { return _htheta; }
-	void	phisteps(int s) { _phisteps = s; _hphi = 2 * M_PI / s; }
-	void	thetasteps(int s) { _thetasteps = s; _htheta = M_PI / s; }
-
-	surface(const std::string& filename, double a, double A)
-		: surfacefunction(a, A) {
-		outfile = fopen(filename.c_str(), "w");
-		phisteps(400);
-		thetasteps(200);
-	}
-
-	~surface() {
-		fclose(outfile);
-	}
-
-private:
-	void	triangle(const vector& v0, const vector& v1, const vector& v2) {
-		fprintf(outfile, "    mesh {\n");
-		vector	c = (v0 + v1 + v2) * (1./3.);
-		vector	color = farbe(c.normalize());
-		vector	V0 = v0 * (1 + F(v0));
-		vector	V1 = v1 * (1 + F(v1));
-		vector	V2 = v2 * (1 + F(v2));
-		fprintf(outfile, "\ttriangle {\n");
-		fprintf(outfile, "\t    <%.6f,%.6f,%.6f>,\n",
-			V0[0], V0[2], V0[1]);
-		fprintf(outfile, "\t    <%.6f,%.6f,%.6f>,\n",
-			V1[0], V1[2], V1[1]);
-		fprintf(outfile, "\t    <%.6f,%.6f,%.6f>\n",
-			V2[0], V2[2], V2[1]);
-		fprintf(outfile, "\t}\n");
-		fprintf(outfile, "\tpigment { color rgb<%.4f,%.4f,%.4f> }\n",
-			color[0], color[1], color[2]);
-		fprintf(outfile, "\tfinish { metallic specular 0.5 }\n");
-		fprintf(outfile, "    }\n");
-	}
-
-	void	northcap() {
-		vector	v0(0, 0, 1);
-		for (int i = 1; i <= phisteps(); i++) {
-			fprintf(outfile, "    // northcap i = %d\n", i);
-			vector	v1(htheta(), (i - 1) * hphi());
-			vector	v2(htheta(),  i      * hphi());
-			triangle(v0, v1, v2);
-		}
-	}
-
-	void	southcap() {
-		vector	v0(0, 0, -1);
-		for (int i = 1; i <= phisteps(); i++) {
-			fprintf(outfile, "    // southcap i = %d\n", i);
-			vector	v1(M_PI - htheta(), (i - 1) * hphi());
-			vector	v2(M_PI - htheta(),  i      * hphi());
-			triangle(v0, v1, v2);
-		}
-	}
-
-	void	zone() {
-		for (int j = 1; j < thetasteps() - 1; j++) {
-			for (int i = 1; i <= phisteps(); i++) {
-				fprintf(outfile, "    // zone j = %d, i = %d\n",
-					j, i);
-				vector v0( j    * htheta(), (i-1) * hphi());
-				vector v1((j+1) * htheta(), (i-1) * hphi());
-				vector v2( j    * htheta(),  i    * hphi());
-				vector v3((j+1) * htheta(),  i    * hphi());
-				triangle(v0, v1, v2);
-				triangle(v1, v2, v3);
-			}
-		}
-	}
-public:
-	void	draw() {
-		northcap();
-		southcap();
-		zone();
-	}
-};
-
-/**
- * \brief main function
- */
-int	main(int argc, char *argv[]) {
-	surface	S("spherecurve.inc", 5, 10);
-	color::green = 1.0;
-	S.draw();
-	std::cout << "umin: " << S.umin() << std::endl;
-	std::cout << "umax: " << S.umax() << std::endl;
-	return EXIT_SUCCESS;
-}
diff --git a/buch/papers/kugel/images/spherecurve.m b/buch/papers/kugel/images/spherecurve.m
deleted file mode 100644
index 99d5c9a..0000000
--- a/buch/papers/kugel/images/spherecurve.m
+++ /dev/null
@@ -1,160 +0,0 @@
