Abbildung kegelschnitte

1 files changed, 183 insertions, 0 deletions

diff --git a/buch/chapters/030-geometrie/images/zylinder.pov b/buch/chapters/030-geometrie/images/zylinder.pov
new file mode 100644
index 0000000..c593379
--- /dev/null
+++ b/buch/chapters/030-geometrie/images/zylinder.pov
@@ -0,0 +1,183 @@
+//
+// zylinder.pov
+//
+// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+//
+#version 3.7;
+#include "colors.inc"
+
+global_settings {
+	assumed_gamma 1
+}
+
+#declare imagescale = 0.064;
+#declare r = 0.025;
+#declare R = 1.3 * r;
+
+camera {
+	location <-43, 20, 40>
+	look_at <1, 0.65, 2.1>
+	right 16/9 * x * imagescale
+	up y * imagescale
+}
+
+light_source {
+	<-40, 20, 10> 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(<-1.5,0,0>, <1.5,0,0>, r, White)
+arrow(<0,-1,0>, <0,2.5,0>, r, White)
+arrow(<0,0,-1.5>, <0,0,2*pi+0.5>, r, White)
+
+#declare cylindercolor = rgb<0.6,0.8,1.0>;
+#declare transparentcylinder = rgbf<0.6,0.8,1.0,0.7>;
+#declare planecolor = rgb<0.2,0.8,0.4>;
+#declare transparentplane = rgbf<0.2,0.8,0.4,0.7>;
+
+difference {
+	cylinder { <0,0,0>, <0,2,0>, 1 }
+	cylinder { <0,-1,0>, <0,3,0>, 0.99 }
+	pigment {
+		color transparentcylinder
+	}
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+
+
+box {
+	<1,0,0>, <0.99,2,2*pi>
+	pigment {
+		color transparentplane
+	}
+	finish {
+		specular 0.9
+		metallic
+	}
+}
+
+#macro punkt(phi) 
+	<cos(phi), phi/pi, sin(phi)>
+#end
+#macro geschwindigkeit(phi)
+	<-sin(phi), 1/pi, cos(phi)>
+#end
+
+union {
+	#declare N = 100;
+	#declare phistep = 2*pi/N;
+	#declare phi = 0;
+	#declare maxphi = 2*pi;
+	#while (phi < maxphi - phistep/2)
+		sphere { punkt(phi), r}
+		cylinder { punkt(phi), punkt(phi+phistep), r }
+		#declare phi = phi + phistep;
+	#end
+	sphere { punkt(phi), r}
+	pigment {
+		color Red
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+union {
+	sphere { <1,0,0>, r }
+	sphere { <1,2,2*pi>, r }
+	cylinder { <1,0,0>, <1,2,2*pi>, r }
+	pigment {
+		color Orange
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+#declare winkel = (130/180) * pi;
+
+#declare rr = 0.5 * r;
+
+union {
+	sphere { <0,winkel/pi,0>, rr }
+	sphere { punkt(winkel), rr }
+	cylinder { <0,winkel/pi,0>, punkt(winkel), rr }
+	sphere { <cos(winkel), 0, sin(winkel)>, rr }
+	sphere { <cos(winkel), 2, sin(winkel)>, rr }
+	cylinder { <cos(winkel), 2, sin(winkel)>, <0, 2, 0>, rr }
+	sphere { <0,2,0>, rr }
+	sphere { <cos(winkel), 0, sin(winkel)>, rr }
+	cylinder { <cos(winkel), 0, sin(winkel)>, <0, 0, 0>, rr }
+	sphere { <0,0,0>, rr }
+	cylinder {
+		<cos(winkel), 0, sin(winkel)>
+		<cos(winkel), 2, sin(winkel)>
+		rr
+	}
+	pigment {
+		color White
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}
+
+#declare geschwindigkeitsfarbe = rgb<1,0.6,1>;
+
+arrow(punkt(winkel), punkt(winkel) + geschwindigkeit(winkel), r, geschwindigkeitsfarbe)
+
+sphere { punkt(winkel), 1.3 * r 
+	pigment {
+		color geschwindigkeitsfarbe
+	}
+	finish {
+		specular 0.95
+		metallic
+	}
+}