solve.h

Go to the documentation of this file.

// ======================================================================
//
// Copyright (c) 1999 The CGAL Consortium

// This software and related documentation is part of the Computational
// Geometry Algorithms Library (CGAL).
// This software and documentation is provided "as-is" and without warranty
// of any kind. In no event shall the CGAL Consortium be liable for any
// damage of any kind. 
//
// Every use of CGAL requires a license. 
//
// Academic research and teaching license
// - For academic research and teaching purposes, permission to use and copy
//   the software and its documentation is hereby granted free of charge,
//   provided that it is not a component of a commercial product, and this
//   notice appears in all copies of the software and related documentation. 
//
// Commercial licenses
// - A commercial license is available through Algorithmic Solutions, who also
//   markets LEDA (http://www.algorithmic-solutions.de). 
// - Commercial users may apply for an evaluation license by writing to
//   Algorithmic Solutions (contact@algorithmic-solutions.com). 
//
// The CGAL Consortium consists of Utrecht University (The Netherlands),
// ETH Zurich (Switzerland), Free University of Berlin (Germany),
// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
// (Germany), Max-Planck-Institute Saarbrucken (Germany), RISC Linz (Austria),
// and Tel-Aviv University (Israel).
//
// ----------------------------------------------------------------------
// 
// release       : CGAL-2.2
// release_date  : 2000, September 30
// 
// source        : solve.fw
// file          : include/CGAL/solve.h
// package       : Kernel_basic (3.14)
// revision      : 3.14
// revision_date : 15 Sep 2000 
// author(s)     : Andreas Fabri
//
// coordinator   : MPI, Saarbruecken  (<Stefan.Schirra>)
// email         : contact@cgal.org
// www           : http://www.cgal.org
//
// ======================================================================
 

#ifndef CGAL_SOLVE_H
#define CGAL_SOLVE_H

CGAL_BEGIN_NAMESPACE


template <class FT>
void solve (const FT &a1, const FT &a2, const FT &a3,
                 const FT &b1, const FT &b2, const FT &b3,
                 const FT &c1, const FT &c2, const FT &c3,
                 const FT &d1, const FT &d2, const FT &d3,
                 FT &x, FT &y, FT &z)
{
  FT denom = b2*c1*a3-b1*c2*a3+c3*b1*a2+b3*c2*a1-c1*b3*a2-b2*c3*a1;

  x = - (b2*c3*d1-b2*c1*d3+c1*b3*d2+b1*c2*d3-c3*b1*d2-b3*c2*d1)/denom;

  z = (b2*d1*a3-b2*a1*d3+b1*a2*d3-b1*d2*a3-d1*b3*a2+a1*b3*d2)/denom;

  y = (a2*c3*d1-a2*c1*d3-c2*d1*a3+c2*a1*d3+d2*c1*a3-d2*c3*a1)/denom;
}


// this is for a parabola c1, c2, c3 are equal to 1
template <class FT>
void solve_quadratic (const FT &a1, const FT &a2, const FT &a3,
                           const FT &b1, const FT &b2, const FT &b3,
                           const FT &d1, const FT &d2, const FT &d3,
                           FT &x, FT &y, FT &z)
{
  FT denom = b2*a3-b1*a3+b1*a2+b3*a1-b3*a2-b2*a1;

  x = - (b2*d1-b2*d3+b3*d2+b1*d3-b1*d2-b3*d1)/denom;

  z = (b2*d1*a3-b2*a1*d3+b1*a2*d3-b1*d2*a3-d1*b3*a2+a1*b3*d2)/denom;

  y = (a2*d1-a2*d3-d1*a3+a1*d3+d2*a3-d2*a1)/denom;
}


CGAL_END_NAMESPACE

#endif // CGAL_SOLVE_H