// Copyright (c) 1999-2004 Utrecht University (The Netherlands),
// ETH Zurich (Switzerland), Freie Universitaet Berlin (Germany),
// INRIA Sophia-Antipolis (France), Martin-Luther-University Halle-Wittenberg
// (Germany), Max-Planck-Institute Saarbruecken (Germany), RISC Linz (Austria),
// and Tel-Aviv University (Israel). All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public License as
// published by the Free Software Foundation; version 2.1 of the License.
// See the file LICENSE.LGPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $Source: /CVSROOT/CGAL/Packages/H2/include/CGAL/Homogeneous/function_objects.h,v $
// $Revision: 1.40 $ $Date: 2004/08/11 14:37:09 $
// $Name: $
//
// Author(s) : Stefan Schirra, Sylvain Pion, Michael Hoffmann
#ifndef CGAL_HOMOGENEOUS_FUNCTION_OBJECTS_H
#define CGAL_HOMOGENEOUS_FUNCTION_OBJECTS_H
#include <CGAL/Kernel/function_objects.h>
#include <CGAL/Cartesian/function_objects.h>
CGAL_BEGIN_NAMESPACE
namespace HomogeneousKernelFunctors {
using namespace CommonKernelFunctors;
// For lazyness...
using CartesianKernelFunctors::Are_parallel_2;
using CartesianKernelFunctors::Are_parallel_3;
using CartesianKernelFunctors::Compute_squared_area_3;
using CartesianKernelFunctors::Collinear_3;
using CartesianKernelFunctors::Construct_line_3;
template <typename K>
class Angle_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Construct_vector_2 Construct_vector_2;
Construct_vector_2 c;
public:
typedef Angle result_type;
typedef Arity_tag< 3 > Arity;
Angle_2() {}
Angle_2(const Construct_vector_2& c_) : c(c_) {}
Angle
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{ return (Angle) CGAL_NTS sign(c(q,p) * c(q,r)); }
// FIXME: scalar product
};
template <typename K>
class Angle_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Construct_vector_3 Construct_vector_3;
Construct_vector_3 c;
public:
typedef Angle result_type;
typedef Arity_tag< 3 > Arity;
Angle_3() {}
Angle_3(const Construct_vector_3& c_) : c(c_) {}
Angle
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{ return (Angle) CGAL_NTS sign(c(q,p) * c(q,r)); }
// FIXME: scalar product
};
template <typename K>
class Bounded_side_3
{
typedef typename K::RT RT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Sphere_3 Sphere_3;
typedef typename K::Tetrahedron_3 Tetrahedron_3;
typedef typename K::Iso_cuboid_3 Iso_cuboid_3;
public:
typedef Bounded_side result_type;
typedef Arity_tag< 2 > Arity;
Bounded_side
operator()( const Sphere_3& s, const Point_3& p) const
{ return s.bounded_side(p); }
Bounded_side
operator()( const Tetrahedron_3& t, const Point_3& p) const
{
RT alpha;
RT beta ;
RT gamma;
Vector_3 v1 = t.vertex(1)-t.vertex(0);
Vector_3 v2 = t.vertex(2)-t.vertex(0);
Vector_3 v3 = t.vertex(3)-t.vertex(0);
Vector_3 vp = p - t.vertex(0);
// want to solve alpha*v1 + beta*v2 + gamma*v3 == vp
// let vi' == vi*vi.hw()
// we solve alpha'*v1' + beta'*v2' + gamma'*v3' == vp' / vp.hw()
// muliplied by vp.hw()
// then we have alpha = alpha'*v1.hw() / vp.hw()
// and beta = beta' *v2.hw() / vp.hw()
// and gamma = gamma'*v3.hw() / vp.hw()
RT v1x = v1.hx();
RT v1y = v1.hy();
RT v1z = v1.hz();
RT v2x = v2.hx();
RT v2y = v2.hy();
RT v2z = v2.hz();
RT v3x = v3.hx();
RT v3y = v3.hy();
RT v3z = v3.hz();
RT vpx = vp.hx();
RT vpy = vp.hy();
RT vpz = vp.hz();
alpha = det3x3_by_formula( vpx, v2x, v3x,
vpy, v2y, v3y,
vpz, v2z, v3z );
beta = det3x3_by_formula( v1x, vpx, v3x,
v1y, vpy, v3y,
v1z, vpz, v3z );
gamma = det3x3_by_formula( v1x, v2x, vpx,
v1y, v2y, vpy,
v1z, v2z, vpz );
RT det= det3x3_by_formula( v1x, v2x, v3x,
v1y, v2y, v3y,
v1z, v2z, v3z );
CGAL_kernel_assertion( det != 0 );
if (det < 0 )
{
alpha = - alpha;
beta = - beta ;
gamma = - gamma;
det = - det ;
}
bool t1 = ( alpha < 0 );
bool t2 = ( beta < 0 );
bool t3 = ( gamma < 0 );
// t1 || t2 || t3 == not contained in cone
RT lhs = alpha*v1.hw() + beta*v2.hw() + gamma*v3.hw();
RT rhs = det * vp.hw();
bool t4 = ( lhs > rhs );
// alpha + beta + gamma > 1 ?
bool t5 = ( lhs < rhs );
// alpha + beta + gamma < 1 ?
bool t6 = ( (alpha > 0) && (beta > 0) && (gamma > 0) );
if ( t1 || t2 || t3 || t4 )
{
return ON_UNBOUNDED_SIDE;
}
return (t5 && t6) ? ON_BOUNDED_SIDE : ON_BOUNDARY;
}
Bounded_side
operator()( const Iso_cuboid_3& c, const Point_3& p) const
{ return c.bounded_side(p); }
};
template <typename K>
class Collinear_are_ordered_along_line_2
{
typedef typename K::RT RT;
typedef typename K::Point_2 Point_2;
#ifdef CGAL_kernel_exactness_preconditions
typedef typename K::Collinear_2 Collinear_2;
Collinear_2 c;
#endif // CGAL_kernel_exactness_preconditions
public:
typedef bool result_type;
typedef Arity_tag< 3 > Arity;
#ifdef CGAL_kernel_exactness_preconditions
Collinear_are_ordered_along_line_2() {}
Collinear_are_ordered_along_line_2(const Collinear_2& c_) : c(c_) {}
#endif // CGAL_kernel_exactness_preconditions
bool
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
CGAL_kernel_exactness_precondition( c(p, q, r) );
const RT& phx = p.hx();
const RT& phy = p.hy();
const RT& phw = p.hw();
const RT& qhx = q.hx();
const RT& qhy = q.hy();
const RT& qhw = q.hw();
const RT& rhx = r.hx();
const RT& rhy = r.hy();
const RT& rhw = r.hw();
if ( !(phx * rhw == rhx * phw ) ) // non-vertical ?
