add lots of images for a new cover

10 files changed, 289 insertions, 0 deletions

diff --git a/buch/chapters/090-pde/kugel/Makefile b/buch/chapters/090-pde/kugel/Makefile
new file mode 100644
index 0000000..4daf173
--- /dev/null
+++ b/buch/chapters/090-pde/kugel/Makefile
@@ -0,0 +1,18 @@
+#
+# Makefile -- build images for cover
+#
+# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+#
+all:	spherical30.png spherical31.png spherical32.png spherical33.png
+
+spherical30.png:	common.inc spherical30.pov
+	povray +A0.1 +UA +W1080 +H1080 -Ospherical30.png spherical30.pov
+
+spherical31.png:	common.inc spherical31.pov
+	povray +A0.1 +UA +W1080 +H1080 -Ospherical31.png spherical31.pov
+
+spherical32.png:	common.inc spherical32.pov
+	povray +A0.1 +UA +W1080 +H1080 -Ospherical32.png spherical32.pov
+
+spherical33.png:	common.inc spherical33.pov
+	povray +A0.1 +UA +W1080 +H1080 -Ospherical33.png spherical33.pov
diff --git a/buch/chapters/090-pde/kugel/common.inc b/buch/chapters/090-pde/kugel/common.inc
new file mode 100644
index 0000000..ed5f78c
--- /dev/null
+++ b/buch/chapters/090-pde/kugel/common.inc
@@ -0,0 +1,227 @@
+//
+// common.inc
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#include "colors.inc"
+#include "math.inc"
+
+global_settings {
+        assumed_gamma 1
+}
+
+#declare imagescale = 0.035;
+#declare thetasteps = 100;
+	#declare phisteps = 200;
+
+#declare PositiveColor = rgb<1.0,0.6,0.2>;
+#declare NegativeColor = rgb<0.6,0.2,0.6>;
+
+camera {
+	location <-33, 20, 50>
+	look_at <0, 0, 0>
+	right x * imagescale
+	up y * imagescale
+}
+
+background { color rgbt <0,0,0,1> }
+
+light_source {
+	<10, 5, 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)
+
+#declare P33 = function(X) { (1-X*X) * sqrt(1-X*X) };
+#declare P33abl = function(X) { -3*X*sqrt(1-X*X) };
+#declare P32 = function(X) { 2.7 * (1-X*X) * X };
+#declare P32abl = function(X) { 2.7 * (1-3*X*X) };
+#declare P31 = function(X) { (0.75) * (5*X*X-1) * sqrt(1-X*X) };
+#declare P31abl = function(X) { 0.75 * (15*X*X-11)*X / sqrt(1-0.9999*X*X) };
+#declare P30 = function(X) { (1/2) * (5*X*X-3)*X };
+#declare P30abl = function(X) { (1/2) * 15*X*X-3 };
+
+#macro kugel0(phi,theta)
+<cos(phi)*sin(theta), cos(theta), sin(phi)*sin(theta)>
+#end
+#macro kugelphi(phi,theta)
+<-sin(phi)*sin(theta), 0, cos(phi)*sin(theta)>
+#end
+#macro kugeltheta(phi,theta)
+<cos(phi)*cos(theta), -sin(theta), sin(phi)*cos(theta)>
+#end
+
+#declare fcos = function(phi,eps) { abs(cos(phi)) * (1+eps*sgn(cos(phi))) }
+#declare fradius = function(r,eps) { sqrt(abs(r)) * (1+eps*sgn(r)) }
+
+#macro kugel(phi, theta, m, eps)
+	#switch (m)
+	#case (0)
+		fradius(P30(cos(theta)) * cos(m*phi),eps) * kugel0(phi,theta)
+	#break
+	#case (1)
+		fradius(P31(cos(theta)) * cos(m*phi),eps) * kugel0(phi,theta)
+	#break
+	#case (2)
+		fradius(P32(cos(theta)) * cos(m*phi),eps) * kugel0(phi,theta)
+	#break
+	#case (3)
+		fradius(P33(cos(theta)) * cos(m*phi),eps) * kugel0(phi,theta)
+	#end
+#end
+
+#macro normale(phi, theta, m, eps)
+	#switch (m)
+	#case (0)
+	vnormalize(vcross(
+		P30(cos(theta))*(-m)*sin(m*phi)*kugelphi(phi,theta)
+		+
+		fradius(P30(cos(theta))*cos(m*phi),eps) * kugelphi(phi,theta),
+		P30abl(cos(theta))*(-sin(theta))*cos(m*phi) * kugel0(phi,theta)
+		+
+		fradius(P30(cos(theta))*cos(m*phi),eps) * kugeltheta(phi,theta)
+		
+	))
+	#break
+	#case (1)
+	vnormalize(vcross(
+		P31(cos(theta))*(-m)*sin(m*phi)*kugelphi(phi,theta)
+		+
+		fradius(P31(cos(theta))*cos(m*phi),eps) * kugelphi(phi,theta),
+		P31abl(cos(theta))*(-sin(theta))*cos(m*phi) * kugel0(phi,theta)
+		+
+		fradius(P31(cos(theta))*cos(m*phi),eps) * kugeltheta(phi,theta)
+		
+	))
+	#break
+	#case (2)
+	vnormalize(vcross(
+		P32(cos(theta))*(-m)*sin(m*phi)*kugelphi(phi,theta)
+		+
+		fradius(P32(cos(theta))*cos(m*phi),eps) * kugelphi(phi,theta),
+		P32abl(cos(theta))*(-sin(theta))*cos(m*phi) * kugel0(phi,theta)
+		+
+		fradius(P32(cos(theta))*cos(m*phi),eps) * kugeltheta(phi,theta)
+		
+	))
+	#break
+	#case (3)
+	vnormalize(vcross(
+		P33(cos(theta))*(-m)*sin(m*phi)*kugelphi(phi,theta)
