Talaksan:Discontinuity removable.eps.png

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 This diagram was created with MATLAB.

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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.

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 } })

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. For more information, see Commons:Threshold of originality § Charts العربية | Deutsch | English | español | français | italiano | 日本語 | македонски | română | русский | slovenščina | 中文（简体） | 中文（繁體） | +/−