Checked content

File:Volume under surface.png

Description Illustration of volume under a surface ( double integral)
Date 03:15, 30 December 2007 (UTC)
Source self-made with MATLAB
Author Oleg Alexandrov
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Source code ( MATLAB)

% 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
   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);
   [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];
%  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)
   Z = X;
   for i=1:N

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