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| Keywords: Analytic continuation along a curve.png Made by myself with MATLAB Source code MATLAB <source lang Matlab > illustrate the analytic continuation along a curve function main lw 2; line width fs 20; font size h 1/100; tinyrad 0 04; red 1 0 0; 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 4 0 28 0 0; YY 1 4 0 1 1 5 2 2 8; Y YY 1 h YY length YY ; X spline YY XX Y ; N length X ; plot the circles of analytic continuation rad 0 8; spacing 1; gap spacing/h; k 1; while k < N plot_circle X k Y k rad lw ; k k+gap; end plot_circle X N Y N rad lw ; plot the curve plot X Y 'color' red 'linewidth' lw ; plot the text tiny 0 003 fs; plot_text X 1 Y 1 -2 tiny -3 5 tiny '\gamma 0 ' fs tinyrad red ; t 0 5; k floor N t ; plot_text X k Y k tiny tiny '\gamma \it t ' fs tinyrad red ; plot_text X N Y N -4 tiny 4 5 tiny '\gamma 1 ' fs tinyrad red ; plot arrows showing the direction along the curve thickness lw; arrow_size 0 27; sharpness 25; arrow_type 1; t 0 2; s 0 1; k floor N t ; l floor N t+s ; arrow X k Y k X l Y l thickness arrow_size sharpness arrow_type red t 0 8; s 0 1; k floor N t ; l floor N t+s ; arrow X k Y k X l Y l thickness arrow_size sharpness arrow_type red plot a phony box around the graph to avoid a bug in matlab with truncating around the edges when exporting to eps white 0 99 1 1 1; factor 1 1; plot X 1 -factor rad Y 1 -factor rad ' ' 'color' white ; plot X N +factor rad Y N +factor rad ' ' 'color' white ; saveas gcf 'analytic_continuation_along_a_curve 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' ; function arrow start stop thickness arrow_size sharpness arrow_type color Function arguments start stop start and end coordinates of arrow vectors of size 2 thickness thickness of arrow stick arrow_size the size of the two sides of the angle in this picture -> sharpness angle between the arrow stick and arrow side in degrees arrow_type 1 for filled arrow otherwise the arrow will be just two segments color arrow color a vector of length three with values in 0 1 convert to complex numbers i sqrt -1 ; start start 1 +i start 2 ; stop stop 1 +i stop 2 ; rotate_angle exp i pi sharpness/180 ; points making up the arrow tip besides the stop point point1 stop - arrow_size rotate_angle stop-start /abs stop-start ; point2 stop - arrow_size/rotate_angle stop-start /abs stop-start ; if arrow_type 1 filled arrow plot the stick but not till the end looks bad t 0 5 arrow_size cos pi sharpness/180 /abs stop-start ; stop1 t start+ 1-t stop; plot real start stop1 imag start stop1 'LineWidth' thickness 'Color' color ; fill the arrow H fill real stop point1 point2 imag stop point1 point2 color ; set H 'EdgeColor' 'none' else two-segment arrow plot real start stop imag start stop 'LineWidth' thickness 'Color' color ; plot real stop point1 imag stop point1 'LineWidth' thickness 'Color' color ; plot real stop point2 imag stop point2 'LineWidth' thickness 'Color' color ; end </source> Analytic continuation Images with Matlab source code Files by User Oleg Alexandrov from en wikipedia math | ||||
