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Summary
| Description |
English: The midsphere of a polyhedron. The red circles indicate the points at which a cone, with its apex at a vertex, is tangent to the sphere. Rendered in POV-ray based on a different rendering of the same model from D. Eppstein (2005), Quasiconvex programming, Combinatorial and Computational Geometry, Goodman, Pach, and Welzl, eds., MSRI Publications 52, 2005, pp. 287-331, arXiv:cs.CG/0412046. |
| Source | Own work |
| Author | David Eppstein |
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
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POV-ray source code
// Edge-tangent polytope and the sphere of edge tangencies
// David Eppstein, UC Irvine, 21 May 2001, modified 10 April 2011
global_settings {
assumed_gamma 2.2
ambient_light <3,3,3>
}
light_source { <-10, 35, -15> color <4,4,4> }
// light_source { <5, -10, -15> color <1.5,1.5,1.5> }
// perp: <5,1,-6> <1,1,1> <7,-11,4>
// perp: <5,2,-2> <0,1,1> <4,-5,5>
#declare p=<1,1,1>/sqrt(3);
#declare q=<7,-11,4>/sqrt(186);
camera {
location <5,1,-6>
look_at <0.5, 0, 0>
up -q*0.65
right p*0.65
translate <-0.1,0,-0.5>
rotate <0,-5,0>
}
sphere { <0.0, 0.0, 0.0>, 2
texture {
finish {
specular 1
roughness 0.002
ambient 0.1
diffuse 0.05
reflection 1
phong 0.3
phong_size 60
}
pigment { color rgbf<0.2, 0.2, 1.5, 0.7> }
}
}
#declare P_Surf =
texture {
finish {
ambient 0.2
diffuse 0.2
}
pigment { color red 1 green 1 blue 1 }
}
polygon {
4,
<0,2,-2>,<0,2,2>,<2,0,1>,<2,0,-1>
texture { P_Surf }
}
polygon {
4,
<0,2,-2>,<0,2,2>,<-2,0,1>,<-2,0,-1>
texture { P_Surf }
}
polygon {
4,
<0,-2,-2>,<0,-2,2>,<2,0,1>,<2,0,-1>
texture { P_Surf }
}
polygon {
4,
<0,-2,-2>,<0,-2,2>,<-2,0,1>,<-2,0,-1>
texture { P_Surf }
}
polygon {
3,
<0,2,2>,<2,0,1>,<0,-2,2>
texture { P_Surf }
}
polygon {
3,
<0,2,-2>,<2,0,-1>,<0,-2,-2>
texture { P_Surf }
}
polygon {
3,
<0,2,2>,<-2,0,1>,<0,-2,2>
texture { P_Surf }
}
polygon {
3,
<0,2,-2>,<-2,0,-1>,<0,-2,-2>
texture { P_Surf }
}
#declare P_Ring =
texture {
finish {
ambient 0.3
diffuse 0.3
}
pigment { color red 1 green 0 blue 0 }
}
torus {
2/sqrt(2), 0.013
texture { P_Ring }
rotate <-45,0,0>
translate <0,1,-1>
}
torus {
2/sqrt(2), 0.013
texture { P_Ring }
rotate <45,0,0>
translate <0,1,1>
}
torus {
2/sqrt(2), 0.013
texture { P_Ring }
rotate <-45,0,0>
translate <0,1,-1>
rotate <180,0,0>
}
torus {
2/sqrt(2), 0.013
texture { P_Ring }
rotate <45,0,0>
translate <0,1,1>
rotate <180,0,0>
}
torus {
2*sqrt(1/5), 0.013
texture { P_Ring }
rotate <90,-asin(2/sqrt(5))*180/pi,0>
translate <8/5,0,-4/5>
}
torus {
2*sqrt(1/5), 0.013
texture { P_Ring }
rotate <90,asin(2/sqrt(5))*180/pi,0>
translate <8/5,0,4/5>
}
torus {
2*sqrt(1/5), 0.013
texture { P_Ring }
rotate <90,-asin(2/sqrt(5))*180/pi,0>
translate <8/5,0,-4/5>
rotate <180,0,0>
}
torus {
2*sqrt(1/5), 0.013
texture { P_Ring }
rotate <90,asin(2/sqrt(5))*180/pi,0>
translate <8/5,0,4/5>
rotate <180,0,0>
}
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 20:49, 10 April 2011 | | 1,024 × 1,024 (115 KB) | David Eppstein | {{Information |Description ={{en|1=The midsphere of a polyhedron. The red circles indicate the points at which a cone, with its apex at a vertex, is tangent to the sphere. Rendered in POV-ray based on a different rendering of the same |
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