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| View Original: | Homotopy with fixed endpoints.png (944x1078) | |||
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| Keywords: Homotopy with fixed endpoints.png Made by myself with MATLAB Source code MATLAB <source lang Matlab > illustrate homotopy with fixed endpoints function main lw 2; line width fs 25; font size h 1/100; tiny 0 004; tinyrad 0 02; red 1 0 0; white 0 99 1 1 1; prepare the figure figure 1 ; clf; hold on; axis equal; axis off; generate the curve on which the analytic continuation will take place XX -0 1 0 3 0 1; YY 0 1 1 5; Y YY 1 h YY length YY ; X spline YY XX Y ; plot a circle rad 0 4; plot_circle X 1 Y 1 rad lw plot the curves t 0; X spline YY XX+0 t 0 Y ; plot X Y 'color' red 'linewidth' lw ; t 0 5; X spline YY XX+0 t 0 Y ; plot X Y 'color' red 'linewidth' lw ; t -0 8; X spline YY XX+0 t 0 Y ; plot X Y 'color' red 'linewidth' lw ; t -0 6; X spline YY XX+0 t 0 Y ; plot X Y 'color' red 'linewidth' lw ; t -0 4; X spline YY XX+0 t 0 Y ; plot X Y 'color' red 'linewidth' lw ; plot text N length X ; Nh floor N/2 ; text X 1 Y 1 -tiny fs '\it P ' 'fontsize' fs text X N Y N +tiny fs '\it Q ' 'fontsize' fs text X Nh -0 65 Y Nh '\gamma_0' 'fontsize' fs text X Nh +0 06 Y Nh '\gamma_s' 'fontsize' fs text X Nh +1 1 Y Nh '\gamma_1' 'fontsize' fs text X 1 -0 26 Y 1 -0 16 '\it U ' 'fontsize' fs plot some balls for emphasis ball X 1 Y 1 tinyrad red ; ball X N Y N tinyrad red ; plot a dummy point to avoid having the picture cutt off at edges when saving to eps a matlab bug plot X 1 Y 1 -1 1 rad ' ' 'color' white saveas gcf 'homotopy_with_fixed_endpoints eps' 'psc2' ; function plot_circle x y r lw N 100; Theta 0 1/N 2 1 pi; X r cos Theta ; Y r sin Theta ; plot x+X y+Y 'linewidth' lw ; function plot_text x y shiftx shifty str fs tinyrad color text x+shiftx y+shifty str 'fontsize' fs ; ball x y tinyrad color ; function ball x y r color Theta 0 0 1 2 pi; X r cos Theta +x; Y r sin Theta +y; H fill X Y color ; set H 'EdgeColor' 'none' ; </source> Analytic continuation Homotopy Images with Matlab source code Files by User Oleg Alexandrov from en wikipedia math | ||||
