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-rw-r--r--buch/chapters/090-pde/membran/Makefile15
-rw-r--r--buch/chapters/090-pde/membran/membran.m109
-rw-r--r--buch/chapters/090-pde/membran/membran.pngbin0 -> 2527711 bytes
-rw-r--r--buch/chapters/090-pde/membran/membran.pov163
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
Binary files differ
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
+ }
+}