File:Discontinuity essential.eps.png

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Summary

Description
English: Discontinuity essential.
 
This diagram was created with MATLAB.
Date 12 September 2005 (original upload date)
Source Transferred from en.wikipedia to Commons by Maksim.
Author Oleg Alexandrov at English Wikipedia
Permission
(Reusing this file)
Public domain This work has been released into the public domain by its author, Oleg Alexandrov at English Wikipedia. This applies worldwide.
In some countries this may not be legally possible; if so:
Oleg Alexandrov grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.
MATLAB source
InfoField
click to expand
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
File:Discontinuity essential.svg is a vector version of this file. It should be used in place of this PNG file when not inferior.

File:Discontinuity essential.eps.png → File:Discontinuity essential.svg

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Original upload log

The original description page is/was here. All following user names refer to en.Wikipedia.

date/time username resolution size edit summary
01:31, 12 September 2005 Oleg Alexandrov 376 × 255 13,023 bytes (source code)
01:25, 12 September 2005 Oleg Alexandrov 376 × 255 13,023 bytes
00:53, 12 September 2005 Oleg Alexandrov 376 × 253 11,802 bytes (Made by me with matlab.)

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Date/TimeThumbnailDimensionsUserComment
current22:18, 10 July 2013Thumbnail for version as of 22:18, 10 July 20132,506 × 1,700 (83 KB)Oleg AlexandrovMade the point on the axis blue, per request, this is how it should be.

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