/* Copyright (c) 1997-2004
   Ewgenij Gawrilow, Michael Joswig (Technische Universitaet Berlin, Germany)
   http://www.math.tu-berlin.de/polymake,  mailto:polymake@math.tu-berlin.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.
*/

#ifndef _POLYMAKE_BISECTOR_H
#define _POLYMAKE_BISECTOR_H "$Project: polymake $$Id: bisector.h 4714 2004-06-22 16:23:15Z gawrilow $"

#include <Rational.h>
#include <Matrix.h>
#include <Vector.h>
#include <cmath>

namespace polymake { namespace polytope {

/** Compute approximately the bisector hyperplane
 *
 * @param F1, F2 side hyperplanes of the angle
 * @param V point on the ridge
 */

template <typename Vector1, typename Vector2, typename Vector3>
Vector<Rational>
bisector(const GenericVector<Vector1,Rational>& F1, const GenericVector<Vector2,Rational>& F2,
	 const GenericVector<Vector3,Rational>& V)
{
   Vector<double> f1(F1), f2(F2);
   f1[0]=0.; f2[0]=0.;
   Vector<Rational> F_bisector(f1/(2.0*sqrt(sqr(f1))) + f2/(2.0*sqrt(sqr(f2))));
   F_bisector[0]=-F_bisector*V;
   return F_bisector;
}

} }

#endif // _POLYMAKE_BISECTOR_H

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