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| Keywords: Argument principle1.png en wikipedia Maksim page en wikipedia Made by myself with Matlab Oleg Alexandrov Argument principle1 svg Source code The function arrow used here is written and copyrighted by somebody else I don't know the terms Everything else is written by me which I put in the public domain Source code MATLAB <source lang Matlab > function main draw a closed spline curve with some points inside curve_linewidth 1 8; arrowsize 8; arrow_type 2; make filled trig arrow ball_radius 0 015; how big to make the points representing the zeros x 0 1 1 2 0 0; y 0 0 1 1 1 0 5; points the spline will go thru n length x ; P 5; Q n+2 P+1; P will denote the amount of overlap of the path with itself Make the 'periodic' sequence xp x 1 x 2 x 3 x n x 1 x 2 x 3 of length Q Same for yp for i 1 Q j rem i n +1; rem is the remainder of division of i by n xp i x j ; yp i y j ; end do the spline interpolation t 1 length xp ; N 100; how fine to make the interpolation tt 1 1/N length xp ; xx spline t xp tt ; yy spline t yp tt ; discard the redundant overlap pieces start N P-1 +1; stop N n+P-1 +1; xx xx start stop ; yy yy start stop ; figure 1 ; clf; hold on; axis equal; axis off; prepare the screen plot xx yy 'k' 'LineWidth' curve_linewidth plot the path plot the residues and the poles -- see the ball function below ball 0 5 0 7 ball_radius 1 0 0 ; red ball 0 3187 0 3024 ball_radius 0 0 1 ; blue ball 0 7231 0 4441 ball_radius 0 0 1 ; ball 0 7981 0 7776 ball_radius 0 0 1 ; ball 0 2854 0 8026 ball_radius 1 0 0 ; ball 0 6397 0 1773 ball_radius 1 0 0 ; ball 0 2896 0 5525 ball_radius 0 0 1 ; ball 0 9774 0 5817 ball_radius 1 0 0 ; ball 0 6189 1 0068 ball_radius 1 0 0 ; place the two arrows showing the orientation of the contour shift 80; arrow xx shift yy shift xx shift+10 yy shift+10 curve_linewidth arrowsize pi/8 arrow_type 0 0 0 shift 270; arrow xx shift yy shift xx shift+10 yy shift+10 curve_linewidth arrowsize pi/8 arrow_type 0 0 0 axis min xx -1 max xx +1 min yy -1 max yy +1 ; image frame saveas gcf 'argument_principle eps' 'psc2' save to file disp 'Saved to argument_principle eps Get antialiased png in an editor ' auxiliary functions ball and arrow function ball x y radius color draw a ball of given uniform color Theta 0 0 1 2 pi; X radius cos Theta +x; Y radius sin Theta +y; H fill X Y color ; set H 'EdgeColor' color ; function arrow start stop thickness arrowsize sharpness arrow_type color draw a line with an arrow at the end start is the x y point where the line starts stop is the x y point where the line stops thickness is an optional parameter giving the thickness of the lines arrowsize is an optional argument that will give the size of the arrow It is assumed that the axis limits are already set 0 < sharpness < pi/4 determines how sharp to make the arrow arrow_type draws the arrow in different styles Values are 0 1 2 3 8/4/93 Jeffery Faneuff Copyright c 1988-93 by the MathWorks Inc Modified by Oleg Alexandrov 2/16/03 if nargin < 6 color 0 0 0; default color end if nargin < 5 arrow_type 0; the default arrow it looks like this -> end if nargin < 4 sharpness pi/4; the arrow sharpness - default pi/4 end if nargin< 3 xl get gca 'xlim' ; yl get gca 'ylim' ; xd xl 2 -xl 1 ; yd yl 2 -yl 1 ; arrowsize xd + yd / 2; this sets the default arrow size end if nargin< 2 thickness 0 5; default thickness end xdif stop 1 - start 1 ; ydif stop 2 - start 2 ; if xdif 0 if ydif >0 theta pi/2; else theta -pi/2; end else theta atan ydif/xdif ; the angle has to point according to the slope end if xdif> 0 arrowsize -arrowsize; end if arrow_type 0 draw the arrow like two sticks originating from its vertex xx start 1 stop 1 stop 1 +0 02 arrowsize cos theta+sharpness NaN stop 1 stop 1 +0 02 arrowsize cos theta-sharpness ; yy start 2 stop 2 stop 2 +0 02 arrowsize sin theta+sharpness NaN stop 2 stop 2 +0 02 arrowsize sin theta-sharpness ; plot xx yy 'LineWidth' thickness 'color' color end if arrow_type 1 draw the arrow like an empty triangle xx stop 1 stop 1 +0 02 arrowsize cos theta+sharpness stop 1 +0 02 arrowsize cos theta-sharpness ; xx xx xx 1 xx 2 ; yy stop 2 stop 2 +0 02 arrowsize sin theta+sharpness stop 2 +0 02 arrowsize sin theta-sharpness ; yy yy yy 1 yy 2 ; plot xx yy 'LineWidth' thickness 'color' color plot the arrow stick plot start 1 stop 1 +0 02 arrowsize cos theta cos sharpness start 2 stop 2 +0 02 arrowsize sin theta cos sharpness 'LineWidth' thickness 'color' color end if arrow_type 2 draw the arrow like a full triangle xx stop 1 stop 1 +0 02 arrowsize cos theta+sharpness stop 1 +0 02 arrowsize cos theta-sharpness stop 1 ; yy stop 2 stop 2 +0 02 arrowsize sin theta+sharpness stop 2 +0 02 arrowsize sin theta-sharpness stop 2 ; H fill xx yy color ; fill with black set H 'EdgeColor' 'none' plot the arrow stick plot start 1 stop 1 +0 01 arrowsize cos theta start 2 stop 2 +0 01 arrowsize sin theta 'LineWidth' thickness 'color' color end if arrow_type 3 draw the arrow like a filled 'curvilinear' triangle curvature 0 5; change here to make the curved part more or less curved radius 0 02 arrowsize max curvature tan sharpness ; x1 stop 1 +0 02 arrowsize cos theta+sharpness ; y1 stop 2 +0 02 arrowsize sin theta+sharpness ; x2 stop 1 +0 02 arrowsize cos theta cos sharpness ; y2 stop 2 +0 02 arrowsize sin theta cos sharpness ; d1 sqrt x1-x2 2+ y1-y2 2 ; d2 sqrt radius 2-d1 2 ; d3 sqrt stop 1 -x2 2+ stop 2 -y2 2 ; center 1 stop 1 + d2+d3 cos theta ; center 2 stop 2 + d2+d3 sin theta ; alpha atan d1/d2 ; Alpha -alpha 0 05 alpha; xx center 1 -radius cos Alpha+theta ; yy center 2 -radius sin Alpha+theta ; xx xx stop 1 xx 1 ; yy yy stop 2 yy 1 ; H fill xx yy color ; fill with black set H 'EdgeColor' 'none' plot the arrow stick plot start 1 center 1 -radius cos theta start 2 center 2 - radius sin theta 'LineWidth' thickness 'color' color ; end </source> 1 date/time username edit summary ---- 19 16 7 March 2006 en User 141 140 104 11 <nowiki> fix deprecated cp tag </nowiki> ---- 01 01 13 June 2005 en User Oleg Alexandrov <nowiki> replacing thru with through in comments of computer code is a bit excessive </nowiki> ---- 22 09 12 June 2005 en User Bratsche <nowiki> 'thru' -> 'through'; -- <a href /wiki/User Humanbot title User Humanbot >Join and fix more </a> </nowiki> ---- 23 19 15 January 2005 en User Oleg Alexandrov <nowiki> added source code </nowiki> ---- 18 04 15 January 2005 en User Oleg Alexandrov <nowiki> Made by myself with Matlab PD </nowiki> Original upload log Legend cur this is the current file del delete this old version rev revert to this old version Click on date to download the file or see the image uploaded on that date del cur 18 04 15 January 2005 en User Oleg_Alexandrov Oleg Alexandrov en User_talk Oleg_Alexandrov Talk 200x168 6960 bytes Made by myself with Matlab PD Complex analysis Images with Matlab source code Files by User Oleg Alexandrov from en wikipedia | ||||
