% illustration of the volume under a surface  function main()    L=5;  % box size    N=100; % number of points in a lot of places    lw=2; % width of lines    alphatop=1; % transparency    alphaside=0.82;    alphabot=0.8;    bluetop =[0, 1, 0.8];    blueside=[0.2, 0.9, 0.8]; %bluetop;%[0, 0, 1];    bluebot=[0.5, 0.5, 0.5]; %bluetop;%[0, 0, 1];    black=[0, 0, 0];     % the function whose surface we will plot    f=inline('10-(x.^2-y.^2)/8', 'x', 'y');    XX=linspace(-L, L, N);    YY=XX;    [X, Y]=meshgrid(XX, YY);    Z=f(X, Y);     % the surface of the side    XS = [XX, 0*XX+L invert_vector(XX), 0*XX-L];    YS = [0*XX-L, YY, 0*XX+L, invert_vector(YY)];     XS = [XS' XS']';    YS = [YS' YS']';     ZS = 0*XS;    ZS(2, :) = f(XS(2, :), YS(2, :));  % the contour of the bottom    XD=[-L, L, L, -L, -L];    YD=[-L, -L, L, L, -L];    ZD=XD*0;  %  prepare figure 1 for plotting    figure(1); clf; hold on; axis equal; axis off;   %  plot the function u    surf(X, Y, Z, 'FaceColor', bluetop, 'EdgeColor','none', 'FaceAlpha', alphatop); % top    surf(X, Y, 0*Z, 'FaceColor', bluebot, 'EdgeColor','none', 'FaceAlpha', alphabot); % bottom     surf(XS, YS, ZS, 'FaceColor', blueside, 'EdgeColor','none', 'FaceAlpha', alphaside); % sides     phi = -68; theta = 28;    view (phi, theta);     camlight headlight; lighting phong; % make nice lightning     print('-dpng',  '-r200', 'Volume_under_surface.png') % save to file.  function Z = invert_vector(X)     N=length(X);    Z = X;    for i=1:N       Z(i)=X(N-i+1);    end