function  out = pluho( in )

% pluho  convert Plucker <--> 4x4 homogeneous coordinate transform.
% X=pluho(T) and T=pluho(X) convert between a Plucker coordinate transform
% matrix X and a 4x4 homogeneous coordinate transform matrix T.  If the
% argument is a 6x6 matrix then it is taken to be X, otherwise T.
% NOTE: the 4x4 matrices used in 3D graphics (e.g. OpenGL and Matlab handle
% graphics) are displacement operators, which are the inverses of
% coordinate transforms.  For example, to set the 'matrix' property of a
% Matlab hgtransform graphics object so as to rotate its children by an
% angle theta about the X axis, use inv(pluho(rotx(theta))).

% Formulae:
%   X = [  E   0 ]   T = [ E  -Er ]
%       [ -Erx E ]       [ 0   1  ]

if all(size(in)==[6 6])			% Plucker -> 4x4 homogeneous
  E = in(1:3,1:3);
  mErx = in(4:6,1:3);			% - E r cross
  out = [ E, skew(mErx*E'); 0 0 0 1 ];
else					% 4x4 homogeneous -> Plucker
  E = in(1:3,1:3);
  mEr = in(1:3,4);			% - E r
  out = [ E, zeros(3); skew(mEr)*E, E ];
end