{
return !( ( ( phx * qhw < qhx * phw)
&&( rhx * qhw < qhx * rhw))
||( ( qhx * phw < phx * qhw)
&&( qhx * rhw < rhx * qhw)) );
}
else if ( !(phy * rhw == rhy * phw ) )
{
return !( ( ( phy * qhw < qhy * phw)
&&( rhy * qhw < qhy * rhw))
||( ( qhy * phw < phy * qhw)
&&( qhy * rhw < rhy * qhw)) );
}
else
return (( phx*qhw == qhx*phw) && ( phy*qhw == qhy*phw));
}
};
template <typename K>
class Collinear_are_ordered_along_line_3
{
typedef typename K::Point_3 Point_3;
#ifdef CGAL_kernel_exactness_preconditions
typedef typename K::Collinear_3 Collinear_3;
Collinear_3 c;
#endif // CGAL_kernel_exactness_preconditions
public:
typedef bool result_type;
typedef Arity_tag< 3 > Arity;
#ifdef CGAL_kernel_exactness_preconditions
Collinear_are_ordered_along_line_3() {}
Collinear_are_ordered_along_line_3(const Collinear_3& c_) : c(c_) {}
#endif // CGAL_kernel_exactness_preconditions
bool
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
CGAL_kernel_exactness_precondition( c(p, q, r) );
typedef typename K::RT RT;
const RT phx = p.hx();
const RT phw = p.hw();
const RT qhx = q.hx();
const RT qhw = q.hw();
const RT rhx = r.hx();
const RT rhw = r.hw();
const RT pqx = phx*qhw;
const RT qpx = qhx*phw;
const RT prx = phx*rhw;
const RT qrx = qhx*rhw;
const RT rqx = rhx*qhw;
const RT rpx = rhx*phw;
if ( prx != rpx ) // px != rx
{
// (px <= qx)&&(qx <= rx) || (px >= qx)&&(qx >= rx)
// !(((qx < px)||(rx < qx))&&((px < qx)||(qx < rx)))
return ! ( ((qpx < pqx) || (rqx < qrx))
&& ((pqx < qpx) || (qrx < rqx)) );
}
const RT phy = p.hy();
const RT qhy = q.hy();
const RT rhy = r.hy();
const RT pqy = phy*qhw;
const RT qpy = qhy*phw;
const RT pry = phy*rhw;
const RT qry = qhy*rhw;
const RT rqy = rhy*qhw;
const RT rpy = rhy*phw;
if ( pry != rpy )
{
return ! ( ((qpy < pqy) || (rqy < qry))
&& ((pqy < qpy) || (qry < rqy)) );
}
const RT phz = p.hz();
const RT qhz = q.hz();
const RT rhz = r.hz();
const RT pqz = phz*qhw;
const RT qpz = qhz*phw;
const RT prz = phz*rhw;
const RT qrz = qhz*rhw;
const RT rqz = rhz*qhw;
const RT rpz = rhz*phw;
if ( prz != rpz )
{
return ! ( ((qpz < pqz) || (rqz < qrz))
&& ((pqz < qpz) || (qrz < rqz)) );
}
// p == r
return ((rqx == qrx) && (rqy == qry) && (rqz == qrz));
}
};
template <typename K>
class Collinear_are_strictly_ordered_along_line_2
{
typedef typename K::Point_2 Point_2;
#ifdef CGAL_kernel_exactness_preconditions
typedef typename K::Collinear_2 Collinear_2;
Collinear_2 c;
#endif // CGAL_kernel_exactness_preconditions
public:
typedef bool result_type;
typedef Arity_tag< 3 > Arity;
#ifdef CGAL_kernel_exactness_preconditions
Collinear_are_strictly_ordered_along_line_2() {}
Collinear_are_strictly_ordered_along_line_2(const Collinear_2& c_) : c(c_)
{}
#endif // CGAL_kernel_exactness_preconditions
bool
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
CGAL_kernel_exactness_precondition( c(p, q, r) );
typedef typename K::RT RT;
const RT& phx = p.hx();
const RT& phy = p.hy();
const RT& phw = p.hw();
const RT& qhx = q.hx();
const RT& qhy = q.hy();
const RT& qhw = q.hw();
const RT& rhx = r.hx();
const RT& rhy = r.hy();
const RT& rhw = r.hw();
if ( !(phx * rhw == rhx * phw ) )
{
return ( ( phx * qhw < qhx * phw)
&&( qhx * rhw < rhx * qhw))
||( ( qhx * phw < phx * qhw) // ( phx * qhw > qhx * phw)
&&( rhx * qhw < qhx * rhw)); // ( qhx * rhw > rhx * qhw)
}
else
{
return ( ( phy * qhw < qhy * phw)
&&( qhy * rhw < rhy * qhw))
||( ( qhy * phw < phy * qhw) // ( phy * qhw > qhy * phw)
&&( rhy * qhw < qhy * rhw)); // ( qhy * rhw > rhy * qhw)
}
}
};
template <typename K>
class Collinear_are_strictly_ordered_along_line_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Direction_3 Direction_3;
#ifdef CGAL_kernel_exactness_preconditions
typedef typename K::Collinear_3 Collinear_3;
Collinear_3 c;
#endif // CGAL_kernel_exactness_preconditions
public:
typedef bool result_type;
typedef Arity_tag< 3 > Arity;
#ifdef CGAL_kernel_exactness_preconditions
Collinear_are_strictly_ordered_along_line_3() {}
Collinear_are_strictly_ordered_along_line_3(const Collinear_3& c_) : c(c_)
{}
#endif // CGAL_kernel_exactness_preconditions
bool
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
CGAL_kernel_exactness_precondition( c(p, q, r) );
if ( p == r) return false;
Direction_3 dir_pq = (p - q).direction();
Direction_3 dir_rq = (r - q).direction();
return (dir_pq == -dir_rq);
} // FIXME
};
template <typename K>
class Collinear_has_on_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Direction_2 Direction_2;
typedef typename K::Ray_2 Ray_2;
typedef typename K::Segment_2 Segment_2;
typedef typename K::Construct_point_on_2 Construct_point_on_2;
typedef typename K::Compare_xy_2 Compare_xy_2;
typedef typename K::Collinear_are_ordered_along_line_2
Collinear_are_ordered_along_line_2;
Collinear_are_ordered_along_line_2 co;
Construct_point_on_2 cp;
Compare_xy_2 cxy;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
Collinear_has_on_2() {}
Collinear_has_on_2(const Construct_point_on_2& cp_,
const Compare_xy_2& cxy_)
: cp(cp_), cxy(cxy_)
{}
bool
operator()( const Ray_2& r, const Point_2& p) const
{
const Point_2 & source = cp(r,0);
return p == source || Direction_2(p - source) == r.direction();
} // FIXME
bool
operator()( const Segment_2& s, const Point_2& p) const
{
return co(cp(s,0), p, cp(s,1));
}
};
template <typename K>
class Collinear_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Orientation_2 Orientation_2;
