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//
// 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(l, b, farbe)
mesh {
triangle { <-l, 0, -b>, < l, 0, -b>, < l, 0, b> }
triangle { <-l, 0, -b>, < l, 0, b>, <-l, 0, b> }
pigment {
color farbe
}
finish {
specular 0.9
metallic
}
}
#end
#macro Ebenengitter(l, b, s, r, farbe)
union {
#declare lmax = floor(l / s);
#declare ll = -lmax;
#while (ll <= lmax)
cylinder { <ll * s, 0, -b>, <ll * s, 0, b>, r }
#declare ll = ll + 1;
#end
#declare bmax = floor(b / s);
#declare bb = -bmax;
#while (bb <= bmax)
cylinder { <-l, 0, bb * s>, <l, 0, bb * s>, r }
#declare bb = bb + 1;
#end
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 breitenkreis(theta, r)
#declare phi = 0;
#declare phimax = 2 * pi;
#declare phisteps = 200;
#declare phistep = phimax / phisteps;
#while (phi < phimax - phistep/2)
cylinder { T(phi, theta), T(phi + phistep, theta), r }
sphere { T(phi, theta), r }
#declare phi = phi + phistep;
#end
#end
#macro laengenkreis(phi, r)
#declare theta = 0;
#declare thetamax = 2 * pi;
#declare thetasteps = 200;
#declare thetastep = thetamax / thetasteps;
#while (theta < thetamax - thetastep/2)
cylinder { T(phi, theta), T(phi, theta + thetastep), r }
sphere { T(phi, theta), r }
#declare theta = theta + thetastep;
#end
#end
#macro Torusgitter(farbe, r)
union {
#declare phi = 0;
#declare phimax = 2 * pi;
#declare phistep = pi / 6;
#while (phi < phimax - phistep/2)
laengenkreis(phi, r)
#declare phi = phi + phistep;
#end
#declare thetamax = pi;
#declare thetastep = pi / 6;
#declare theta = thetastep;
#while (theta < thetamax - thetastep/2)
breitenkreis(theta, r)
breitenkreis(thetamax + theta, r)
#declare theta = theta + thetastep;
#end
breitenkreis(0, 1.5 * r)
breitenkreis(pi, 1.5 * r)
pigment {
color farbe
}
finish {
specular 0.9
metallic
}
}
#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(1.8, 1.4, ebenenfarbe)
Ebenengitter(1.8, 1.4, 0.5, 0.005, rgb<0.4,1,1>)
Torus(torusfarbe)
Torusgitter(Yellow, 0.005)
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