curvature graph

3 files changed, 168 insertions, 0 deletions

diff --git a/buch/papers/kugel/images/Makefile b/buch/papers/kugel/images/Makefile
new file mode 100644
index 0000000..8efa228
--- /dev/null
+++ b/buch/papers/kugel/images/Makefile
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+#
+# Makefile -- build images
+#
+# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+all: curvature.png
+
+curvature.inc:	curvgraph.m
+	octave curvgraph.m
+
+curvature.png:	curvature.pov curvature.inc
+	povray +A0.1 +W1920 +H1080 +Ocurvature.png curvature.pov
+
diff --git a/buch/papers/kugel/images/curvature.pov b/buch/papers/kugel/images/curvature.pov
new file mode 100644
index 0000000..3535488
--- /dev/null
+++ b/buch/papers/kugel/images/curvature.pov
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+//
+// curvature.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+
+#version 3.7;
+#include "colors.inc"
+
+global_settings {
+	assumed_gamma 1
+}
+
+#declare imagescale = 0.1;
+
+camera {
+	location <40, 10, -20>
+	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"
diff --git a/buch/papers/kugel/images/curvgraph.m b/buch/papers/kugel/images/curvgraph.m
new file mode 100644
index 0000000..96ca4b1
--- /dev/null
+++ b/buch/papers/kugel/images/curvgraph.m
@@ -0,0 +1,83 @@
+#
+# curvature.m
+#
+# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+
+global N;
+N = 10;
+
+global sigma2;
+sigma2 = 1;
+
+global s;
+s = 1;
+
+xmin = -3;
+xmax = 3;
+xsteps = 1000;
+hx = (xmax - xmin) / xsteps;
+
+ymin = -2;
+ymax = 2;
+ysteps = 1000;
+hy = (ymax - ymin) / ysteps;
+
+function retval = f0(r)
+	global sigma2;
+	retval = exp(-r^2/sigma2)/sigma2 - exp(-r^2/(2*sigma2))/(sqrt(2)*sigma2);
+end
+
+global N0;
+N0 = f0(0);
+
+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 = (
+		(2*sigma2-r^2)*exp(-r^2/(2*sigma2))
+		+
+		4*(r^2-sigma2)*exp(-r^2/sigma2)
+	) / (sigma2^2);
+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)
+	c = curvature(x, y);
+	retval = c * ones(1,3);
+endfunction
+
+fn = fopen("curvature.inc", "w");
+
+for ix = (0:xsteps)
+	x = xmin + ix * hx;
+	for iy = (0:ysteps)
+		y = ymin + iy * hy;
+		fprintf(fn, "sphere { <%.4f, %.4f, %.4f>, 0.01\n",
+			x, f(x, y), y);
+		color = farbe(x, y);
+		fprintf(fn, "pigment { color rgb<%.4f,%.4f,%.4f> }\n",
+			color(1,1), color(1,2), color(1,3));
+		fprintf(fn, "finish { metallic specular 0.5 }\n");
+		fprintf(fn, "}\n");
+	end
+end
+
+fclose(fn);