Imagen:Discontinuity removable.eps.png

La bildo estas kopiita de wikipedia:en. La originala priskribo estas:

[edit] Summary

Made by me with matlab.

This file has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. This applies worldwide.

Note: This tag is obsolete! Don't use this generic template - please use instead: {{PD-old}} (for works out of copyright where the author has been dead for over 70 years), {{PD-Art}} (for photos of old paintings and art out of copyright), {{PD-ineligible}} (for trivial work), {{PD-USGov}} (for work by the U.S. federal government), {{PD-self}} (if the uploader and creator releases the rights), {{PD-user|user}} (if another user released his/her rights), or {{Copyrighted free use}}. use {{PD-user-w|projectcode|projectname|username}} for users with no account on Commons. {{PD-author|Author's name}} - for works released into the public domain by non-Wikimedia users. If the work is PD for another reason, check the copyright tag page or use {{PD-because|reason}}. العربية | česky | Deutsch | English | Español | Français | हिन्दी | Italiano | 日本語 | Norsk (nynorsk) | Português | Русский | Slovenčina | Slovenščina | Српски | Polski | Türkçe | 简体中文 | +/-

[edit] Licensing

I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide. In case this is not legally possible: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. Afrikaans | Alemannisch | Aragonés | العربية‎ | Български | Català | Česky | Cymraeg | Dansk | Deutsch | Ελληνικά | English | Español | Esperanto | Euskara | فارسی‎ | Français | Galego | 한국어 | हिन्दी | Hrvatski | Ido | Bahasa Indonesia | Íslenska | Italiano | עברית‎ | Kurdî / كوردي | Latina | Lietuvių | Magyar | Bahasa Melayu | Nederlands | Norsk (bokmål) | Norsk (nynorsk) | 日本語 | Polski | Português | Ripoarish | Română | Русский | Shqip | Slovenčina | Slovenščina | Српски | Svenska | ไทย | Türkçe | Українська | Tiếng Việt | Walon | 简体中文 | 繁體中文 | 粵語 | +/-

Source code:

function discontinuity()

   % set up the plotting window
   thick_line=2.5; thin_line=2; arrow_size=14; arrow_type=2;
   fs=30; circrad=0.06;

% picture 1   
   a=-1.5; b=3; h=0.02; x0=1;
   X1=a:h:x0; X2=x0:h:b; X=[X1 X2];
   Y1=X1.^2; Y2=Y1(length(Y1))+(-1)*(X2-X2(1)); Y=[Y1 Y2]; y01=Y1(length(Y1)); y02=Y2(1);

   figure(1); clf; hold on; axis equal; axis off;
   axes_points(a, b, thin_line, thick_line, arrow_size, arrow_type, x0, y01, y02, circrad, fs, X, Y, X1, Y1, X2, Y2)
   saveas(gcf, 'discontinuity_removable.eps', 'psc2')

% picture 2   
   a=-1.5; b=3; h=0.02; x0=1;
   X1=a:h:x0; X2=x0:h:b; X=[X1 X2];
   Y1=X1.^2; Y2=2-(X2-x0).^2; Y=[Y1 Y2]; y01=Y1(length(Y1)); y02=Y2(1);

   figure(2); clf; hold on; axis equal; axis off;
   axes_points(a, b, thin_line, thick_line, arrow_size, arrow_type, x0, y01, y02, circrad, fs, X, Y, X1, Y1, X2, Y2)
   saveas(gcf, 'discontinuity_jump.eps', 'psc2')
   
% picture 3   
   a=-1.5; b=3; h=0.001; x0=1;
   X1=a:h:x0; X2=x0:h:b; X=[X1 X2];
   Y1=sin(5./(X1-x0-eps)); Y2=0.1./(X2-x0+50*h); Y=[Y1 Y2]; y01=Y1(length(Y1)); y02=Y2(1);

   figure(3); clf; hold on; axis equal; axis off;
   axes_points2(a, b, thin_line, thick_line, arrow_size, arrow_type, x0, NaN, NaN, circrad, fs, X, Y, X1, Y1, X2, Y2)
   saveas(gcf, 'discontinuity_essential.eps', 'psc2')

   
function axes_points(a, b, thin_line, thick_line, arrow_size, arrow_type, x0, y01, y02, circrad, fs, X, Y, X1, Y1, X2, Y2)
   arrow([a 0], [b, 0], thin_line, arrow_size, pi/8,arrow_type, [0, 0, 0]) % xaxis
   small=0.2; arrow([0, min(Y)], [0, max(Y)], thin_line, arrow_size, pi/8,arrow_type, [0, 0, 0]); % y axis

   plot(X1, Y1, 'linewidth', thick_line); plot(X2, Y2, 'linewidth', thick_line)

   ball(x0, 0, circrad, [0 0 0 ]); 
   ball_empty(x0, y01, thick_line, circrad, [1 0 0 ]); ball_empty(x0, y02, thick_line, circrad, [1 0 0 ]); 
   H=text(x0, -0.006*fs,  'x_0'); set(H, 'fontsize', fs, 'HorizontalAlignment', 'c', 'VerticalAlignment', 'c')

function axes_points2(a, b, thin_line, thick_line, arrow_size, arrow_type, x0, y01, y02, circrad, fs, X, Y, X1, Y1, X2, Y2)
   arrow([a 0], [b, 0], thin_line, arrow_size, pi/8,arrow_type, [0, 0, 0]) % xaxis
   small=0.2; arrow([0, min(Y)], [0, max(Y)], thin_line, arrow_size, pi/8,arrow_type, [0, 0, 0]); % y axis

   plot(X1, Y1, 'linewidth', thick_line); plot(X2, Y2, 'linewidth', thick_line)

   ball(x0, 0, circrad, [0 0 0 ]); 
   ball_empty(x0, y01, thick_line, circrad, [1 0 0 ]); ball_empty(x0, y02, thick_line, circrad, [1 0 0 ]); 
   H=text(x0+0.2, -0.006*fs,  'x_0'); set(H, 'fontsize', fs, 'HorizontalAlignment', 'c', 'VerticalAlignment', 'c')

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 ball_empty(x, y, thick_line, r, color)
   Theta=0:0.1:2*pi;
   X=r*cos(Theta)+x;
   Y=r*sin(Theta)+y;
   H=fill(X, Y, [1 1 1]);
   %set(H, 'EdgeColor', color);
  plot(X, Y, 'color', color, 'linewidth', thick_line);
   

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];
   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 curved (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

[edit] Historio de la dosiero

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) 01:28, 12 September 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 376x277 (9967 bytes)
• (del) (rev) 00:51, 12 September 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 376x275 (7002 bytes) (Made by me with matlab. { { PD } })