diff options
Diffstat (limited to 'buch/chapters/110-elliptisch/images/torusschnitt.pov')
| -rw-r--r-- | buch/chapters/110-elliptisch/images/torusschnitt.pov | 185 |
1 files changed, 185 insertions, 0 deletions
diff --git a/buch/chapters/110-elliptisch/images/torusschnitt.pov b/buch/chapters/110-elliptisch/images/torusschnitt.pov new file mode 100644 index 0000000..94190be --- /dev/null +++ b/buch/chapters/110-elliptisch/images/torusschnitt.pov @@ -0,0 +1,185 @@ +// +// kegelpara.pov +// +// (c) 2022 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule +// +#version 3.7; +#include "colors.inc" + +#declare O = <0,0,0>; + +global_settings { + assumed_gamma 1 +} + +#declare imagescale = 0.060; + +camera { + location <28, 20, -40> + look_at <0, 0.55, 0> + right (16/9) * x * imagescale + up y * imagescale +} + +light_source { + <30, 10, -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(<-2,0,0>,<2,0,0>,0.02,White) +arrow(<0,-1.1,0>,<0,2.2,0>,0.02,White) +arrow(<0,0,-1.6>,<0,0,2.4>,0.02,White) + +#declare epsilon = 0.001; +#declare l = 1.5; + + +#declare a = sqrt(2); +#macro G2(phi,sg) + a * sqrt(cos(2*phi)) * < sg * cos(phi), 0, sin(phi)> +#end + +#macro Lemniskate(s, farbe) +union { + #declare phi = -pi / 4; + #declare phimax = pi / 4; + #declare phisteps = 100; + #declare phistep = phimax / phisteps; + #while (phi < phimax - phistep/2) + sphere { G2(phi,1), s } + cylinder { G2(phi,1), G2(phi+phistep,1), s } + sphere { G2(phi,-1), s } + cylinder { G2(phi,-1), G2(phi+phistep,-1), s } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro Projektion(s, farbe) +union { + #declare phistep = pi / 16; + #declare phi = -pi / 4 + phistep; + #declare phimax = pi / 4; + #while (phi < phimax - phistep/2) + cylinder { G(phi, 1), G2(phi, 1), s } + cylinder { G(phi, -1), G2(phi, -1), s } + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#macro Ebene(farbe) +box { + <-1.8, 0, -1.4>, <1.8, 0.001, 1.4> + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare b = 0.5; +#macro T(phi, theta) + b * < (2 + cos(theta)) * cos(phi), (2 + cos(theta)) * sin(phi) + 1, sin(theta) > +#end + +#macro Torus(farbe) +mesh { + #declare phi = 0; + #declare phimax = 2 * pi; + #declare phisteps = 200; + #declare phistep = phimax/phisteps; + #while (phi < phimax - phistep/2) + #declare theta = 0; + #declare thetamax = 2 * pi; + #declare thetasteps = 200; + #declare thetastep = thetamax / thetasteps; + #while (theta < thetamax - thetastep/2) + triangle { + T(phi, theta), + T(phi + phistep, theta), + T(phi + phistep, theta + thetastep) + } + triangle { + T(phi, theta), + T(phi + phistep, theta + thetastep), + T(phi, theta + thetastep) + } + #declare theta = theta + thetastep; + #end + #declare phi = phi + phistep; + #end + pigment { + color farbe + } + finish { + specular 0.9 + metallic + } +} +#end + +#declare torusfarbe = rgbt<0.2,0.6,0.2,0.2>; +#declare ebenenfarbe = rgbt<0.2,0.6,1.0,0.2>; + +Lemniskate(0.02, Red) +Ebene(ebenenfarbe) +Torus(torusfarbe) |