Orientation_2 o;
public:
typedef bool result_type;
typedef Arity_tag< 3 > Arity;
Collinear_2() {}
Collinear_2(const Orientation_2 o_) : o(o_) {}
bool
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
typedef typename K::RT RT;
const RT& phx = p.hx();
const RT& phy = p.hy();
const RT& phw = p.hw();
const RT& qhx = q.hx();
const RT& qhy = q.hy();
const RT& qhw = q.hw();
const RT& rhx = r.hx();
const RT& rhy = r.hy();
const RT& rhw = r.hw();
const RT RT0 = RT(0);
// | A B |
// | C D |
RT A = phx*rhw - phw*rhx;
RT B = phy*rhw - phw*rhy;
RT C = qhx*rhw - qhw*rhx;
RT D = qhy*rhw - qhw*rhy;
RT det = A*D - B*C;
/*
RT det_old = p.hx() * (q.hy()*r.hw() - q.hw()*r.hy() )
+ p.hy() * (q.hw()*r.hx() - q.hx()*r.hw() )
+ p.hw() * (q.hx()*r.hy() - q.hy()*r.hx() );
if ( !(CGAL_NTS sign(det) == CGAL_NTS sign(det_old)) )
{
std::cerr << "det: " << det << " det_old: " << det_old << flush;
}
*/
return ( det == RT0 );
}
};
template <typename K>
class Compare_angle_with_x_axis_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
typedef typename K::Direction_2 Direction_2;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 2 > Arity;
Comparison_result
operator()(const Direction_2& d1, const Direction_2& d2) const
{
typedef typename K::RT RT;
CGAL_kernel_precondition(
static_cast<int>(COUNTERCLOCKWISE) == static_cast<int>(LARGER)
&& static_cast<int>(COLLINEAR) == static_cast<int>(EQUAL)
&& static_cast<int>(CLOCKWISE) == static_cast<int>(SMALLER) );
const RT RT0(0);
Vector_2 dirvec1(d1.x(), d1.y()); // Added
Point_2 p1 = CGAL::ORIGIN + dirvec1; // Added
Vector_2 dirvec2(d2.x(), d2.y()); // Added
Point_2 p2 = ORIGIN + dirvec2; // Added
// Point_2 p1 = ORIGIN + d1.vector(); // Commented out
// Point_2 p2 = ORIGIN + d2.vector(); // Commented out
CGAL_kernel_precondition( RT0 < p1.hw() );
CGAL_kernel_precondition( RT0 < p2.hw() );
int x_sign1 = static_cast<int>(CGAL_NTS sign( p1.hx() ));
int x_sign2 = static_cast<int>(CGAL_NTS sign( p2.hx() ));
int y_sign1 = static_cast<int>(CGAL_NTS sign( p1.hy() ));
int y_sign2 = static_cast<int>(CGAL_NTS sign( p2.hy() ));
if ( y_sign1 * y_sign2 < 0)
{
return (0 < y_sign1 ) ? SMALLER : LARGER;
}
Point_2 origin( RT0 , RT0 );
if ( 0 < y_sign1 * y_sign2 )
{
return static_cast<Comparison_result>(static_cast<int>(
orientation(origin, p2, p1)));
// Precondition on the enums:
// COUNTERCLOCKWISE == LARGER ( == 1 )
// COLLINEAR == EQUAL ( == 0 )
// CLOCKWISE == SMALLER ( == -1 )
}
// ( y_sign1 * y_sign2 == 0 )
bool b1 = (y_sign1 == 0) && (x_sign1 >= 0);
bool b2 = (y_sign2 == 0) && (x_sign2 >= 0);
if ( b1 ) { return b2 ? EQUAL : SMALLER; }
if ( b2 ) { return b1 ? EQUAL : LARGER; }
if ( y_sign1 == y_sign2 ) // == 0
{
return EQUAL;
}
else
{
return (orientation(origin, p1, p2) == COUNTERCLOCKWISE) ?
static_cast<Comparison_result>(SMALLER) :
static_cast<Comparison_result>(LARGER);
}
}
};
template <typename K>
class Compare_distance_2
{
typedef typename K::Point_2 Point_2;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 3 > Arity;
Comparison_result
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
typedef typename K::RT RT;
const RT phx = p.hx();
const RT phy = p.hy();
const RT phw = p.hw();
const RT qhx = q.hx();
const RT qhy = q.hy();
const RT qhw = q.hw();
const RT rhx = r.hx();
const RT rhy = r.hy();
const RT rhw = r.hw();
const RT RT0 = RT(0);
const RT RT2 = RT(2);
RT dosd = // difference of squared distances
// phx * phx * qhw * qhw * rhw * rhw
// -RT(2) * phx * qhx * phw * qhw * rhw * rhw
// + qhx * qhx * phw * phw * rhw * rhw
//
// + phy * phy * qhw * qhw * rhw * rhw
// -RT(2) * phy * qhy * phw * qhw * rhw * rhw
// + qhy * qhy * phw * phw * rhw * rhw
//
// - ( phx * phx * qhw * qhw * rhw * rhw
// -RT(2) * phx * rhx * phw * qhw * qhw * rhw
// + rhx * rhx * phw * phw * qhw * qhw
//
// + phy * phy * qhw * qhw * rhw * rhw
// -RT(2) * phy * rhy * phw * qhw * qhw * rhw
// + rhy * rhy * phw * phw * qhw * qhw
rhw*rhw * ( phw * ( qhx*qhx + qhy*qhy )
- RT2 * qhw * ( phx*qhx + phy*qhy )
)
- qhw*qhw * ( phw * ( rhx*rhx + rhy*rhy )
- RT2 * rhw * ( phx*rhx + phy*rhy )
);
if ( RT0 < dosd )
{
return LARGER;
}
else
{
return (dosd < RT0) ? SMALLER : EQUAL;
}
}
};
template <typename K>
class Compare_distance_3
{
typedef typename K::Point_3 Point_3;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 3 > Arity;
Comparison_result
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
typedef typename K::RT RT;
const RT phx = p.hx();
const RT phy = p.hy();
const RT phz = p.hz();
const RT phw = p.hw();
const RT qhx = q.hx();
const RT qhy = q.hy();
const RT qhz = q.hz();
const RT qhw = q.hw();
const RT rhx = r.hx();
const RT rhy = r.hy();
const RT rhz = r.hz();
const RT rhw = r.hw();
const RT RT0 = RT(0);
const RT RT2 = RT(2);
RT dosd = // difference of squared distances
rhw*rhw * ( phw * ( qhx*qhx + qhy*qhy + qhz*qhz )
- RT2 * qhw * ( phx*qhx + phy*qhy + phz*qhz )
)
- qhw*qhw * ( phw * ( rhx*rhx + rhy*rhy + rhz*rhz )
- RT2 * rhw * ( phx*rhx + phy*rhy + phz*rhz )
);
if ( RT0 < dosd )
{ return LARGER; }
else
{ return (dosd < RT0) ? SMALLER : EQUAL; }
}
};
template <typename K>
class Compare_slope_2
{
typedef typename K::Line_2 Line_2;
typedef typename K::Segment_2 Segment_2;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 2 > Arity;
Comparison_result
operator()(const Line_2& l1, const Line_2& l2) const
{
typedef typename K::RT RT;
if (l1.is_horizontal())
return l2.is_vertical() ?
