File:Villarceau_circles.gif
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Villarceau_circles.gif (480 × 360 pixels, file size: 582 KB, MIME type: image/gif, looped, 39 frames, 17 s)
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Summary
DescriptionVillarceau circles.gif |
This image was created with POV-Ray. |
Source | Own work |
Author | Lucas Vieira |
|
Licensing
Public domainPublic domainfalsefalse |
I, the copyright holder of this work, release this work into the public domain. This applies worldwide. In some countries this may not be legally possible; if so: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
POV-Ray source code
/*
Villarceau circles 2.0, by Lucas Vieira - October 2, 2006 - Coded in: POV-Ray 3.6
License: Public Domain
Info
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Author user page: http://en.wikipedia.org/wiki/User:LucasVB
The final animation at Wikimedia Commons: http://commons.wikimedia.org/wiki/Image:Villarceau_circles.gif
Notes
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Several modifications were done for each part of the animation and I didn't keep them all here.
So if you wish to reproduce the animation, you'll have to play with this code quite a bit. :)
*/
background { color rgb 1 }
global_settings {
assumed_gamma 1.5
}
camera {
orthographic
location <0,4,-5>*0.75
look_at <0,0,0>
rotate 5*y // slight camera angle so the cutting plane doesn't look too boring
//rotate 90*y // debug rotation
}
light_source {
<0,0,0>, 1
translate <-5,5,0>*1
shadowless // makes everything softer, because shading comes entirely from the surface normal
// this removes specular reflections, but I thought it looked a lot better
}
//Several rotation codes used for various parts of the animation.
//#declare rotation = (-95*sin(clock*pi/2))*y; // 360*clock*y;
#declare rotation = -90*y;
//#declare rotation = (-85 * sin(clock*pi/2))*y;
//Bottom half-torus
#if (1)
difference {
difference {
torus {
1, 0.5
}
torus {
1, 0.499
pigment {
image_map {
//surface inside the torus
png "checker2.png" // 1024x512 checkered image, with 64x64 cells.
interpolate 4
map_type 5
//transmit all 1-sin(clock*pi/2)
//transmit all 0.85
}
}
}
}
box {
-3*<1,0,1>, <1,1,1>*3
rotate degrees(asin(0.5-0.001))*z
}
pigment {
image_map {
png "checker.png" // 1024x512 checkered image, with 64x64 cells.
interpolate 4
map_type 5
//transmit all 1-sin(clock*pi/2)
//transmit all 0.85
}
}
finish {
specular 0.5
roughness 0.01
ambient 0.5
}
rotate rotation
}
#end
//Top half-torus (the one discarded during the animation)
//Notice it doesn't have an inner surface like the other half
#if (0)
intersection {
difference {
torus {
1, 0.5
}
torus {
1, 0.499
}
}
box {
-3*<1,0,1>, <1,1,1>*3
rotate degrees(asin(0.5-0.001))*z
}
pigment {
image_map {
png "checker.png" // 1024x512 checkered image, with 64x64 cells.
interpolate 4
map_type 5
//transmit all 1-sin(clock*pi/2) // Fades it away while moving to the left (see below)
//transmit all 0.85
}
}
finish {
specular 0.5
roughness 0.01
ambient 0.5
}
//translate -x*0.5*sin(clock*pi/2) // Moves this part to the left. Should be enabled along with the fade code above
rotate rotation
}
#end
//Cutting plane
#if (0)
box {
<1.8,0.001,1.8>, -<1.8,0.001,1.8>
pigment {
color rgb <1,0.8,0.5>
//transmit 1-sin(clock*pi/2)*0.4
//transmit 0.6+0.4*sin(clock*pi/2)
transmit 0.6
}
finish {
specular 0.5
roughness 0.01
ambient 0.3
}
//translate 3.5*x - sin(clock*pi/2)*3.5*x
rotate degrees(asin(0.5-0.001))*z
}
#end
//The Villarceau circles
#if (0)
union {
torus {
1, 0.01
translate 0.5*z
}
torus {
1, 0.01
translate -0.5*z
}
pigment {
color rgb <1,0,0>
//transmit clock
}
finish {
ambient 1
}
no_shadow
rotate degrees(asin(0.5-0.001))*z
rotate -85*y
}
#end
/* END OF FILE */
Items portrayed in this file
depicts
some value
image/gif
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 22:43, 2 October 2006 | 480 × 360 (582 KB) | LucasVB | Larger version (480x360) | |
21:31, 2 October 2006 | 320 × 240 (336 KB) | LucasVB | Improved version. :) | ||
06:18, 1 October 2006 | 480 × 360 (689 KB) | LucasVB | added an extra frame highlighting the circles | ||
05:52, 1 October 2006 | 480 × 360 (671 KB) | LucasVB | w:Villarceau circles in a w:Torus |
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):
- Hopf fibration
- Villarceau circles
- User:Holly Cheng/Picture of the day/January 2007
- User:JPxG/SP 2006-2010
- User:LucasVB/Gallery
- User:Passargea/Favourite pictures/Animations
- User:SteveChervitzTrutane
- User talk:Cleonis/Archive 2
- User talk:LucasVB/Archive1
- User talk:Mistin
- Wikipedia:Featured picture candidates/October-2006
- Wikipedia:Featured picture candidates/Villarceau circles
- Wikipedia:Featured pictures/Sciences/Mathematics
- Wikipedia:Featured pictures thumbs/05
- Wikipedia:Picture of the day/January 2007
- Wikipedia:Reference desk/Archives/Mathematics/2006 October 7
- Wikipedia:Today's featured picture (animation)/January 8, 2007
- Wikipedia:WikiProject Mathematics/Recognized content
- Wikipedia:Wikipedia Signpost/2006-10-16/Features and admins
- Wikipedia:Wikipedia Signpost/2006-10-16/SPV
- Wikipedia:Wikipedia Signpost/Single/2006-10-16
- Template:POTD/2007-01-08
- Portal:Mathematics/Featured picture/2009 08
- Portal:Mathematics/Featured picture/2009 09
- Portal:Mathematics/Featured picture archive
- Portal:Mathematics/Recognized content
- Portal:Mathematics/Selected picture
- Portal:Mathematics/Selected picture/27
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