%
% Problem Epage 200 
% Example 5.18 Epage 162
% 
% 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 multidimensional 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; 

% draw a slice at an ARBITRARY angle: 
hs = surf(linspace(-3,3,20),linspace(-3,3,20),zeros(20)); 
% rotate the surface about the direction vector [1,-1,1] and 30 degrees: 
rotate(hs,[1,-1,1],30); 
% get the data that will define the surface at an arbitrary angle.
xd = get(hs,'XData'); 
yd = get(hs,'YData'); 
zd = get(hs,'ZData'); 
delete(hs);
% draw this slice: 
slice(x,y,z,prob,xd,yd,zd); 
axis tight; 
title('a slice through the multidimensional Gaussian'); 

%--
% now plot slices using the peak surface: 
%--
[xd,yd,zd] = peaks; 
figure; slice(x,y,z,prob,xd,yd,zd); 
axis tight; 
title('slicing with peaks through the multidimensional Gaussian');