-#
-# spherecurve.m
-#
-# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-#
-global a;
-a = 5;
-global A;
-A = 10;
-
-phisteps = 400;
-hphi = 2 * pi / phisteps;
-thetasteps = 200;
-htheta = pi / thetasteps;
-
-function retval = f(z)
-	global a;
-	global A;
-	retval = A * exp(a * (z^2 - 1));
-endfunction
-
-function retval = g(z)
-	global a;
-	retval = -f(z) * 2 * a * (2 * a * z^4 + (3 - 2*a) * z^2 - 1);
-	#                                                              2
-	#                   - a     2  4             2   2          a z
-	#(%o6)          - %e    (4 a  z  + (6 a - 4 a ) z  - 2 a) %e
-endfunction
-
-phi = (1 + sqrt(5)) / 2;
-
-global axes;
-axes = [
-     0,   0,   1,  -1, phi, -phi;
-     1,  -1, phi, phi,   0,    0;
-   phi, phi,   0,   0,   1,    1;
-];
-axes = axes / (sqrt(phi^2+1));
-
-function retval = kugel(theta, phi)
-	retval = [
-	    cos(phi) * sin(theta);
-	    sin(phi) * sin(theta);
-	               cos(theta)
-	];
-endfunction
-
-function retval = F(v)
-	global axes;
-	s = 0;
-	for i = (1:6)
-		z = axes(:,i)' * v;
-		s = s + f(z);
-	endfor
-	retval = s / 6;
-endfunction
-
-function retval = F2(theta, phi)
-	v = kugel(theta, phi);
-	retval = F(v);
-endfunction
-
-function retval = G(v)
-	global axes;
-	s = 0;
-	for i = (1:6)
-		s = s + g(axes(:,i)' * v);
-	endfor
-	retval = s / 6;
-endfunction
-
-function retval = G2(theta, phi)
-	v = kugel(theta, phi);
-	retval = G(v);
-endfunction
-
-function retval = cnormalize(u)
-	utop = 11;
-	ubottom = -30;
-	retval = (u - ubottom)  / (utop - ubottom);
-	if (retval > 1) 
-		retval = 1;
-	endif
-	if (retval < 0)
-		retval = 0;
-	endif
-endfunction
-
-global umin;
-umin = 0;
-global umax;
-umax = 0;
-
-function color = farbe(v)
-	global umin;
-	global umax;
-	u = G(v);
-	if (u < umin) 
-		umin = u;
-	endif
-	if (u > umax)
-		umax = u;
-	endif
-	u = cnormalize(u);
-	color = [ u, 0.5, 1-u ];
-	color = color/max(color);
-endfunction
-
-function dreieck(fn, v0, v1, v2)
-	fprintf(fn, "    mesh {\n");
-	c = (v0 + v1 + v2) / 3;
-	c = c / norm(c);
-	color = farbe(c);
-	v0 = v0 * (1 + F(v0));
-	v1 = v1 * (1 + F(v1));
-	v2 = v2 * (1 + F(v2));
-	fprintf(fn, "\ttriangle {\n");
-	fprintf(fn, "\t    <%.6f,%.6f,%.6f>,\n", v0(1,1), v0(3,1), v0(2,1));
-	fprintf(fn, "\t    <%.6f,%.6f,%.6f>,\n", v1(1,1), v1(3,1), v1(2,1));
-	fprintf(fn, "\t    <%.6f,%.6f,%.6f>\n",  v2(1,1), v2(3,1), v2(2,1));
-	fprintf(fn, "\t}\n");
-	fprintf(fn, "\tpigment { color rgb<%.4f,%.4f,%.4f> }\n",
-		color(1,1), color(1,2), color(1,3));
-	fprintf(fn, "\tfinish { metallic specular 0.5 }\n");
-	fprintf(fn, "    }\n");
-endfunction
-
-fn = fopen("spherecurve2.inc", "w");
-
-	for i = (1:phisteps)
-		# Polkappe nord