+		+
+		fradius(P33(cos(theta))*cos(m*phi),eps) * kugelphi(phi,theta),
+		P33abl(cos(theta))*(-sin(theta))*cos(m*phi) * kugel0(phi,theta)
+		+
+		fradius(P33(cos(theta))*cos(m*phi),eps) * kugeltheta(phi,theta)
+		
+	))
+	#break
+	#end
+#end
+
+#macro kugelflaeche(m, eps, farbe)
+mesh {
+	#declare thetastep = pi / thetasteps;
+	#declare thetamin = thetastep;
+	#declare thetamax = pi - thetastep;
+
+	#declare phistep = pi / phisteps;
+	#declare phimin = 0;
+	#declare phimax = 2 * pi;
+
+	#declare phi = phimin;
+	#while (phi < phimax - phistep/2)
+		triangle {
+			kugel(0, 0, m, eps),
+			kugel(phi, thetamin, m, eps),
+			kugel(phi + phistep, thetamin, m, eps)
+		}
+
+		#declare theta = thetamin;
+		#while (theta < thetamax - thetastep/2)
+			triangle {
+				kugel(phi, theta, m, eps),
+				kugel(phi + phistep, theta, m, eps),
+				kugel(phi + phistep, theta + thetastep, m, eps)
+			}
+			triangle {
+				kugel(phi, theta, m, eps),
+				kugel(phi, theta + thetastep, m, eps),
+				kugel(phi + phistep, theta + thetastep, m, eps)
+			}
+			#declare theta = theta + thetastep;
+		#end
+
+		triangle {
+			kugel(0, pi, m, eps),
+			kugel(phi, thetamax, m, eps),
+			kugel(phi + phistep, thetamax, m, eps)
+		}
+
+		#declare phi = phi + phistep;
+	#end
+	pigment {
+		color farbe
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+#end
+
+//sphere {
+//	<0,0,0>, 1
+//	pigment {
+//		color rgbt<1,1,1,0.7>
+//	}
+//	finish {
+//		specular 0.95
+//		metallic
+//	}
+//}
+
+
diff --git a/buch/chapters/090-pde/kugel/spherical30.png b/buch/chapters/090-pde/kugel/spherical30.png
new file mode 100644
index 0000000..d24d786
--- /dev/null
+++ b/buch/chapters/090-pde/kugel/spherical30.png
diff --git a/buch/chapters/090-pde/kugel/spherical30.pov b/buch/chapters/090-pde/kugel/spherical30.pov
new file mode 100644
index 0000000..1a7d979
--- /dev/null
+++ b/buch/chapters/090-pde/kugel/spherical30.pov
@@ -0,0 +1,11 @@
+//
+// spherical30.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+
+#version 3.7;
+#include "common.inc"
+
+kugelflaeche(0, 0.001, PositiveColor)
+kugelflaeche(0, -0.001, NegativeColor)
diff --git a/buch/chapters/090-pde/kugel/spherical31.png b/buch/chapters/090-pde/kugel/spherical31.png
new file mode 100644
index 0000000..95d9789
--- /dev/null
+++ b/buch/chapters/090-pde/kugel/spherical31.png
diff --git a/buch/chapters/090-pde/kugel/spherical31.pov b/buch/chapters/090-pde/kugel/spherical31.pov
new file mode 100644
index 0000000..bc161f0
--- /dev/null
+++ b/buch/chapters/090-pde/kugel/spherical31.pov
@@ -0,0 +1,11 @@
+//
+// spherical30.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+
+#version 3.7;
+#include "common.inc"
+
+kugelflaeche(1, 0.001, PositiveColor)
+kugelflaeche(1, -0.001, NegativeColor)
diff --git a/buch/chapters/090-pde/kugel/spherical32.png b/buch/chapters/090-pde/kugel/spherical32.png
new file mode 100644
index 0000000..1ba6bd0
--- /dev/null
+++ b/buch/chapters/090-pde/kugel/spherical32.png
diff --git a/buch/chapters/090-pde/kugel/spherical32.pov b/buch/chapters/090-pde/kugel/spherical32.pov
new file mode 100644
index 0000000..6cb20c8
--- /dev/null
+++ b/buch/chapters/090-pde/kugel/spherical32.pov
@@ -0,0 +1,11 @@
+//
+// spherical30.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+
+#version 3.7;
+#include "common.inc"
+
+kugelflaeche(2, 0.001, PositiveColor)
+kugelflaeche(2, -0.001, NegativeColor)
diff --git a/buch/chapters/090-pde/kugel/spherical33.png b/buch/chapters/090-pde/kugel/spherical33.png
new file mode 100644
index 0000000..fb9de45
--- /dev/null
+++ b/buch/chapters/090-pde/kugel/spherical33.png
diff --git a/buch/chapters/090-pde/kugel/spherical33.pov b/buch/chapters/090-pde/kugel/spherical33.pov
new file mode 100644
index 0000000..8a9a53a
--- /dev/null
+++ b/buch/chapters/090-pde/kugel/spherical33.pov
@@ -0,0 +1,11 @@
+//
+// spherical30.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+
+#version 3.7;
+#include "common.inc"
+
+kugelflaeche(3, 0.001, PositiveColor)
+kugelflaeche(3, -0.001, NegativeColor)