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Summary

Made by myself with Matlab.

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.


Source code (MATLAB)

function discontinuity()

   % set up the plotting window
   thick_line=2.5; thin_line=2; arrow_size=3; arrow_type=2;
   fs=30; circrad=0.06;

   
   a=0; b=2/pi; h=0.0001; x0=1;
   X=a:h:b;
%   Y=0.5*sin(1./(X+eps));
   f=inline('X');
   Y=f(X).*sin(1./(X+eps));
   Z=f(X);
   

   figure(3); clf; hold on; axis equal; axis off;

   Q=-0.3; R=2/pi;
   arrow([Q 0], [R, 0], thin_line, arrow_size, pi/8,arrow_type, [0, 0, 0]) % xaxis
   arrow([0 Q], [0, R], thin_line, arrow_size, pi/8,arrow_type, [0, 0, 0]); % y axis


   plot(X, Z, 'linewidth', thin_line, 'linestyle', '--', 'color', [1, 0, 0]);
   plot(X, -Z, 'linewidth', thin_line, 'linestyle', '--', 'color', [1, 0, 0]);
   plot(X, Y, 'linewidth', thick_line);
   
   axis ([-0.2, R, -0.3, R]);
   saveas(gcf, 'TV_pic2.eps', 'psc2');


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

Captions

Graph of the function sin(1/x)

Items portrayed in this file

depicts

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current06:26, 25 February 2007Thumbnail for version as of 06:26, 25 February 2007886 × 989 (19 KB)Oleg Alexandrov
06:21, 25 February 2007Thumbnail for version as of 06:21, 25 February 2007886 × 989 (25 KB)Oleg AlexandrovMade by myself with Matlab.
06:20, 25 February 2007Thumbnail for version as of 06:20, 25 February 2007886 × 989 (25 KB)Oleg AlexandrovMade by myself with Matlab.
06:13, 25 February 2007Thumbnail for version as of 06:13, 25 February 2007481 × 500 (9 KB)Oleg AlexandrovMade by myself with Matlab.
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