File:Discontinuity jump.eps.png
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Size of this preview: 643 × 599 pixels. Other resolutions: 258 × 240 pixels | 515 × 480 pixels | 824 × 768 pixels | 1,099 × 1,024 pixels | 2,122 × 1,978 pixels.
Original file (2,122 × 1,978 pixels, file size: 81 KB, MIME type: image/png)
This file is from Wikimedia Commons and may be used by other projects. The description on its file description page there is shown below.
Transferred from en.wikipedia to Commons by Maksim.
The original description page was here. All following user names refer to en.wikipedia.
Summary
Made by me with matlab. {PD.}
This diagram was created with MATLAB.
Licensing
Public domainPublic domainfalsefalse |
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=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
date/time | username | edit summary |
---|---|---|
04:49, 5 December 2005 | en:User:Oleg Alexandrov | (clean up code) |
00:01, 22 November 2005 | en:User:Oleg Alexandrov | (+ source code) |
00:52, 12 September 2005 | en:User:Oleg Alexandrov | (Made by me with matlab. {PD.}) |
Original upload log
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) 10:30, 20 January 2006 . . DavidHouse ( en:User_talk:DavidHouse Talk) . . 318x297 (10408 bytes) (Reverted to earlier revision)
- (del) (rev) 10:30, 20 January 2006 . . DavidHouse ( en:User_talk:DavidHouse Talk) . . 317x297 (8531 bytes) (Reverted to earlier revision)
- (del) (rev) 01:28, 12 September 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 318x297 (10408 bytes)
- (del) (rev) 00:52, 12 September 2005 . . en:User:Oleg_Alexandrov Oleg Alexandrov ( en:User_talk:Oleg_Alexandrov Talk) . . 317x297 (8531 bytes) (Made by me with matlab. { PD. })
derivative works
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File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 06:17, 11 July 2013 | 2,122 × 1,978 (81 KB) | wikimediacommons>Oleg Alexandrov | Made the point on the axis blue, per request, this is how it should be. |
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