File:Partition of unity illustration.svg
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DescriptionPartition of unity illustration.svg | Illustration of en:Partition of unity |
Date | (UTC) |
Source | self-made with MATLAB, tweaked in Inkscape |
Author | Oleg Alexandrov |
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. |
% illustration of partitition of unity.
% For simplicity, we cheat by using scaled sums of gaussians
% instead of bump functions.
function main()
figure(1); clf; hold on; axis equal; axis off;
lw = 2; % linewidth
h=0.1; % grid size
% endpoints of the interval
a = -5; b = 10;
Sample=[-2.1 -1.3 -0.4 1.3 1.8 3.1 4.5];
red = [0.867 0.06 0.14];
blue = [0, 129, 205]/256;
green = [0, 200, 70]/256;
yellow = [254, 194, 0]/256;
Colors = [red', blue', green', yellow']';
L = [2 4 6 8];
X=a:h:b;
Y = zeros(length(L), length(X));
Yt = 0*X;
% gaussian with mean zero variance zsigma
zsigma=0.55;
f=inline('exp(-x.^2/2/zsigma)/zsigma/sqrt(2*pi)');
pos = 1;
for i=1:length(Sample)
if i > L(pos)
pos = pos+1;
end
Ycur = f(X-Sample(i), zsigma);
Y(pos, :) = Y(pos, :) + Ycur;
Yt = Yt+Ycur;
end
[Xtp, Ytp] = make_periodic (a, b, h, X, Yt);
Yr = 0*Xtp;
for pos=1:length(L)
[Xp, Yp] = make_periodic (a, b, h, X, Y(pos, :));
Yp = Yp./Ytp;
Yr = Yr + Yp;
plot(Xp, Yp, 'color', Colors(pos, :), 'linewidth', lw);
end
plot(Xtp, 0*Yr, 'k', 'linewidth', lw);
plot(Xtp, Yr, 'k', 'linewidth', lw/1.4, 'linestyle', '--');
fs = 20;
shiftx = -0.3;
shifty = -0.0;
text(Xtp(1)+shiftx, 0+shifty, '0', 'fontsize', fs);
text(Xtp(1)+shiftx, 1+shifty, '1', 'fontsize', fs);
saveas(gcf, 'Partition_of_unity_illustration.eps', 'psc2');
%plot2svg('Partition_of_unity_illustration.svg');
function [Xp, Yp] = make_periodic (a, b, h, X, Y)
% Take a function defined on the real line.
% Wrap the real line around. Sum the overlapping parts.
% Get a periodic function.
T = 8;
as = -3; bs = as+T;
A = (as-a)/h;
B = (bs-a)/h;
N = length(Y);
Y((B-A+1):B) = Y((B-A+1):B) + Y(1:A);
Y((A+1):(A+N-B)) = Y((A+1):(A+N-B)) + Y((B+1):N);
Yp = Y((A+1):B);
Xp = X((A+1):B);
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 04:03, 9 August 2007 | 5,400 × 891 (12 KB) | Oleg Alexandrov (talk | contribs) | Fix bug | |
04:00, 9 August 2007 | 512 × 84 (12 KB) | Oleg Alexandrov (talk | contribs) | Fix bug | ||
03:38, 9 August 2007 | 579 × 89 (10 KB) | Oleg Alexandrov (talk | contribs) | {{Information |Description=Illustration of en:Partition of unity |Source=self-made with MATLAB, tweaked in Inkscape |Date=~~~~~ |Author= Oleg Alexandrov }} {{PD-self}} Category:Differential geometry |
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