-		v0 = [ 0; 0; 1 ];
-		v1 = kugel(htheta, (i-1) * hphi);
-		v2 = kugel(htheta,  i    * hphi);
-		fprintf(fn, "    // i = %d\n", i);
-		dreieck(fn, v0, v1, v2);
-
-		# Polkappe sued
-		v0 = [ 0; 0; -1 ];
-		v1 = kugel(pi-htheta, (i-1) * hphi);
-		v2 = kugel(pi-htheta,  i    * hphi);
-		dreieck(fn, v0, v1, v2);
-	endfor
-
-	for j = (1:thetasteps-2)
-		for i = (1:phisteps)
-			v0 = kugel( j    * htheta, (i-1) * hphi);
-			v1 = kugel((j+1) * htheta, (i-1) * hphi);
-			v2 = kugel( j    * htheta,  i    * hphi);
-			v3 = kugel((j+1) * htheta,  i    * hphi);
-			fprintf(fn, "    // i = %d, j = %d\n", i, j);
-			dreieck(fn, v0, v1, v2);
-			dreieck(fn, v1, v2, v3);
-		endfor
-	endfor
-
-fclose(fn);
-
-umin
-umax
diff --git a/buch/papers/kugel/images/spherecurve.maxima b/buch/papers/kugel/images/spherecurve.maxima
deleted file mode 100644
index 1e9077c..0000000
--- a/buch/papers/kugel/images/spherecurve.maxima
+++ /dev/null
@@ -1,13 +0,0 @@
-/*
- * spherecurv.maxima
- *
- * (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
- */
-f: exp(-a * sin(theta)^2);
-
-g: ratsimp(diff(sin(theta) * diff(f, theta), theta)/sin(theta));
-g: subst(z, cos(theta), g);
-g: subst(sqrt(1-z^2), sin(theta), g);
-ratsimp(g);
-
-f: ratsimp(subst(sqrt(1-z^2), sin(theta), f));
diff --git a/buch/papers/kugel/images/spherecurve.pov b/buch/papers/kugel/images/spherecurve.pov
deleted file mode 100644
index b1bf4b8..0000000
--- a/buch/papers/kugel/images/spherecurve.pov
+++ /dev/null
@@ -1,73 +0,0 @@
-//
-// curvature.pov
-//
-// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
-//
-
-#version 3.7;
-#include "colors.inc"
-
-global_settings {
-	assumed_gamma 1
-}
-
-#declare imagescale = 0.13;
-
-camera {
-	location <10, 10, -40>
-	look_at <0, 0, 0>
-	right x * imagescale
-	up y * imagescale
-}
-
-light_source {
-	<-10, 10, -40> color White
-	area_light <1,0,0> <0,0,1>, 10, 10
-	adaptive 1
-	jitter
-}
-
-sky_sphere {
-	pigment {
-		color rgb<1,1,1>
-	}
-}
-
-//
-// draw an arrow from <from> to <to> with thickness <arrowthickness> with
-// color <c>
-//
-#macro arrow(from, to, arrowthickness, c)
-#declare arrowdirection = vnormalize(to - from);
-#declare arrowlength = vlength(to - from);
-union {
-	sphere {
-		from, 1.1 * arrowthickness
-	}
-	cylinder {
-		from,
-		from + (arrowlength - 5 * arrowthickness) * arrowdirection,
-		arrowthickness
-	}
-	cone {
-		from + (arrowlength - 5 * arrowthickness) * arrowdirection,
-		2 * arrowthickness,
-		to,
-		0
-	}
-	pigment {
-		color c
-	}
-	finish {
-		specular 0.9
-		metallic
-	}
-}
-#end
-
-arrow(<-2.7,0,0>, <2.7,0,0>, 0.03, White)
-arrow(<0,-2.7,0>, <0,2.7,0>, 0.03, White)
-arrow(<0,0,-2.7>, <0,0,2.7>, 0.03, White)
-
-#include "spherecurve.inc"
-