function [ u, v ] = segment_contains_point_2d ( p1, p2, p )
%*****************************************************************************80
%
%% segment_contains_point_2d() reports if a line segment contains a point in 2D.
%
% Discussion:
%
% A line segment is the finite portion of a line that lies between
% two points.
%
% In exact arithmetic, point P is on the line segment between
% P1 and P2 if and only if 0 <= U <= 1 and V = 0.
%
% Thanks to Lars Cremean for corecting a MATLAB error in which
% elementwise multiplication was needed.
%
% Licensing:
%
% This code is distributed under the MIT license.
%
% Modified:
%
% 12 May 2005
%
% Author:
%
% John Burkardt
%
% Input:
%
% real P1(2), P2(2), the endpoints of the line segment.
%
% real P(2), a point to be tested.
%
% Output:
%
% real U, the coordinate of P3 along the axis from
% with origin at P1 and unit at P2.
%
% real V, the magnitude of the off-axis portion of the
% vector P3-P1, measured in units of (P2-P1).
%
dim_num = 2;
normsq = sum ( ( p2(1:dim_num) - p1(1:dim_num) ).^2 );
if ( normsq == 0.0 )
if ( p(1:dim_num) == p1(1:dim_num) )
u = 0.5;
v = 0.0;
else
u = 0.5;
v = Inf;
end
else
u = ( ( p(1:dim_num) - p1(1:dim_num) ) ...
* ( p2(1:dim_num) - p1(1:dim_num) )' ) / normsq;
v = sqrt ( ( ( u - 1.0 ) * p1(1) - u * p2(1) + p(1) ).^2 ...
+ ( ( u - 1.0 ) * p1(2) - u * p2(2) + p(2) ).^2 ) ...
/ sqrt ( normsq );
end
return
end