SMALLER : Comparison_result(CGAL_NTS sign<RT>(l2.a() * l2.b()));
if (l2.is_horizontal())
return l1.is_vertical() ?
LARGER : Comparison_result(- CGAL_NTS sign<RT>(l1.a() * l1.b()));
if (l1.is_vertical()) return l2.is_vertical() ? EQUAL : LARGER;
if (l2.is_vertical()) return SMALLER;
int l1_sign = CGAL_NTS sign<RT>(-l1.a() * l1.b());
int l2_sign = CGAL_NTS sign<RT>(-l2.a() * l2.b());
if (l1_sign < l2_sign) return SMALLER;
if (l1_sign > l2_sign) return LARGER;
if (l1_sign > 0)
return CGAL_NTS compare( CGAL_NTS abs<RT>(l1.a() * l2.b()),
CGAL_NTS abs<RT>(l2.a() * l1.b()) );
return CGAL_NTS compare( CGAL_NTS abs<RT>(l2.a() * l1.b()),
CGAL_NTS abs<RT>(l1.a() * l2.b()) );
} // FIXME
Comparison_result
operator()(const Segment_2& s1, const Segment_2& s2) const
{
typedef typename K::FT FT;
Comparison_result cmp_y1 = compare_y(s1.source(), s1.target());
if (cmp_y1 == EQUAL) // horizontal
{
Comparison_result cmp_x2 = compare_x(s2.source(), s2.target());
if (cmp_x2 == EQUAL) return SMALLER;
FT s_hw = s2.source().hw();
FT t_hw = s2.target().hw();
return Comparison_result (
- CGAL_NTS sign((s2.source().hy()*t_hw - s2.target().hy()*s_hw) *
(s2.source().hx()*t_hw - s2.target().hx()*s_hw)) );
}
Comparison_result cmp_y2 = compare_y(s2.source(), s2.target());
if (cmp_y2 == EQUAL)
{
Comparison_result cmp_x1 = compare_x(s1.source(), s1.target());
if (cmp_x1 == EQUAL) return LARGER;
FT s_hw = s1.source().hw();
FT t_hw = s1.target().hw();
return Comparison_result (
CGAL_NTS sign((s1.source().hy()*t_hw - s1.target().hy()*s_hw) *
(s1.source().hx()*t_hw - s1.target().hx()*s_hw)) );
}
Comparison_result cmp_x1 = compare_x(s1.source(), s1.target());
Comparison_result cmp_x2 = compare_x(s2.source(), s2.target());
if (cmp_x1 == EQUAL)
return cmp_x2 == EQUAL ? EQUAL : LARGER;
if (cmp_x2 == EQUAL) return SMALLER;
FT s1_s_hw = s1.source().hw();
FT s1_t_hw = s1.target().hw();
FT s2_s_hw = s2.source().hw();
FT s2_t_hw = s2.target().hw();
FT s1_xdiff = s1.source().hx()*s1_t_hw - s1.target().hx()*s1_s_hw;
FT s1_ydiff = s1.source().hy()*s1_t_hw - s1.target().hy()*s1_s_hw;
FT s2_xdiff = s2.source().hx()*s2_t_hw - s2.target().hx()*s2_s_hw;
FT s2_ydiff = s2.source().hy()*s2_t_hw - s2.target().hy()*s2_s_hw;
Sign s1_sign = CGAL_NTS sign(s1_ydiff * s1_xdiff);
Sign s2_sign = CGAL_NTS sign(s2_ydiff * s2_xdiff);
if (s1_sign < s2_sign) return SMALLER;
if (s1_sign > s2_sign) return LARGER;
if (s1_sign > 0)
return Comparison_result(
CGAL_NTS sign ( CGAL_NTS abs(s1_ydiff * s2_xdiff) -
CGAL_NTS abs(s2_ydiff * s1_xdiff)) );
return Comparison_result(
CGAL_NTS sign ( CGAL_NTS abs(s2_ydiff * s1_xdiff) -
CGAL_NTS abs(s1_ydiff * s2_xdiff)) );
}
};
template <typename K>
class Compare_x_at_y_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 3 > Arity;
Comparison_result
operator()( const Point_2& p, const Line_2& h) const
{
typedef typename K::RT RT;
CGAL_kernel_precondition( ! h.is_horizontal() );
Oriented_side ors = h.oriented_side( p );
if ( h.a() < RT(0) )
ors = opposite( ors );
if ( ors == ON_POSITIVE_SIDE )
return LARGER;
return ( ors == ON_NEGATIVE_SIDE ) ? SMALLER : EQUAL;
} // FIXME
Comparison_result
operator()( const Point_2& p, const Line_2& h1, const Line_2& h2) const
{ return CGAL_NTS compare(h1.x_at_y( p.y() ), h2.x_at_y( p.y() )); }
// FIXME
Comparison_result
operator()( const Line_2& l1, const Line_2& l2, const Line_2& h) const
{ return compare_x_at_y( gp_linear_intersection( l1, l2 ), h); }
// FIXME
Comparison_result
operator()( const Line_2& l1, const Line_2& l2,
const Line_2& h1, const Line_2& h2) const
{ return compare_x_at_y( gp_linear_intersection( l1, l2 ), h1, h2 ); }
// FIXME
};
template <typename K>
class Compare_xyz_3
{
typedef typename K::Point_3 Point_3;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 2 > Arity;
Comparison_result
operator()( const Point_3& p, const Point_3& q) const
{
typedef typename K::RT RT;
RT pV = p.hx()*q.hw();
RT qV = q.hx()*p.hw();
if ( pV < qV )
{
return SMALLER;
}
if ( qV < pV ) // ( pV > qV )
{
return LARGER;
}
// same x
pV = p.hy()*q.hw();
qV = q.hy()*p.hw();
if ( pV < qV )
{
return SMALLER;
}
if ( qV < pV ) // ( pV > qV )
{
return LARGER;
}
// same x and y
pV = p.hz()*q.hw();
qV = q.hz()*p.hw();
if ( pV < qV )
{
return SMALLER;
}
else
{
return (qV < pV) ? LARGER : EQUAL;
}
}
};
template <typename K>
class Compare_xy_2
{
typedef typename K::Point_2 Point_2;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 2 > Arity;
