% illustration of a bump function in two dimensions function main()     % the number of data points. More points means prettier picture.    N = 300;     % a function close to what we want, but not smooth    Z = get_step_function (N);     % a smooth function with small support, that will serve as mollifier    W = get_mollifier     (N);  % get the convolution of the two, so a mollified step function    S = conv2(Z, W);  % truncate S at the edges, and scale it    p=0.2;    [m, n] = size(S);    m1 = floor(p*m)+1; m2=floor((1-p)*m)-1;    n1 = floor(p*n)+1; n2=floor((1-p)*n)-1;    S = S(m1:m2, n1:n2);    S = 100*S/max(max(S));     % plot the surface    figure(2); clf; hold on; axis equal; axis off;    surf(S);     % make the surface beautiful    shading interp;    colormap autumn;  % add in a source of light    camlight (-50, 54);     % viewing angle    view(-40, 38);     % save as png   print('-dpng', '-r400', 'Bump2D_illustration_uncropped.png');    % optionally, crop the margins   !convert -trim Bump2D_illustration_uncropped.png Bump2D_illustration.png    % get a function which is 1 on a set, and 0 outside of it function Z = get_step_function(N)    XX = linspace(-1.5, 4, N);    YY = linspace(-4, 4, N);    [X, Y] = meshgrid(XX, YY);        c = 2;    k=1.2;    shift=10;    Z = (c^2-X.^2-Y.^2).^2 + k*(c-X).^3-shift;        Z =1-max(sign(Z), 0);  function W = get_mollifier(N) % now try to get a function with compact support % as a mollifier % We will cheat by using a gaussian     a = 4;    XX = linspace(-a, a, N);    YY = linspace(-a, a, N);    [X, Y] = meshgrid(XX, YY);        K = 4;    W = exp(-K*(X.^2+Y.^2));     % truncate the Gaussian to make it with compact support    trunc = 1e-2;    W = max(W-trunc, 0);