5 files changed, 309 insertions, 0 deletions
diff --git a/buch/chapters/060-integral/experiments/rxy.maxima b/buch/chapters/060-integral/experiments/rxy.maxima
new file mode 100644
index 0000000..0d5a56d
--- /dev/null
+++ b/buch/chapters/060-integral/experiments/rxy.maxima
@@ -0,0 +1,9 @@
+y: sqrt(a*x^2+b*x+c);
+
+F: log(x + b/(2 * a) + y/sqrt(a))/sqrt(a);
+
+f: diff(F, x);
+
+ratsimp(f);
+
+ratsimp(y*f);
diff --git a/buch/papers/kugel/images/Makefile b/buch/papers/kugel/images/Makefile
new file mode 100644
index 0000000..e8bf919
--- /dev/null
+++ b/buch/papers/kugel/images/Makefile
@@ -0,0 +1,15 @@
+#
+# Makefile -- build images
+#
+# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+all: curvature.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
diff --git a/buch/papers/kugel/images/curvature.maxima b/buch/papers/kugel/images/curvature.maxima
new file mode 100644
index 0000000..6313642
--- /dev/null
+++ b/buch/papers/kugel/images/curvature.maxima
@@ -0,0 +1,6 @@
+
+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
new file mode 100644
index 0000000..3b15d77
--- /dev/null
+++ b/buch/papers/kugel/images/curvature.pov
@@ -0,0 +1,139 @@
+//
+// 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
new file mode 100644
index 0000000..75effd6
--- /dev/null
+++ b/buch/papers/kugel/images/curvgraph.m
@@ -0,0 +1,140 @@
+#
+# 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);