function diameter = polygon_diameter_2d ( n, v )
%*****************************************************************************80
%
%% POLYGON_DIAMETER_2D computes the diameter of a polygon in 2D.
%
% Discussion:
%
% The diameter of a polygon is the maximum distance between any
% two points on the polygon. It is guaranteed that this maximum
% distance occurs between two vertices of the polygon. It is
% sufficient to check the distance between all pairs of vertices.
% This is an N^2 algorithm. There is an algorithm by Shamos which
% can compute this quantity in order N time instead.
%
% Licensing:
%
% This code is distributed under the GNU LGPL license.
%
% Modified:
%
% 02 February 2005
%
% Author:
%
% John Burkardt
%
% Input:
%
% integer N, the number of vertices of the polygon.
%
% real V(2,N), the vertices.
%
% Output:
%
% real DIAMETER, the diameter of the polygon.
%
diameter = 0.0;
for i = 1 : n
for j = i + 1 : n
diameter = max ( diameter, ...
sqrt ( ( v(1,i) - v(1,j) ).^2 + ( v(2,i) - v(2,j) ).^2 ) );
end
end
return
end