File:Homotopy with fixed endpoints.png
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Made by myself with MATLAB.
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. |
% illustrate homotopy with fixed endpoints
function main()
lw=2; % line width
fs=25; % font size
h=1/100;
tiny = 0.004;
tinyrad=0.02;
red = [1, 0, 0];
white = 0.99*[1 1 1];
% prepare the figure
figure(1); clf; hold on; axis equal; axis off;
% generate the curve on which the analytic continuation will take place
XX=[-0.1, 0.3, 0.1]; YY=[0, 1, 1.5];
Y=YY(1):h:YY(length(YY)); X=spline(YY, XX, Y);
% plot a circle
rad=0.4; plot_circle(X(1), Y(1), rad, lw)
% plot the curves
t=0; X=spline(YY, XX+[0, t, 0], Y); plot(X, Y, 'color', red, 'linewidth', lw);
t=0.5; X=spline(YY, XX+[0, t, 0], Y); plot(X, Y, 'color', red, 'linewidth', lw);
t=-0.8; X=spline(YY, XX+[0, t, 0], Y); plot(X, Y, 'color', red, 'linewidth', lw);
t=-0.6; X=spline(YY, XX+[0, t, 0], Y); plot(X, Y, 'color', red, 'linewidth', lw);
t=-0.4; X=spline(YY, XX+[0, t, 0], Y); plot(X, Y, 'color', red, 'linewidth', lw);
% plot text
N = length(X);
Nh = floor(N/2);
text(X(1), Y(1)-tiny*fs, '\it{P}', 'fontsize', fs)
text(X(N), Y(N)+tiny*fs, '\it{Q}', 'fontsize', fs)
text(X(Nh)-0.65, Y(Nh), '\gamma_0', 'fontsize', fs)
text(X(Nh)+0.06, Y(Nh), '\gamma_s', 'fontsize', fs)
text(X(Nh)+1.1, Y(Nh), '\gamma_1', 'fontsize', fs)
text(X(1)-0.26, Y(1)-0.16, '\it{U}', 'fontsize', fs)
% plot some balls for emphasis
ball(X(1), Y(1), tinyrad, red);
ball(X(N), Y(N), tinyrad, red);
% plot a dummy point to avoid having the picture cutt off at edges
% when saving to eps (a matlab bug)
plot(X(1), Y(1)-1.1*rad, '*', 'color', white)
saveas(gcf, 'homotopy_with_fixed_endpoints.eps', 'psc2');
function plot_circle(x, y, r, lw)
N=100;
Theta=0:(1/N):2.1*pi;
X=r*cos(Theta);
Y=r*sin(Theta);
plot(x+X, y+Y, 'linewidth', lw);
function plot_text(x, y, shiftx, shifty, str, fs, tinyrad, color)
text(x+shiftx, y+shifty, str, 'fontsize', fs);
ball(x, y, tinyrad, color);
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');
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 “Homotopy with fixed endpoints.svg”—then the template Vector version available (or Vva) does not need the new image name parameter. |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 01:45, 9 April 2007 | 944 × 1,078 (39 KB) | Oleg Alexandrov (talk | contribs) | Made by myself with MATLAB. {{PD-self}} | |
01:39, 9 April 2007 | 925 × 1,053 (39 KB) | Oleg Alexandrov (talk | contribs) | Made by myself with MATLAB. {{PD-self}} | ||
01:39, 9 April 2007 | 925 × 1,053 (39 KB) | Oleg Alexandrov (talk | contribs) | Made by myself with MATLAB. {{PD}} |
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