function UVW = gtHex2Cart(uvtw, latticepar, convention)
% GTHEX2CART  Converts a direction in direct hexagonal space described by 
%             Miller-Bravais indexes (uvtw) to the Crystal Cartesian coordinates in the 
%             real space (UVW) normalising it
%     UVW = gtHex2Cart(uvtw, latticepar, convention)
%     ----------------------------------------------
%     It follows the X-convention using right handed CS
%     From (uvtw) direction in Hexagonal direct space to (UVW) direction 
%     in crystal cartesian space
%     Same as the old function gtCrystHKL2Cart
%
%     INPUT:
%       uvtw       = <double>   Miller-Bravais indexes (N,4) [row vectors]
%       latticepar = <double>   Lattice parameters (1,6)
%       convention = <string>   hexagonal unit cell convention {'X'}/'Y'
%
%     OUTPUT:
%       UVW        = <double>   Direction of plane normal in the cartesian
%                               normalised space (N,3)
%
%     Version 002 25-10-2013 by LNervo


if ~exist('convention','var') || isempty(convention)
    convention = 'X';
end

if size(uvtw,2) == 3
    uvtw = gtCrystMiller2FourIndexes(uvtw,'dir');
end
% going to cartesian reciprocal space + normalisation of the cartesian
% space
UVW(:,1) = uvtw(:,1) + 0.5 * uvtw(:,2);
UVW(:,2) = 3^0.5/2 * uvtw(:,2);
UVW(:,3) = uvtw(:,4);

% scale with unit cell parameters
UVW(:,1) = UVW(:,1)*2/(sqrt(3)*latticepar(1));
UVW(:,2) = UVW(:,2)*2/(sqrt(3)*latticepar(1));
UVW(:,3) = UVW(:,3)/latticepar(3);

% normalise hkls vector
tmp = sqrt(sum((UVW.*UVW),2));
UVW = UVW./(repmat(tmp,1,3));

if strcmpi(convention, 'X')
    % rotates counterclockwise
    UVW = rotateVectors(UVW,'angle',30,'axis',[0 0 1]);
end

end % end of function