File:Mayer Vietoris sequence boundary map on torus.png
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editDescriptionMayer Vietoris sequence boundary map on torus.png |
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
editThe 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}
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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.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 12:23, 16 May 2011 | 700 × 750 (172 KB) | Quilbert (talk | contribs) | {{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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