4 files changed, 287 insertions, 0 deletions
diff --git a/buch/chapters/090-pde/membran/Makefile b/buch/chapters/090-pde/membran/Makefile
new file mode 100644
index 0000000..35dfd14
--- /dev/null
+++ b/buch/chapters/090-pde/membran/Makefile
@@ -0,0 +1,15 @@
+#
+# Makefile
+#
+# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+all:	membran.png
+
+membran.inc:	membran.m
+	octave membran.m
+
+size="+W1920 +H540"
+size="+W3840 +H1080"
+
+membran.png:	membran.pov membran.inc
+	povray +A0.1 +UA $(size) -Omembran.png membran.pov
diff --git a/buch/chapters/090-pde/membran/membran.m b/buch/chapters/090-pde/membran/membran.m
new file mode 100644
index 0000000..acc45b9
--- /dev/null
+++ b/buch/chapters/090-pde/membran/membran.m
@@ -0,0 +1,109 @@
+#
+# membran.m
+#
+# (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+global n;
+n = 3;
+global A;
+A = 0.2;
+global nullstelle;
+nullstelle = 13.0152;
+global skala;
+skala = 1 / nullstelle;
+phisteps = 628;
+phistep = 2 * pi / phisteps;
+rsteps = 200;
+rstep = 1 / rsteps;
+
+fn = fopen("membran.inc", "w");
+fprintf(fn, "#macro flaeche()\n");
+
+function retval = punkt(fn, phi, r, n)
+	global nullstelle;
+	global skala;
+	global A;
+	fprintf(fn, "\n\t    <%.4f, %.4f, %.4f>",
+		r * cos(phi),
+		A * besselj(n, nullstelle * r) * cos(n * phi),
+		r * sin(phi)
+	);
+endfunction
+
+for i = (0:phisteps)
+	phi = i * phistep;
+	r = rstep;
+	fprintf(fn, "\ttriangle {");
+	punkt(fn, 0, 0, n);		fprintf(fn, ",");
+	punkt(fn, phi, rstep, n);	fprintf(fn, ",");
+	punkt(fn, phi+phistep, rstep, n);
+	fprintf(fn, "\n\t}\n");
+
+	for j = (1:rsteps-1)
+		r = j * rstep;
+		fprintf(fn, "\ttriangle {");
+		punkt(fn, phi, r, n);			fprintf(fn, ",");
+		punkt(fn,  phi+phistep, r, n);		fprintf(fn, ",");
+		punkt(fn, phi+phistep, r+rstep, n);
+		fprintf(fn, "\n\t}\n");
+		fprintf(fn, "\ttriangle {");
+		punkt(fn, phi, r, n);			fprintf(fn, ",");
+		punkt(fn, phi+phistep, r+rstep, n);	fprintf(fn, ",");
+		punkt(fn, phi, r+rstep, n);
+		fprintf(fn, "\n\t}\n");
+	end
+end
+
+fprintf(fn, "#end\n");
+
+function retval = ring(fn, r, n)
+	phisteps = 100;
+	phistep = 2 * pi / phisteps;
+	for i = (1:phisteps)
+		phi = phistep * i;
+		fprintf(fn, "\tcylinder {");
+		punkt(fn, phi - phistep, r, n);		fprintf(fn, ",");
+		punkt(fn, phi, r, n);			fprintf(fn, ",");
+		fprintf(fn, "\n\t    r");
+		fprintf(fn, "\n\t}\n")
+		fprintf(fn, "\tsphere {");
+		punkt(fn, phi - phistep, r, n);		fprintf(fn, ",");
+		fprintf(fn, "\n\t    r");
+		fprintf(fn, "\n\t}\n")
+	end
+end
+
+function retval = radius(fn, phi, n)
+	rsteps = 100;
+	rstep = 1 / rsteps;
+	for i = (0:rsteps-1)
+		r = i * rstep;
+		fprintf(fn, "\tcylinder {");
+		punkt(fn, phi, r, n);		fprintf(fn, ",");
+		punkt(fn, phi, r+rstep, n);	fprintf(fn, ",");
+		fprintf(fn, "\n\t    r");
+		fprintf(fn, "\n\t}\n")
+		fprintf(fn, "\tsphere {");
