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| View Original: | Jordan illustration.png (1064x1006) | |||
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| Keywords: Jordan illustration.png Made by myself with Matlab Source code MATLAB <source lang Matlab > function main the function whose zero level set and inner and outer approximations will be drawn f inline '60-real z 2-1 2 imag z 2-0 006 real z -6 4-0 01 imag z -5 4' 'z' ; M 10; i sqrt -1 ; lw 2 5; figure 1 ; clf; hold on; axis equal; axis off; if 1 0 for p -M M for q -M M z p+i q; if f z >0 plot real z imag z 'r ' else plot real z imag z 'b ' end end end end draw the zero level set of f h 0 1; XX -M h M; YY -M h M; X Y meshgrid XX YY ; Z f X+i Y ; C H contour X Y Z 0 0 ; set H 'linewidth' lw 'EdgeColor' 0;0;156/256 ; plot the outer polygonal curve Start 5+6 i; Dir -i; Sign -1; plot_poly Start Dir Sign f lw 139;10;80/256 ; plot the inner polygonal curve Sign 1; Start 4+5 i; plot_poly Start Dir Sign f lw 0;100;0/256 ; a dummy plot to avoid a matlab bug causing some lines to appear too thin plot 8 5 7 5 ' ' 'color' 0 99 1 1 1 ; plot -4 5 -5 ' ' 'color' 0 99 1 1 1 ; saveas gcf 'jordan_illustration eps' 'psc2' ; function plot_poly Start Dir Sign f lw color Current_point Start; Current_dir Dir; Ball_rad 0 03; for k 1 100 Next_dir -Current_dir; from the current point search to the left down and right and see where to go next for l 1 3 Next_dir Next_dir Sign i ; if Sign f Current_point+Next_dir > 0 Sign f Current_point+ Sign i Next_dir < 0 break; end end Next_point Current_point+Next_dir; plot real Current_point real Next_point imag Current_point imag Next_point 'linewidth' lw 'color' color ; round_ball Current_point Ball_rad color' ; just for beauty to round off some rough corners Current_dir Next_dir; Current_point Next_point; end function round_ball z r color x real z ; y imag z ; Theta 0 0 1 2 pi; X r cos Theta +x; Y r sin Theta +y; Handle fill X Y color ; set Handle 'EdgeColor' color ; </source> Measure theory Jordan curves Images with Matlab source code Files by User Oleg Alexandrov from en wikipedia math | ||||
