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File:Discontinuity removable.eps.png

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Original file(2,506 × 1,844 pixels, file size: 72 KB, MIME type: image/png)

Summary

Matlab Logo.png This diagram was created with MATLAB.

Converted to SVG.svg
This math image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}.
It is recommended to name the SVG file "Discontinuity removable.eps.svg" – then the template Vector version available (or Vva) does not need the new image name parameter.

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')

disp('Converting to png...')
! convert -density 400 -antialias discontinuity_removable.eps discontinuity_removable.png
! convert -density 400 -antialias discontinuity_jump.eps discontinuity_jump.png
! convert -density 400 -antialias discontinuity_essential.eps discontinuity_essential.png

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 1 ]);
   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 1 ]);
   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

Transferred from en.wikipedia to Commons by Maksim.

The original description page was removable.eps.png here. All following user names refer to en.wikipedia.
date/time username edit summary
03:11, 14 September 2005 en:User:Oleg Alexandrov (<span class="autocomment"><a href="/wiki/Image:Discontinuity_removable.eps.png#Licensing" title="Image:Discontinuity removable.eps.png">→</a>Licensing</span>)
00:51, 12 September 2005 en:User:Oleg Alexandrov (Made by me with matlab. )

Original upload log

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Licensing

Public domain This chart is ineligible for copyright and therefore in the public domain, because it consists entirely of information that is common property and contains no original authorship. See the charts section of Commons:Threshold of originality.

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File history

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Date/TimeThumbnailDimensionsUserComment
current04:17, 11 July 2013Thumbnail for version as of 04:17, 11 July 20132,506 × 1,844 (72 KB)Oleg AlexandrovMade the point on the axis blue, per request, this is how it should be.
18:09, 18 March 2006Thumbnail for version as of 18:09, 18 March 2006376 × 277 (10 KB)MaksimLa bildo estas kopiita de wikipedia:en. La originala priskribo estas: == Summary == Made by me with matlab. {{PD}} == Licensing == {{PD-self}} Source code: <pre> function discontinuity() % set up the plotting window thick_line=2.5; thin_line=2
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