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File:Mayer Vietoris sequence boundary map on torus.png

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Original file(700 × 750 pixels, file size: 172 KB, MIME type: image/png)

Summary

Description
English: Illustration of the boundary map ∂* for the Mayer-Vietoris sequence on the 2-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, heavily based on DoubleTorusCover.png by RobHar, the description of which says:

“Own work using POV-Ray and Inkscape. Based on a drawing by User:GeometryGirl (public domain)”
Author Quilbert
Other versions File:DoubleTorusCover.png

Data file

The 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 0.07
               finish { ambient 0.3 }
               rotate <0,0,90>
       }
       
#declare redstripes = texture
       {
               pigment
               {
                       gradient z
                       colour_map{[0 rgb <0.8,0,0>][0.25 rgb <1,1,1>]}
               }
               scale 0.07
               finish { ambient 0.3 }
       }
       
#declare blueredstripes = texture
       {        
               pigment
               {
                       gradient z
                       colour_map{[0 rgb <0.8,0,0>][0.25 rgb <1,1,1>]}
               }
               scale 0.07
               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 0.07
               finish { ambient 0.3 }
               rotate <0,0,90>  
       }

#declare Blob_threshold=0.0001;

#declare double_torus=isosurface
{
       function        //Smoothed sum of two level surfaces
       {
		f_torus((abs(x)-0.15+abs(abs(x)-0.15))/2,y,z+0.012,0.7,0.28)
       }
       contained_by { box { <-1.5,-0.3,-1.5>, <1.5,0.3,1.5> } }      //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

I, the copyright holder of this work, hereby publish it under the following licenses:
w:en:Creative Commons
attribution share alike
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.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
You may select the license of your choice.

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depicts

14 July 2010

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Date/TimeThumbnailDimensionsUserComment
current12:23, 16 May 2011Thumbnail for version as of 12:23, 16 May 2011700 × 750 (172 KB)Quilbert{{Information |Description ={{en|1=Illustration of the boundary map ∂<sub>*</sub> for the Mayer-Vietoris sequence on the 2-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

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