File:Partition of unity illustration.svg

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Description	Partition of unity illustration.svg Illustration of en:Partition of unity
Date	03:38, 9 August 2007 (UTC)
Source	self-made with MATLAB, tweaked in Inkscape
Author	Oleg Alexandrov
Permission (Reusing this image)	See below.

I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide. In case this is not legally possible: I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. Afrikaans | Alemannisch | Aragonés | العربية | Asturianu | Azərbaycan | Беларуская (тарашкевіца) | Български | Català | Cebuano | Soranî / کوردی | Česky | Cymraeg | Dansk | Deutsch | Ελληνικά | English | Esperanto | Español | Eesti | Euskara | Estremeñu | فارسی | Suomi | Français | Galego | עברית | हिन्दी | Hrvatski | Magyar | Հայերեն | Bahasa Indonesia | Ido | Íslenska | Italiano | 日本語 | ქართული | ភាសាខ្មែរ | 한국어 | Ripoarisch | Kurdî / كوردی | Latina | Lietuvių | Latviešu | 文言 | Македонски | Bahasa Melayu | Plattdüütsch | Nederlands | ‪Norsk (nynorsk)‬ | ‪Norsk (bokmål)‬ | Polski | Português | Română | Русский | Slovenčina | Slovenščina | Shqip | Српски / Srpski | Svenska | ไทย | Tagalog | Türkçe | Українська | Vèneto | Tiếng Việt | Walon | 吴语 | 中文 | ‪中文(简体)‬ | ‪中文(繁體)‬ | 粵語 | +/−

[edit] MATLAB source code

% 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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• Usage of Partition of unity illustration.svg on enwiki
  • Partition of unity