mirror of https://github.com/CGAL/cgal
235 lines
6.3 KiB
C++
235 lines
6.3 KiB
C++
// ======================================================================
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//
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// Copyright (c) 1999 The CGAL Consortium
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//
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// This software and related documentation is part of an INTERNAL release
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// of the Computational Geometry Algorithms Library (CGAL). It is not
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// intended for general use.
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//
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// ----------------------------------------------------------------------
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//
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// release :
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// release_date :
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//
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// file : basic_constructionsH2.h
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// package : H2
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// revision : $Revision$
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// revision_date : $Date$
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// author(s) : Sven Schoenherr
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// Stefan Schirra
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//
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// coordinator : MPI, Saarbruecken (<Stefan.Schirra@mpi-sb.mpg.de>)
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// ======================================================================
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#ifndef CGAL_BASIC_CONSTRUCTIONSH2_H
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#define CGAL_BASIC_CONSTRUCTIONSH2_H
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#include <CGAL/PointH2.h>
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#include <CGAL/LineH2.h>
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#include <CGAL/TriangleH2.h>
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CGAL_BEGIN_NAMESPACE
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template <class R>
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CGAL_KERNEL_MEDIUM_INLINE
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PointH2<R>
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gp_linear_intersection(const LineH2<R>& l1, const LineH2<R>& l2)
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{
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return PointH2<R>( l1.b()*l2.c() - l2.b()*l1.c(),
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l2.a()*l1.c() - l1.a()*l2.c(),
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l1.a()*l2.b() - l2.a()*l1.b() );
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}
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template <class R>
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CGAL_KERNEL_MEDIUM_INLINE
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LineH2<R>
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bisector( const PointH2<R>& p, const PointH2<R>& q )
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{
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typedef typename R::RT RT;
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// Bisector equation is based on equation
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// ( X - p.x())^2 + (Y - p.y())^2 == ( X - q.x())^2 + (Y - q.y())
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// and x() = hx()/hw() ...
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RT phx = p.hx();
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RT phy = p.hy();
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RT phw = p.hw();
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RT qhx = q.hx();
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RT qhy = q.hy();
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RT qhw = q.hw();
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RT a = RT(2) * ( qhx*qhw*phw*phw - phx*phw*qhw*qhw );
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RT b = RT(2) * ( qhy*qhw*phw*phw - phy*phw*qhw*qhw );
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RT c = phx*phx*qhw*qhw + phy*phy*qhw*qhw - qhx*qhx*phw*phw - qhy*qhy*phw*phw;
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return LineH2<R>( a, b, c );
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}
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template <class R>
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CGAL_KERNEL_MEDIUM_INLINE
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typename R::FT
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squared_distance( const PointH2<R>& p, const PointH2<R>& q )
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{
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typedef typename R::RT RT;
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typedef typename R::FT FT;
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const RT phx = p.hx();
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const RT phy = p.hy();
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const RT phw = p.hw();
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const RT qhx = q.hx();
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const RT qhy = q.hy();
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const RT qhw = q.hw();
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RT sq_dist_numerator =
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phx * phx * qhw * qhw
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- RT(2) * phx * qhx * phw * qhw
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+ qhx * qhx * phw * phw
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+ phy * phy * qhw * qhw
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- RT(2) * phy * qhy * phw * qhw
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+ qhy * qhy * phw * phw ;
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RT sq_dist_denominator = qhw * qhw * phw * phw ;
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return FT( sq_dist_numerator ) / FT( sq_dist_denominator );
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}
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template < class R >
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CGAL_KERNEL_MEDIUM_INLINE
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PointH2<R>
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midpoint( PointH2<R> const& p, PointH2<R> const& q )
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{
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typedef typename R::RT RT;
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const RT phw( p.hw());
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const RT qhw( q.hw());
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RT hx( p.hx()*qhw + q.hx()*phw);
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RT hy( p.hy()*qhw + q.hy()*phw);
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RT hw( phw * qhw * RT( 2));
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return( PointH2<R>( hx, hy, hw));
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}
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template < class R >
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CGAL_KERNEL_MEDIUM_INLINE
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PointH2<R>
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centroid( const PointH2<R>& p,
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const PointH2<R>& q,
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const PointH2<R>& r )
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{
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typedef typename R::RT RT;
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const RT phw(p.hw());
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const RT qhw(q.hw());
