File:DoubleTorusCover.png
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Size of this preview: 653 × 600 pixels. Other resolutions: 261 × 240 pixels | 522 × 480 pixels | 776 × 713 pixels.
Original file (776 × 713 pixels, file size: 210 KB, MIME type: image/png)
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Summary[edit]
DescriptionDoubleTorusCover.png |
English: Illustration of the boundary map ∂* for the Mayer-Vietoris sequence on the double-torus where the 1-cycle x = u + v is the sum of two 1-chains whose boundary lies in the intersection of A and B. |
Date | |
Source | Own work using POV-Ray and Inkscape. Based on a drawing by User:GeometryGirl (public domain) |
Author | RobHar |
Data file[edit]
The double-torus was produced using POV-Ray v3.6 using the following code:
#include "colors.inc" #include "shapes.inc" #include "textures.inc" #include "functions.inc" camera { location <-0.5, 3, -2> look_at <0, 0, 0> } //Striped textures #declare bluestripes = texture { pigment { gradient y colour_map{[0 rgb <0,0,1>][0.15 rgb <1,1,1>]} } scale 0.1 finish { ambient 0.3 } rotate <0,0,90> } #declare redstripes = texture { pigment { spiral1 1 colour_map{[0 rgb <0.8,0,0>][0.25 rgb <1,1,1>]} } scale 0.1 finish { ambient 0.3 } } #declare blueredstripes = texture { pigment { spiral1 1 colour_map{[0 rgb <0.8,0,0>][0.25 rgb <1,1,1>]} } scale 0.1 finish { ambient 0.3 } } texture { pigment { gradient y colour_map{[0 rgb <0,0,0.8>][0.15 rgb <1,1,1> filter 1]} } scale 0.1 finish { ambient 0.3 } rotate <0,0,90> } #declare Blob_threshold=0.0001; #declare double_torus=isosurface { function //Smoothed sum of two level surfaces { (1+Blob_threshold) -pow(Blob_threshold,f_torus(x+0.6, y, z, 0.5, 0.2)) -pow(Blob_threshold,f_torus(x-0.6, y, z, 0.5, 0.2)) } contained_by { box { <-1.5,-0.3,-0.9>, <1.5,0.3,0.9> } } //Set containing box, default is too small max_gradient 15 } //Red part object { double_torus clipped_by{plane{-x,-0.15}} texture { redstripes } } //Blue part object { double_torus clipped_by{plane{x,-0.15}} texture { bluestripes } } //Intersection part object { double_torus clipped_by{plane{x,0.15}} clipped_by{plane{-x,0.15}} texture { blueredstripes } } //Empty background plane { <0, 1, 0>, -2 no_image } light_source { <0, 1.5, -2> color White}
Licensing[edit]
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. |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 22:51, 18 December 2008 | 776 × 713 (210 KB) | RobHar (talk | contribs) | {{Information |Description={{en|1=Illustration of the boundary map ∂<sub>*</sub> for the Mayer-Vietoris sequence on the double-torus where the 1-cycle x = u + v is the sum of two 1-chains whose boundary lies in the intersection of A and B.}} |Source=Own |
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