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| Keywords: Triple torus illustration.png Illustration of a triple torus own MATLAB source code below Created with MATLAB 18 01 7 September 2007 UTC Oleg Alexandrov math Source code MATLAB <source lang matlab > function main illustration of a triple torus torus radii r 1; R 3; Kb R+r; Ks R-r; Km controls the smoothness of the transition from one ring to the others Km 0 5125 Kb; L 2 5 r+R ; h 0 2; grid size X -L h L; m length X ; Y -L h L; n length Y ; Z -1 1 r h 1 1 r ; k length Z ; W zeros m n k ; for i 1 length X for j 1 length Y x X i ; y Y j ; x y triple_torus_function x y r R Kb Km ; val sqrt x 2+y 2 -R 2-r 2; W i j val + Z 2; end end figure 1 ; clf; hold on; axis equal; axis off; light_green 184 224 98/256; light green H patch isosurface X Y Z W 0 ; isonormals X Y Z W H ; mycolor light_green; set H 'FaceColor' mycolor 'EdgeColor' 'none' 'FaceAlpha' 1 ; set H 'SpecularColorReflectance' 0 1 'DiffuseStrength' 0 8 ; set H 'FaceLighting' 'phong' 'AmbientStrength' 0 3 ; set H 'SpecularExponent' 108 ; daspect 1 1 1 ; axis tight; colormap prism 28 view -12 40 ; add in a source of light camlight -50 54 ; lighting phong; print '-dpng' '-r400' sprintf 'Triple_torus_illustration png' ; function x y triple_torus_function x y r R Kb Km a deformation in the plane which when comosed with a torus will give a triple torus center of one of the torii O -Kb -Kb/sqrt 3 ; angle 2 pi/3; Mat cos angle -sin angle ; sin angle cos angle ; p x y'; phi atan2 y x ; if phi > pi/6 phi < 5 pi/6 p Mat p; rotate 120 degree counterclockwise elseif phi > -pi/2 phi < pi/6 p Mat p; p Mat p; rotate 240 degrees counterclockwise end x p 1 ; y p 2 ; reflect against a line to merge two cases in one if y > x/sqrt 3 p x y; v cos 2 pi/3 sin 2 pi/3 ; p p - 2 v dot p v /dot v v ; x p 1 ; y p 2 ; end if x > O 1 project to the y axis to a point B if y < O 2 A O 1 y; B 0 y; else A O; p x y; rho norm p-O ; B O+ Kb/rho p-O ; t -O 1 / x-O 1 ; B 0 O 2 +t y-O 2 ; end p x y; d norm p-A ; q norm B-A ; d my_map d q Km ; p d/q B+ 1-d/q A; x p 1 ; y p 2 ; end shift towards the origin x x-O 1 ; y y-O 2 ; function y my_map x Kb Km if x > Kb y Km + 1; elseif x < Km y x; else y Km+sin pi/2 x-Km / Kb-Km ; end </source> Higher genus Files by User Oleg Alexandrov from en wikipedia Isosurfaces Images with Matlab source code math | ||||