Comparison_result
operator()( const Point_2& p, const Point_2& q) const
{
typedef typename K::RT RT;
const RT& phx = p.hx();
const RT& phy = p.hy();
const RT& phw = p.hw();
const RT& qhx = q.hx();
const RT& qhy = q.hy();
const RT& qhw = q.hw();
RT pV = phx*qhw;
RT qV = qhx*phw;
if ( pV == qV )
{
pV = phy*qhw;
qV = qhy*phw;
}
if ( pV < qV )
{
return SMALLER;
}
else
{
return (qV < pV) ? LARGER : EQUAL;
}
}
};
template <typename K>
class Compare_xy_3
{
typedef typename K::Point_3 Point_3;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 2 > Arity;
Comparison_result
operator()( const Point_3& p, const Point_3& q) const
{
typedef typename K::RT RT;
RT pV = p.hx()*q.hw();
RT qV = q.hx()*p.hw();
if ( pV < qV )
{
return SMALLER;
}
if ( qV < pV ) // ( pV > qV )
{
return LARGER;
}
// same x
pV = p.hy()*q.hw();
qV = q.hy()*p.hw();
if ( pV < qV )
{
return SMALLER;
}
if ( qV < pV ) // ( pV > qV )
{
return LARGER;
}
// same x and y
return EQUAL;
}
};
template <typename K>
class Compare_x_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 2 > Arity;
Comparison_result
operator()( const Point_2& p, const Point_2& q) const
{
return CGAL_NTS compare(p.hx()*q.hw(), q.hx()*p.hw());
}
Comparison_result
operator()( const Point_2& p, const Line_2& l1, const Line_2& l2) const
{
Point_2 ip = gp_linear_intersection( l1, l2 );
return this->operator()(p, ip);
} // FIXME
Comparison_result
operator()( const Line_2& l, const Line_2& h1, const Line_2& h2) const
{
return this->operator()(l, h1, l, h2);
} // FIXME
Comparison_result
operator()( const Line_2& l1, const Line_2& l2,
const Line_2& h1, const Line_2& h2) const
{
Point_2 lip = gp_linear_intersection( l1, l2 );
Point_2 hip = gp_linear_intersection( h1, h2 );
return this->operator()(lip, hip);
} // FIXME
};
template <typename K>
class Compare_x_3
{
typedef typename K::Point_3 Point_3;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 2 > Arity;
Comparison_result
operator()( const Point_3& p, const Point_3& q) const
{ return CGAL_NTS compare(p.hx() * q.hw(), q.hx() * p.hw() ); }
};
template <typename K>
class Compare_y_at_x_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
typedef typename K::Segment_2 Segment_2;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 3 > Arity;
Comparison_result
operator()( const Point_2& p, const Line_2& h) const
{
typedef typename K::RT RT;
CGAL_kernel_precondition( ! h.is_vertical() );
Oriented_side ors = h.oriented_side( p );
if ( h.b() < RT(0) )
{
ors = opposite( ors );
}
if ( ors == ON_POSITIVE_SIDE )
{
return LARGER;
}
return ( ors == ON_NEGATIVE_SIDE ) ? SMALLER : EQUAL;
} // FIXME
Comparison_result
operator()( const Point_2& p, const Line_2& h1, const Line_2& h2) const
{ return CGAL_NTS compare(h1.y_at_x( p.x() ), h2.y_at_x( p.x() )); }
// FIXME
Comparison_result
operator()( const Line_2& l1, const Line_2& l2, const Line_2& h) const
{ return compare_y_at_x( gp_linear_intersection( l1, l2 ), h); }
// FIXME
Comparison_result
operator()( const Line_2& l1, const Line_2& l2,
const Line_2& h1, const Line_2& h2) const
{ return compare_y_at_x( gp_linear_intersection( l1, l2 ), h1, h2 ); }
// FIXME
Comparison_result
operator()( const Point_2& p, const Segment_2& s) const
{
// compares the y-coordinates of p and the vertical projection of p on s.
// Precondition : p is in the x-range of s.
if (compare_x(s.source(), s.target()) == SMALLER) {
CGAL_kernel_precondition(compare_x(s.source(), p) != LARGER
&& compare_x(p, s.target()) != LARGER);
return (Comparison_result) orientation(p, s.source(), s.target());
}
else if (compare_x(s.source(), s.target()) == LARGER) {
CGAL_kernel_precondition(compare_x(s.target(), p) != LARGER
&& compare_x(p, s.source()) != LARGER);
return (Comparison_result) orientation(p, s.target(), s.source());
}
else {
CGAL_kernel_precondition(compare_x(s.target(), p) == EQUAL);
if (compare_y(p, s.source()) == SMALLER &&
compare_y(p, s.target()) == SMALLER)
return SMALLER;
if (compare_y(p, s.source()) == LARGER &&
compare_y(p, s.target()) == LARGER)
return LARGER;
return EQUAL;
}
} // FIXME
Comparison_result
operator()( const Point_2& p,
const Segment_2& s1, const Segment_2& s2) const
{
// compares the y-coordinates of the vertical projections
// of p on s1 and s2
// Precondition : p is in the x-range of s1 and s2.
// - if one or two segments are vertical :
// - if the segments intersect, return EQUAL
// - if not, return the obvious SMALLER/LARGER.
