function quality = tetrahedron_quality1_3d ( tetra )
%*****************************************************************************80
%
%% tetrahedron_quality1_3d(): "quality" of a tetrahedron in 3D.
%
% Discussion:
%
% The quality of a tetrahedron is 3.0 times the ratio of the radius of
% the inscribed sphere divided by that of the circumscribed sphere.
%
% An equilateral tetrahredron achieves the maximum possible quality of 1.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 09 August 2005
%
% Author:
%
% John Burkardt
%
% Input:
%
% real TETRA(3,4), the tetrahedron vertices.
%
% Output:
%
% real QUALITY, the quality of the tetrahedron.
%
dim_num = 3;
[ r_out, pc ] = tetrahedron_circumsphere_3d ( tetra );
[ r_in, pc ] = tetrahedron_insphere_3d ( tetra );
quality = 3.0 * r_in / r_out;
return
end