% 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);