function value = lines_exp_parallel_2d ( p1, p2, q1, q2 )
%*****************************************************************************80
%
%% lines_exp_parallel_2d() determines if two lines are parallel in 2D.
%
% Discussion:
%
% The explicit form of a line in 2D is:
%
% the line through the points P1, P2.
%
% The test is essentially a comparison of slopes, but should be
% more accurate than an explicit slope comparison, and unfazed
% by degenerate cases.
%
% On the other hand, there is NO tolerance for error. If the
% slopes differ by a single digit in the last place, then the
% lines are judged to be nonparallel. A more robust test would
% be to compute the angle between the lines, because then it makes
% sense to say the lines are "almost" parallel: the angle is small.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 23 February 2005
%
% Author:
%
% John Burkardt
%
% Input:
%
% real P1(2,1), P2(2,1), two points on the first line.
%
% real Q1(2,1), Q2(2,1), two points on the second line.
%
% Output:
%
% logical VALUE is TRUE if the lines are parallel.
%
value = ...
( ...
( p2(1,1) - p1(1,1) ) * ( q2(2,1) - q1(2,1) ) ==
( q2(1,1) - q1(1,1) ) * ( p2(2,1) - p1(2,1) ) ...
);
return
end