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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:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
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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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