function u = polygon_vertices_to_minkowski ( v )

%*****************************************************************************80
%
%% polygon_vertices_to_minkowski() computes a Minkowshi representation from vertices.
%
%  Licensing:
%
%    This code is distributed under the MIT license.
%
%  Modified:
%
%    13 November 2024
%
%  Author:
%
%    John Burkardt
%
%  Input:
%
%    real v(n,2): the polygon vertices.
%
%  Output:
%
%    real u(n,2): the Minkowski polygon representation.
%
  nv = size ( v, 1 );
  nu = nv;
  u = zeros ( nu, 2 );

  iv0 = 1;
  iv1 = 2;
  for iu = 1 : nu
    u(iu,1:2) = [ ( v(iv1,2)-v(iv0,2) ), - ( v(iv1,1)-v(iv0,1) ) ];
    iv0 = iv1;
    iv1 = mod ( iv1, nv ) + 1;
  end

  return
end

