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-rw-r--r--buch/papers/kugel/images/Makefile30
-rw-r--r--buch/papers/kugel/images/curvature.maxima6
-rw-r--r--buch/papers/kugel/images/curvature.pov139
-rw-r--r--buch/papers/kugel/images/curvgraph.m140
-rw-r--r--buch/papers/kugel/images/spherecurve.cpp292
-rw-r--r--buch/papers/kugel/images/spherecurve.m160
-rw-r--r--buch/papers/kugel/images/spherecurve.maxima13
-rw-r--r--buch/papers/kugel/images/spherecurve.pov73
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"
-
generated by cgit v1.2.1 (git 2.18.0) at 2024-12-23 14:21:35 +0100