function B = randompolyori (N,T)

% RANDOMPOLYORI Creates random polygon orientations in Partiview format
%  In Partiview, a polygon in a plane defined by orthonormal vectors 
%   u,v in R^3 is represented by the 1x6 vector [u(1) u(2) u(3) v(1) v(2) v(3)]
%
% B = randompolyori (N,T)         % full version
% B = randompolyori (N)           % T is 1000. This is the most common option.
% B = randompolyori ()            % returns a 1x6 vector with one random orientation.
%
%   N is a positive integer (default = 1)
%   T is a positive integer (default = 1000)
% 
%   B is a N x 6 matrix with each row having 
%      6 values representing a random orientation
%   
%   Especially if N is large, it may not be necessary to generate
%    N random orientations. Thus T are generated, and then 
%    repeated (about) N/T times.
%
% Dinoj Surendran dinoj@cs.uchicago.edu (28 Feb 04)

if nargin < 1, N=1; end;
if nargin < 2, T=1000; end;

for r = 1 : min (T,N)
  a = orth(rand(3,3));
  B (r,1:6) = [a(:,1)' a(:,2)'];
end

if N > T
  B = repmat (B,ceil(N/T),1);
end;  
B = B (1:N,:);

% rem: to add this to a P x Q matrix R repesentnig a speck file, use
%  R = horzcat ( R, randompolyori(P) );