+		punkt(fn, phi, r, n);		fprintf(fn, ",");
+		fprintf(fn, "\n\t    r");
+		fprintf(fn, "\n\t}\n")
+	end
+end
+
+fprintf(fn, "#macro phigitter()\n");
+rsteps = 20;
+rstep = 1 / rsteps;
+for j = (1:rsteps-1)
+	ring(fn, rstep * j, n);
+end
+fprintf(fn, "#end\n");
+
+fprintf(fn, "#macro rgitter()\n");
+phisteps = 72;
+phistep = 2 * pi / phisteps;
+for i = (0:phisteps-1)
+	radius(fn, phistep * i, n);
+end
+fprintf(fn, "#end\n");
+
+fclose(fn);
diff --git a/buch/chapters/090-pde/membran/membran.png b/buch/chapters/090-pde/membran/membran.png
new file mode 100644
index 0000000..154a4a7
--- /dev/null
+++ b/buch/chapters/090-pde/membran/membran.png
diff --git a/buch/chapters/090-pde/membran/membran.pov b/buch/chapters/090-pde/membran/membran.pov
new file mode 100644
index 0000000..d64294f
--- /dev/null
+++ b/buch/chapters/090-pde/membran/membran.pov
@@ -0,0 +1,163 @@
+//
+// membran.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "colors.inc"
+#include "math.inc"
+#include "membran.inc"
+
+global_settings {
+        assumed_gamma 1
+}
+
+#declare imagescale = 0.037;
+
+camera {
+	location <-33, 20, 50>
+	look_at <0, -0.005, 0>
+	right x * imagescale
+	up (9/32) * y * imagescale
+}
+
+background { color rgbt <0,0,0,1> }
+
+light_source {
+	<10, 15, 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(<-1.1,0,0>, <1.1,0,0>, 0.01, White)
+//arrow(<0,-1.1,0>, <0,1.1,0>, 0.01, White)
+//arrow(<0,0,-1.1>, <0,0,1.1>, 0.01, White)
+
+mesh {
+	flaeche()
+	pigment {
+		color rgb<0.8,0.8,0.8> * 1.2
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+#declare randr = 0.01;
+
+#macro zylinder(k,n,r)
+	cylinder {
+		< cos((2*k+1)*pi/(2*n)), 0, sin((2*k+1)*pi/(2*n)) >,
+		< -cos((2*k+1)*pi/(2*n)), 0, -sin((2*k+1)*pi/(2*n)) >,
+		r
+	}
+#end
+
+#macro ring(R,r)
+	#declare phisteps = 100;
+	#declare phistep = 2 * pi / 100;
+	#declare phimin = 0;
+	#declare phimax = 2 * pi;
+	#declare phi = phimin;
+	#while (phi < phimax - phistep/2)
+		cylinder {
+			<R*cos(phi), 0, R*sin(phi)>,
+			<R*cos(phi+phistep), 0, R*sin(phi+phistep)>,
+			r
+		}
+		sphere {
+			<R*cos(phi), 0, R*sin(phi)>, r
+		}
+		#declare phi = phi + phistep;
+	#end
+#end
+
+#declare nullstelle = 13.0152;
+
+union {
+	ring(1, randr)
+	pigment {
+		color rgb<1.0,0.8,0.6>
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+union {
+	zylinder(0, 3, 0.5*randr)
+	zylinder(1, 3, 0.5*randr)
+	zylinder(2, 3, 0.5*randr)
+	ring(6.3802/nullstelle, 0.5*randr)
+	ring(9.7610/nullstelle, 0.5*randr)
+	pigment {
+		color rgb<1.0,0.8,0.6>
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+#declare r = 0.2*randr;
+union {
+	phigitter()
+	pigment {
+		color rgb<0.2,0.6,1.0>
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+union {
+	rgitter()
+	pigment {
+		color rgb<1.0,0.4,0.6>
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}