typedef typename K::FT FT;
FT px = p.x();
FT s1sx = s1.source().x();
FT s1sy = s1.source().y();
FT s1tx = s1.target().x();
FT s1ty = s1.target().y();
FT s2sx = s2.source().x();
FT s2sy = s2.source().y();
FT s2tx = s2.target().x();
FT s2ty = s2.target().y();
CGAL_kernel_precondition(px >= CGAL_NTS min(s1sx, s1tx) &&
px <= CGAL_NTS max(s1sx, s1tx));
CGAL_kernel_precondition(px >= CGAL_NTS min(s2sx, s2tx) &&
px <= CGAL_NTS max(s2sx, s2tx));
if (s1sx != s1tx && s2sx != s2tx) {
FT s1stx = s1sx-s1tx;
FT s2stx = s2sx-s2tx;
return Comparison_result(
CGAL_NTS compare(s1sx, s1tx) *
CGAL_NTS compare(s2sx, s2tx) *
CGAL_NTS compare(-(s1sx-px)*(s1sy-s1ty)*s2stx,
(s2sy-s1sy)*s2stx*s1stx
-(s2sx-px)*(s2sy-s2ty)*s1stx ));
}
else {
if (s1sx == s1tx) { // s1 is vertical
Comparison_result c1, c2;
c1 = compare_y_at_x(s1.source(), s2);
c2 = compare_y_at_x(s1.target(), s2);
if (c1 == c2)
return c1;
return EQUAL;
}
// s2 is vertical
Comparison_result c3, c4;
c3 = compare_y_at_x(s2.source(), s1);
c4 = compare_y_at_x(s2.target(), s1);
if (c3 == c4)
return opposite(c3);
return EQUAL;
}
} // FIXME
};
template <typename K>
class Compare_y_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 2 > Arity;
Comparison_result
operator()( const Point_2& p, const Point_2& q) const
{
typedef typename K::RT RT;
const RT& phy = p.hy();
const RT& phw = p.hw();
const RT& qhy = q.hy();
const RT& qhw = q.hw();
const RT RT0 = RT(0);
RT com = phy * qhw - qhy * phw;
if ( com < RT0 )
return SMALLER;
else if ( RT0 < com )
return LARGER;
return EQUAL;
}
Comparison_result
operator()( const Point_2& p, const Line_2& l1, const Line_2& l2) const
{
Point_2 ip = gp_linear_intersection( l1, l2 );
return compare_y( p, ip );
} // FIXME
Comparison_result
operator()( const Line_2& l, const Line_2& h1, const Line_2& h2) const
{
return this->operator()(l, h1, l, h2);
}
Comparison_result
operator()( const Line_2& l1, const Line_2& l2,
const Line_2& h1, const Line_2& h2) const
{
Point_2 lip = gp_linear_intersection( l1, l2 );
Point_2 hip = gp_linear_intersection( h1, h2 );
return this->operator()( lip, hip );
} // FIXME
};
template <typename K>
class Compare_y_3
{
typedef typename K::Point_3 Point_3;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 2 > Arity;
Comparison_result
operator()( const Point_3& p, const Point_3& q) const
{ return CGAL_NTS compare(p.hy() * q.hw(), q.hy() * p.hw() ); }
};
template <typename K>
class Compare_z_3
{
typedef typename K::Point_3 Point_3;
public:
typedef Comparison_result result_type;
typedef Arity_tag< 2 > Arity;
Comparison_result
operator()( const Point_3& p, const Point_3& q) const
{ return CGAL_NTS compare(p.hz() * q.hw(), q.hz() * p.hw() ); }
};
template <typename K>
class Compute_area_2
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Iso_rectangle_2 Iso_rectangle_2;
typedef typename K::Triangle_2 Triangle_2;
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
typedef typename K::Construct_vector_2 Construct_vector_2;
Construct_vector_2 co;
public:
typedef FT result_type;
typedef Arity_tag< 1 > Arity;
FT
operator()( const Point_2& p, const Point_2& q, const Point_2& r ) const
{
Vector_2 v1 = co(p, q);
Vector_2 v2 = co(p, r);
RT num = v1.hx()*v2.hy() - v2.hx()*v1.hy();
RT den = RT(2) * v1.hw() * v2.hw();
return FT(num)/FT(den);
}
FT
operator()( const Iso_rectangle_2& r ) const
{ return r.area(); }
FT
operator()( const Triangle_2& t ) const
{ return t.area(); }
};
template <typename K>
class Compute_scalar_product_2
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Vector_2 Vector_2;
public:
typedef FT result_type;
typedef Arity_tag< 2 > Arity;
FT
operator()(const Vector_2& v, const Vector_2& w) const
{
return FT( RT(v.hx()*w.hx() + v.hy()*w.hy()) ) /
FT( RT(v.hw()*w.hw() ) );
}
};
template <typename K>
class Compute_scalar_product_3
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Vector_3 Vector_3;
public:
typedef FT result_type;
typedef Arity_tag< 2 > Arity;
FT
operator()(const Vector_3& v, const Vector_3& w) const
{
return FT( RT(v.hx()*w.hx() + v.hy()*w.hy()) + v.hz()*w.hz() ) /
FT( RT(v.hw()*w.hw() ) );
}
};
// TODO ...
template <typename K>
class Compute_squared_radius_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Circle_2 Circle_2;
public:
typedef FT result_type;
typedef Arity_tag< 1 > Arity;
FT
operator()( const Circle_2& c) const
{ return c.squared_radius(); }
FT
operator()( const Point_2& p, const Point_2& q) const
{
typedef typename K::FT FT;
return squared_distance(p, q)/FT(4);
} // FIXME
FT
operator()( const Point_2& p, const Point_2& q, const Point_2& r) const
{ return squared_distance(p, circumcenter(p, q, r)); }
// FIXME
};
template <typename K>
class Compute_squared_radius_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Sphere_3 Sphere_3;
public:
typedef FT result_type;
typedef Arity_tag< 1 > Arity;
FT
operator()( const Sphere_3& s) const
{ return s.squared_radius(); }
FT
operator()( const Point_3& p, const Point_3& q) const
{
typedef typename K::FT FT;
return squared_distance(p, q) / FT(4);
} // FIXME
FT
operator()( const Point_3& p, const Point_3& q, const Point_3& r) const
{
return squared_distance(p, circumcenter(p, q, r));
} // FIXME
FT
operator()( const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& s) const
{
return squared_distance(p, circumcenter(p, q, r, s));
} // FIXME
};
template <typename K>
class Compute_volume_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Tetrahedron_3 Tetrahedron_3;
typedef typename K::Iso_cuboid_3 Iso_cuboid_3;
public:
typedef FT result_type;
typedef Arity_tag< 1 > Arity;
FT
operator()(const Point_3& p0, const Point_3& p1,
const Point_3& p2, const Point_3& p3) const
{
Vector_3 vec1 = p1 - p0;
Vector_3 vec2 = p2 - p0;
Vector_3 vec3 = p3 - p0;
// first compute (vec1.hw * vec2.hw * vec3.hw * det(vec1, vec2, vec3))
// then divide by (6 * vec1.hw * vec2.hw * vec3.hw)
const FT w123 = vec1.hw() * vec2.hw() * vec3.hw();
const FT& hx1 = vec1.hx();
const FT& hy1 = vec1.hy();
const FT& hz1 = vec1.hz();
const FT& hx2 = vec2.hx();
const FT& hy2 = vec2.hy();
const FT& hz2 = vec2.hz();
const FT& hx3 = vec3.hx();
const FT& hy3 = vec3.hy();
const FT& hz3 = vec3.hz();
return ( (hx1 * (hy2 * hz3 - hy3 * hz2))
- (hy1 * (hx2 * hz3 - hx3 * hz2))
+ (hz1 * (hx2 * hy3 - hx3 * hy2)))/ (6 * w123);
}
FT
operator()( const Tetrahedron_3& t ) const
{
return this->operator()(t.vertex(0), t.vertex(1),
t.vertex(2), t.vertex(3));
}
FT
operator()( const Iso_cuboid_3& c ) const
{ return c.volume(); }
};
template <typename K>
class Construct_base_vector_3
{
typedef typename K::Vector_3 Vector_3;
typedef typename K::Plane_3 Plane_3;
typedef typename K::RT RT;
typedef typename K::Construct_orthogonal_vector_3
Construct_orthogonal_vector_3;
Construct_orthogonal_vector_3 co;
public:
typedef Vector_3 result_type;
typedef Arity_tag< 2 > Arity;
Construct_base_vector_3() {}
Construct_base_vector_3(const Construct_orthogonal_vector_3& co_)
: co(co_)
{}
Vector_3
operator()( const Plane_3& h, int index ) const
{
if (index == 1) {
// point():
// a() != RT0 : Point_3( -d(), RT0, RT0, a() );
// b() != RT0 : Point_3( RT0, -d(), RT0, b() );
// : Point_3( RT0, RT0, -d(), c() );
// point1():
// a() != RT0 : Point_3( -b()-d(), a(), RT0, a() );
// b() != RT0 : Point_3( RT0, -c()-d(), b(), b() );
// : Point_3( c(), RT0, -a()-d(), c() );
const RT RT0(0);
if ( h.a() != RT0 )
{
return Vector_3( -h.b(), h.a(), RT0, h.a() );
}
if ( h.b() != RT0 )
{
return Vector_3( RT0, -h.c(), h.b(), h.b() );
}
CGAL_kernel_assertion ( h.c() != RT(0) );
return Vector_3( h.c(), RT0, -h.a(), h.c() );
} else {
Vector_3 a = co(h);
Vector_3 b = this->operator()(h, 1);
return Vector_3(a.hy()*b.hz() - a.hz()*b.hy(),
a.hz()*b.hx() - a.hx()*b.hz(),
a.hx()*b.hy() - a.hy()*b.hx(),
a.hw()*b.hw() );
}
}
};
template <typename K>
class Construct_bisector_2
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
public:
typedef Line_2 result_type;
typedef Arity_tag< 2 > Arity;
Line_2
operator()(const Point_2& p, const Point_2& q) const
{
// Bisector equation is based on equation
// ( X - p.x())^2 + (Y - p.y())^2 == ( X - q.x())^2 + (Y - q.y())
// and x() = hx()/hw() ...