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const RT rhw(r.hw());
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RT hx(p.hx()*qhw*rhw + q.hx()*phw*rhw + r.hx()*phw*qhw);
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RT hy(p.hy()*qhw*rhw + q.hy()*phw*rhw + r.hy()*phw*qhw);
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RT hw( phw*qhw*rhw * 3);
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return PointH2<R>(hx, hy, hw);
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}
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template < class R >
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CGAL_KERNEL_MEDIUM_INLINE
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PointH2<R>
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centroid( const PointH2<R>& p,
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const PointH2<R>& q,
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const PointH2<R>& r,
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const PointH2<R>& s )
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{
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typedef typename R::RT RT;
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const RT phw(p.hw());
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const RT qhw(q.hw());
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const RT rhw(r.hw());
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const RT shw(s.hw());
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RT hx(p.hx()*qhw*rhw*shw + q.hx()*phw*rhw*shw + r.hx()*phw*qhw*shw
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+ s.hx()*phw*qhw*rhw);
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RT hy(p.hy()*qhw*rhw*shw + q.hy()*phw*rhw*shw + r.hy()*phw*qhw*shw
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+ s.hy()*phw*qhw*rhw);
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RT hw( phw*qhw*rhw*shw * 4);
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return PointH2<R>(hx, hy, hw);
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}
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template <class R>
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CGAL_KERNEL_LARGE_INLINE
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PointH2<R>
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circumcenter( const PointH2<R>& p,
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const PointH2<R>& q,
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const PointH2<R>& r )
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{
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typedef typename R::RT RT;
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RT phx = p.hx();
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RT phy = p.hy();
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RT phw = p.hw();
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RT qhx = q.hx();
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RT qhy = q.hy();
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RT qhw = q.hw();
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RT rhx = r.hx();
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RT rhy = r.hy();
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RT rhw = r.hw();
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#ifdef CGAL_EXPANDED_CIRCUMCENTER_COMPUTATION
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RT vvx =
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( qhy*qhw*phw*phw - phy*phw*qhw*qhw )
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*( phx*phx*rhw*rhw + phy*phy*rhw*rhw - rhx*rhx*phw*phw - rhy*rhy*phw*phw )
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- ( rhy*rhw*phw*phw - phy*phw*rhw*rhw )
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*( phx*phx*qhw*qhw + phy*phy*qhw*qhw - qhx*qhx*phw*phw - qhy*qhy*phw*phw );
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RT vvy =
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- ( qhx*qhw*phw*phw - phx*phw*qhw*qhw )
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*( phx*phx*rhw*rhw + phy*phy*rhw*rhw - rhx*rhx*phw*phw - rhy*rhy*phw*phw )
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+ ( rhx*rhw*phw*phw - phx*phw*rhw*rhw )
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*( phx*phx*qhw*qhw + phy*phy*qhw*qhw - qhx*qhx*phw*phw - qhy*qhy*phw*phw );
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RT vvw = RT(2) *
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( ( qhx*qhw*phw*phw - phx*phw*qhw*qhw )
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*( rhy*rhw*phw*phw - phy*phw*rhw*rhw )
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- ( rhx*rhw*phw*phw - phx*phw*rhw*rhw )
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*( qhy*qhw*phw*phw - phy*phw*qhw*qhw ) );
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#endif // CGAL_EXPANDED_CIRCUMCENTER_COMPUTATION
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RT qy_py = ( qhy*qhw*phw*phw - phy*phw*qhw*qhw );
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RT qx_px = ( qhx*qhw*phw*phw - phx*phw*qhw*qhw );
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RT rx_px = ( rhx*rhw*phw*phw - phx*phw*rhw*rhw );
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RT ry_py = ( rhy*rhw*phw*phw - phy*phw*rhw*rhw );
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RT px2_py2_rx2_ry_2 =
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phx*phx*rhw*rhw + phy*phy*rhw*rhw - rhx*rhx*phw*phw - rhy*rhy*phw*phw ;
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RT px2_py2_qx2_qy_2 =
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phx*phx*qhw*qhw + phy*phy*qhw*qhw - qhx*qhx*phw*phw - qhy*qhy*phw*phw ;
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RT vvx = qy_py * px2_py2_rx2_ry_2 - ry_py * px2_py2_qx2_qy_2;
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RT vvy = rx_px * px2_py2_qx2_qy_2 - qx_px * px2_py2_rx2_ry_2;
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RT vvw = RT(2) * ( qx_px * ry_py - rx_px * qy_py );
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return PointH2<R>( vvx, vvy, vvw );
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}
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template <class R>
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CGAL_KERNEL_INLINE
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typename R::FT
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squared_radius( const PointH2<R>& p,
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const PointH2<R>& q,
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const PointH2<R>& r )
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{
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return squared_distance(p, circumcenter(p, q, r));
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}
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template <class R>
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CGAL_KERNEL_LARGE_INLINE
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typename R::FT
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area(const TriangleH2<R>& t)
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{
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typedef typename R::RT RT;
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typedef typename R::FT FT;
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RT num = determinant_3x3_by_formula(
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t.vertex(0).hx(), t.vertex(0).hy(), t.vertex(0).hw(),
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t.vertex(1).hx(), t.vertex(1).hy(), t.vertex(1).hw(),
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t.vertex(2).hx(), t.vertex(2).hy(), t.vertex(2).hw() );
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RT den = t.vertex(0).hw() * t.vertex(1).hw() * t.vertex(2).hw();
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return FT(num) / FT(den);
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}
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CGAL_END_NAMESPACE
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#endif // CGAL_BASIC_CONSTRUCTIONSH2_H
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