%
% Problem Epage 201 
% Example 5.18 Epage 162/Example on Epage 165
% 
% isosurface/isocaps
% 
% Written by:
% -- 
% John L. Weatherwax                2008-02-20
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear all; 
close all; 
clc; 

%--
% plot the isosurfaces of the trivariate Gaussian
%--
% create a grid for the domain: 
[x,y,z] = meshgrid(-3:.1:3,-3:.1:3,-3:.1:3); 
[n,d]   = size(x(:)); 
% fill our volume with values of the trivariate normal density:
a    = (2*pi)^(3/2);
arg  = (x.^2+y.^2+z.^2);
prob = exp((-0.5)*arg)/a; % <- this is the data we want to plot an isosurface for: 

% plot some alpha-level contours: 
mymx=max(prob(:)); 

% Use isosurfac: 
% 
for i = [0.4,0.6]  % <- the alpha to use 
  figure; 
  val    = i*mymx; 
  hpatch = patch(isosurface(prob,val),'FaceColor','blue'); 
  isonormals(prob,hpatch); 
end

% Use isocaps: 
% 
for i = [0.4,0.6]  % <- the alpha to use 
  figure; 
  val    = i*mymx; 
  hpatch = patch(isosurface(prob,val),'FaceColor','blue'); 
  isonormals(prob,hpatch); 
  patch(isocaps(prob,val),'FaceColor','interp','EdgeColor','none');
end