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| View Original: | DoubleTorusCover.png (776x713) | |||
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| Keywords: DoubleTorusCover.png en Illustration of the boundary map ˆ‚<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 Own work using POV-Ray and Inkscape Based on a drawing by User GeometryGirl public domain RobHar 2008-12-18 Data file 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 Algebraic topology Blobs Created_with_Persistence_of_Vision Isosurfaces | ||||