const RT &phx = p.hx();
const RT &phy = p.hy();
const RT &phw = p.hw();
const RT &qhx = q.hx();
const RT &qhy = q.hy();
const RT &qhw = q.hw();
RT a = RT(2) * ( phx*phw*qhw*qhw - qhx*qhw*phw*phw );
RT b = RT(2) * ( phy*phw*qhw*qhw - qhy*qhw*phw*phw );
RT c = qhx*qhx*phw*phw + qhy*qhy*phw*phw
- phx*phx*qhw*qhw - phy*phy*qhw*qhw;
return Line_2( a, b, c );
}
Line_2
operator()(const Line_2& p, const Line_2& q) const
{
RT a, b, c;
bisector_of_linesC2(p.a(), p.b(), p.c(),
q.a(), q.b(), q.c(),
a, b, c);
return Line_2(a, b, c);
}
};
template <typename K>
class Construct_bisector_3
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Plane_3 Plane_3;
public:
typedef Plane_3 result_type;
typedef Arity_tag< 2 > Arity;
Plane_3
operator()(const Point_3& p, const Point_3& q) const
{
// Bisector equation is based on equation
// ( X - p.x())^2 + (Y - p.y())^2 == ( X - q.x())^2 + (Y - q.y())
// and x() = hx()/hw() ...
const RT& phx = p.hx();
const RT& phy = p.hy();
const RT& phz = p.hz();
const RT& phw = p.hw();
const RT& qhx = q.hx();
const RT& qhy = q.hy();
const RT& qhz = q.hz();
const RT& qhw = q.hw();
RT a = RT(2) * ( phx*phw*qhw*qhw - qhx*qhw*phw*phw );
RT b = RT(2) * ( phy*phw*qhw*qhw - qhy*qhw*phw*phw );
RT c = RT(2) * ( phz*phw*qhw*qhw - qhz*qhw*phw*phw );
RT d = qhx*qhx*phw*phw + qhy*qhy*phw*phw + qhz*qhz*phw*phw
- phx*phx*qhw*qhw - phy*phy*qhw*qhw - phz*phz*qhw*qhw;
return Plane_3( a, b, c, d );
}
Plane_3
operator()(const Plane_3& p, const Plane_3& q) const
{
RT a, b, c, d;
bisector_of_planesC3(p.a(), p.b(), p.c(), p.d(),
q.a(), q.b(), q.c(), q.d(),
a, b, c, d);
return Plane_3(a, b, c, d);
}
};
template <typename K>
class Construct_centroid_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
public:
typedef Point_2 result_type;
typedef Arity_tag< 3 > Arity;
Point_2
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
typedef typename K::RT RT;
const RT phw(p.hw());
const RT qhw(q.hw());
const RT rhw(r.hw());
RT hx(p.hx()*qhw*rhw + q.hx()*phw*rhw + r.hx()*phw*qhw);
RT hy(p.hy()*qhw*rhw + q.hy()*phw*rhw + r.hy()*phw*qhw);
RT hw( phw*qhw*rhw * 3);
return Point_2(hx, hy, hw);
}
Point_2
operator()(const Point_2& p, const Point_2& q,
const Point_2& r, const Point_2& s) const
{
typedef typename K::RT RT;
const RT phw(p.hw());
const RT qhw(q.hw());
const RT rhw(r.hw());
const RT shw(s.hw());
RT hx(p.hx()*qhw*rhw*shw + q.hx()*phw*rhw*shw + r.hx()*phw*qhw*shw
+ s.hx()*phw*qhw*rhw);
RT hy(p.hy()*qhw*rhw*shw + q.hy()*phw*rhw*shw + r.hy()*phw*qhw*shw
+ s.hy()*phw*qhw*rhw);
RT hw( phw*qhw*rhw*shw * 4);
return Point_2(hx, hy, hw);
}
};
template <typename K>
class Construct_centroid_3
{
typedef typename K::RT RT;
typedef typename K::Point_3 Point_3;
public:
typedef Point_3 result_type;
typedef Arity_tag< 3 > Arity;
Point_3
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
const RT& phw = p.hw();
const RT& qhw = q.hw();
const RT& rhw = r.hw();
RT hx(p.hx()*qhw*rhw + q.hx()*phw*rhw + r.hx()*phw*qhw);
RT hy(p.hy()*qhw*rhw + q.hy()*phw*rhw + r.hy()*phw*qhw);
RT hz(p.hz()*qhw*rhw + q.hz()*phw*rhw + r.hz()*phw*qhw);
RT hw( phw*qhw*rhw * RT(3));
return Point_3(hx, hy, hz, hw);
}
Point_3
operator()(const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& s) const
{
const RT& phw = p.hw();
const RT& qhw = q.hw();
const RT& rhw = r.hw();
const RT& shw = s.hw();
RT hx(p.hx()*qhw*rhw*shw + q.hx()*phw*rhw*shw + r.hx()*phw*qhw*shw
+ s.hx()*phw*qhw*rhw);
RT hy(p.hy()*qhw*rhw*shw + q.hy()*phw*rhw*shw + r.hy()*phw*qhw*shw
+ s.hy()*phw*qhw*rhw);
RT hz(p.hz()*qhw*rhw*shw + q.hz()*phw*rhw*shw + r.hz()*phw*qhw*shw
+ s.hz()*phw*qhw*rhw);
RT hw( phw*qhw*rhw*shw * RT(4));
return Point_3(hx, hy, hz, hw);
}
};
template <typename K>
class Construct_circumcenter_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Triangle_2 Triangle_2;
public:
typedef Point_2 result_type;
typedef Arity_tag< 3 > Arity;
Point_2
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
typedef typename K::RT RT;
RT phx = p.hx();
RT phy = p.hy();
RT phw = p.hw();
RT qhx = q.hx();
RT qhy = q.hy();
