% An illustration of the surface integral. % It shows how a surface is split into surface elements.   function main()   % the function giving the surface and its gradient    f=inline('10-(x.^2+y.^2)/15', 'x', 'y');      BoxSize=5; % surface dimensions are 2*BoxSize x 2*BoxSize    M = 10; % M x M = the number of surface elements into which to split the surface    N=10;  % N x N = number of points in each surface element    spacing = 0.1; % spacing between surface elements    H=2*BoxSize/(M-1); % size of each surface element    gridsize=H/N;      % distance between points on a surface element       figure(1); clf; hold on; axis equal; axis off;      for i=1:(M-1) 	  for j=1:(M-1) 		 Lx = -BoxSize + (i-1)*H+spacing; Ux = -BoxSize + (i  )*H-spacing; 		 Ly = -BoxSize + (j-1)*H+spacing; Uy = -BoxSize + (j  )*H-spacing;   %        calc the surface element 		 XX=Lx:gridsize:Ux;  		 YY=Ly:gridsize:Uy; 		 [X, Y]=meshgrid(XX, YY); 		 Z=f(X, Y);   %        plot the surface element 		 surf(X, Y, Z, 'FaceColor','red', 'EdgeColor','none', ... 			  'AmbientStrength', 0.3, 'SpecularStrength', 1, 'DiffuseStrength', 0.8);   	  end    end        view (-18, 40);                     % viewing angle     %camlight headlight; lighting phong; % make nice lightning    %  save to file    plot2svg('Surface_integral_illustration.svg');