function r = radong(xyz)% RADONG : Radon point of d+2 points in d dimensions.%%      r = radong(xyz);%      Each row of xyz is the coordinates of a point.%      The number of dimensions is the number of columns of xyz.%% See GEOPART.%% John Gilbert and Shanghua Teng, 1992-1993.% Copyright (c) 1990-1996 by Xerox Corporation.  All rights reserved.% HELP COPYRIGHT for complete copyright and licensing notice.%% Modified by Tim Davis, for Matlab 5.1.  July 6, 1998% Modified by John Gilbert for Matlab 6, Feb 2002[dplus2, d] = size(xyz);if dplus2 ~= d+2, error('xyz must have exactly d+2 rows'); end;% The radon point is in the intersection of the convex hulls% of two disjoint subsets of the input.  % To find it, we first express zero as a homogeneous linear combination% of the input points (i.e. find a null vector):nullvec = null([ones(d+2,1) xyz]');nullvec = nullvec(:,1);% The positive coefficients and the negative coefficients each% identify one of the subsets.  We'll take the positive:positives = find(nullvec>0);r = nullvec(positives)' * xyz(positives,:) / sum(nullvec(positives));