From 0ae2acadcf667fcd3d2cfc76aad9a7a754cb0f61 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andreas=20M=C3=BCller?= <andreas.mueller@ost.ch>
Date: Mon, 17 Jan 2022 14:05:05 +0100
Subject: add lots of images for a new cover

---
 buch/chapters/090-pde/membran/membran.m | 109 ++++++++++++++++++++++++++++++++
 1 file changed, 109 insertions(+)
 create mode 100644 buch/chapters/090-pde/membran/membran.m

(limited to 'buch/chapters/090-pde/membran/membran.m')

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);
-- 
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