% HNORMALISE - Normalises array of homogeneous coordinates to a scale of 1
%
% Usage:  nx = hnormalise(x)
%
% Argument:
%         x  - an Nxnpts array of homogeneous coordinates.
%
% Returns:
%         nx - an Nxnpts array of homogeneous coordinates rescaled so
%              that the scale values nx(N,:) are all 1.
%
% Note that any homogeneous coordinates at infinity (having a scale value of
% 0) are left unchanged.

% Peter Kovesi  
% School of Computer Science & Software Engineering
% The University of Western Australia
% pk at csse uwa edu au
% http://www.csse.uwa.edu.au/~pk
%
% February 2004

function nx = hnormalise(x)
    
    [rows,npts] = size(x);
    nx = x;

    % Find the indices of the points that are not at infinity
    finiteind = find(abs(x(rows,:)) > eps);

    if length(finiteind) ~= npts
        warning('Some points are at infinity');
    end

    % Normalise points not at infinity
    for r = 1:rows-1
	nx(r,finiteind) = x(r,finiteind)./x(rows,finiteind);
    end
    nx(rows,finiteind) = 1;