/* Copyright (c) 1997-2009
   Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Darmstadt, Germany)
   http://www.polymake.de

   This program is free software; you can redistribute it and/or modify it
   under the terms of the GNU General Public License as published by the
   Free Software Foundation; either version 2, or (at your option) any
   later version: http://www.gnu.org/licenses/gpl.txt.

   This program is distributed in the hope that it will be useful,
   but WITHOUT ANY WARRANTY; without even the implied warranty of
   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
   GNU General Public License for more details.
--------------------------------------------------------------------------------
   $Project: polymake $$Id: inner_point.cc 9542 2010-03-08 16:26:25Z herr $
*/

#include <polymake.h>
#include <linalg.h>
#include <Matrix.h>

namespace polymake { namespace polytope {

   template <typename Coord>
   Vector<Coord> inner_point(const Matrix<Coord> &V)
   {
      const Set<int> b=basis_rows(V);

      // center of gravity of the basis vectors
      const Vector<Coord> rel_int_pt=average(rows(V.minor(b,All)));

      // we require rel_int_pt to be affine
      // otherwise we might be in trouble with the orientation
      if (!rel_int_pt[0])
	 throw std::runtime_error("computed point not affine");

      return rel_int_pt;
   }

   UserFunctionTemplate4perl("# @category Linear optimization"
			     "# Compute a true inner point of a convex hull of the given set of //points//."
			     "# @param Matrix points",
			     "inner_point(Matrix)");
} }
