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File:WedgeSumSpheres.png

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Original file (1,024 × 768 pixels, file size: 230 KB, MIME type: image/png)

Summary

Description
English: A wedge sum of two spheres with a cover appropriate to apply the Mayer-Vietoris sequence to calculate its homology groups.
Date
Source Own work using POV-Ray and Inkscape. Based on a drawing by User:GeometryGirl (public domain)
Author RobHar

Data file

The spheres were produced using POV-Ray v3.6 using the following code:

 #include "colors.inc"
 #include "shapes.inc"   
 #include "textures.inc"
 
 camera
 {
        location <0, 0, -2>
        look_at <0, 0, 0>
 }
 
 //Striped textures
 #declare bluestripes = texture
        {
                pigment
                { 
                        gradient y
                        colour_map{[0 rgb <0,0,1>][0.1 rgb <1,1,1>]}
                }
                scale 0.05
                finish { ambient 0.3 }
                rotate <0,0,45>
        }
        
 #declare redstripes = texture
        {
                pigment
                {
                        gradient y
                        colour_map{[0 rgb <0.8,0,0>][0.1 rgb <1,1,1>]}
                }
                scale 0.05
                finish { ambient 0.3 }
                rotate <0,0,-45>          
        }
        
 #declare blueredstripes = texture
        {        
                pigment
                {
                        gradient y
                        colour_map{[0 rgb <0.8,0,0>][0.1 rgb <1,1,1>]}
                }                                                    
                scale 0.05
                finish { ambient 0.3 }
                rotate <0,0,-45>   
        }              
        texture
        {
                pigment
                {
                        gradient y
                        colour_map{[0 rgb <0,0,0.8>][0.1 rgb <1,1,1> filter 1]}
                }
                scale 0.05
                finish { ambient 0.3 }
                rotate <0,0,45>  
        }
 
 //Blue sphere
 object
 {
 sphere
 {
        <-0.5, 0, 0>, 0.5
        texture
        {
                bluestripes
        }
 }
 clipped_by{plane{x,-0.20}}
 }
 
 //Red sphere
 object
 {
 sphere
 {
        <0.5, 0, 0>, 0.5
        texture
        {
                redstripes          
        }
 }
 clipped_by{plane{-x,-0.20}}   
 }
 
 //Middle part
 union
 {
 sphere
 {
        <-0.5, 0, 0>, 0.5
        clipped_by{plane{-x,0.2}}       
 }
 sphere
 {
        <0.5, 0, 0>, 0.5
        clipped_by{plane{x,0.2}}       
 }
 
 texture
 {
        blueredstripes
 }
 }
 
 //Basepoint
 sphere
 {
        <0,0,-0.2> 0.02
        pigment {colour Black}
 }   
 
 //Empty background
 plane
 {
        <0, 1, 0>, -2
        no_image
 }                               
 
 light_source { <0, 1.5, -2> color White}

Licensing

Public domain 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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depicts

17 December 2008

File history

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Date/TimeThumbnailDimensionsUserComment
current00:44, 18 December 2008Thumbnail for version as of 00:44, 18 December 20081,024 × 768 (230 KB)RobHar{{Information |Description={{en|1=A wedge sum of two spheres with a cover appropriate to apply the Mayer-Vietoris sequence to calculate its homology groups.}} |Source=Own work using POV-Ray and Inkscape |Author=RobHar |Date=2008-12-17 |Per

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