RT qhw = q.hw();
RT rhx = r.hx();
RT rhy = r.hy();
RT rhw = r.hw();
#ifdef CGAL_EXPANDED_CIRCUMCENTER_COMPUTATION
RT vvx =
( qhy*qhw*phw*phw - phy*phw*qhw*qhw )
*( phx*phx*rhw*rhw + phy*phy*rhw*rhw -
rhx*rhx*phw*phw - rhy*rhy*phw*phw )
- ( rhy*rhw*phw*phw - phy*phw*rhw*rhw )
*( phx*phx*qhw*qhw + phy*phy*qhw*qhw -
qhx*qhx*phw*phw - qhy*qhy*phw*phw );
RT vvy =
- ( qhx*qhw*phw*phw - phx*phw*qhw*qhw )
*( phx*phx*rhw*rhw + phy*phy*rhw*rhw -
rhx*rhx*phw*phw - rhy*rhy*phw*phw )
+ ( rhx*rhw*phw*phw - phx*phw*rhw*rhw )
*( phx*phx*qhw*qhw + phy*phy*qhw*qhw -
qhx*qhx*phw*phw - qhy*qhy*phw*phw );
RT vvw = RT(2) *
( ( qhx*qhw*phw*phw - phx*phw*qhw*qhw )
*( rhy*rhw*phw*phw - phy*phw*rhw*rhw )
- ( rhx*rhw*phw*phw - phx*phw*rhw*rhw )
*( qhy*qhw*phw*phw - phy*phw*qhw*qhw ) );
#endif // CGAL_EXPANDED_CIRCUMCENTER_COMPUTATION
RT qy_py = ( qhy*qhw*phw*phw - phy*phw*qhw*qhw );
RT qx_px = ( qhx*qhw*phw*phw - phx*phw*qhw*qhw );
RT rx_px = ( rhx*rhw*phw*phw - phx*phw*rhw*rhw );
RT ry_py = ( rhy*rhw*phw*phw - phy*phw*rhw*rhw );
RT px2_py2_rx2_ry_2 =
phx*phx*rhw*rhw + phy*phy*rhw*rhw -
rhx*rhx*phw*phw - rhy*rhy*phw*phw ;
RT px2_py2_qx2_qy_2 =
phx*phx*qhw*qhw + phy*phy*qhw*qhw -
qhx*qhx*phw*phw - qhy*qhy*phw*phw ;
RT vvx = qy_py * px2_py2_rx2_ry_2 - ry_py * px2_py2_qx2_qy_2;
RT vvy = rx_px * px2_py2_qx2_qy_2 - qx_px * px2_py2_rx2_ry_2;
RT vvw = RT(2) * ( qx_px * ry_py - rx_px * qy_py );
return Point_2( vvx, vvy, vvw );
}
Point_2
operator()(const Triangle_2& t) const
{
return this->operator()(t.vertex(0), t.vertex(1), t.vertex(2));
}
};
template <typename K>
class Construct_circumcenter_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
typedef typename K::Triangle_3 Triangle_3;
typedef typename K::Tetrahedron_3 Tetrahedron_3;
typedef typename K::Plane_3 Plane_3;
public:
typedef Point_3 result_type;
typedef Arity_tag< 4 > Arity;
Point_3
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
return gp_linear_intersection( Plane_3(p,q,r),
bisector(p,q),
bisector(p,r));
} // FIXME
Point_3
operator()(const Triangle_3& t) const
{
return this->operator()(t.vertex(0), t.vertex(1), t.vertex(2));
}
Point_3
operator()(const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& s) const
{
typedef typename K::RT RT;
RT phw( p.hw() );
RT qhw( q.hw() );
RT rhw( r.hw() );
RT shw( s.hw() );
RT phx( p.hx() );
RT phy( p.hy() );
RT phz( p.hz() );
RT qhx( q.hx() );
RT qhy( q.hy() );
RT qhz( q.hz() );
RT rhx( r.hx() );
RT rhy( r.hy() );
RT rhz( r.hz() );
RT shx( s.hx() );
RT shy( s.hy() );
RT shz( s.hz() );
RT pssq( phx*phx + phy*phy + phz*phz );
RT qssq( qhx*qhx + qhy*qhy + qhz*qhz );
RT rssq( rhx*rhx + rhy*rhy + rhz*rhz );
RT sssq( shx*shx + shy*shy + shz*shz );
phx *= phw;
phy *= phw;
phz *= phw;
phw *= phw;
qhx *= qhw;
qhy *= qhw;
qhz *= qhw;
qhw *= qhw;
rhx *= rhw;
rhy *= rhw;
rhz *= rhw;
rhw *= rhw;
shx *= shw;
shy *= shw;
shz *= shw;
shw *= shw;
RT chx = det4x4_by_formula(phy, phz, pssq, phw,
qhy, qhz, qssq, qhw,
rhy, rhz, rssq, rhw,
shy, shz, sssq, shw );
RT chy = det4x4_by_formula(phx, phz, pssq, phw,
qhx, qhz, qssq, qhw,
rhx, rhz, rssq, rhw,
shx, shz, sssq, shw );
RT chz = det4x4_by_formula(phx, phy, pssq, phw,
qhx, qhy, qssq, qhw,
rhx, rhy, rssq, rhw,
shx, shy, sssq, shw );
RT chw = det4x4_by_formula(phx, phy, phz, phw,
qhx, qhy, qhz, qhw,
rhx, rhy, rhz, rhw,
shx, shy, shz, shw );
return Point_3( chx, -chy, chz, RT(2)*chw);
}
Point_3
operator()(const Tetrahedron_3& t) const
{
return this->operator()(t.vertex(0), t.vertex(1),
t.vertex(2), t.vertex(3));
}
};
template <typename K>
class Construct_cross_product_vector_3
{
typedef typename K::Vector_3 Vector_3;
public:
typedef Vector_3 result_type;
typedef Arity_tag< 2 > Arity;
Vector_3
operator()(const Vector_3& a, const Vector_3& b) const
{
return Vector_3(a.hy()*b.hz() - a.hz()*b.hy(),
a.hz()*b.hx() - a.hx()*b.hz(),
a.hx()*b.hy() - a.hy()*b.hx(),
a.hw()*b.hw() );
}
};
template <typename K>
class Construct_lifted_point_3
{
typedef typename K::RT RT;
typedef typename K::Point_2 Point_2;
typedef typename K::Point_3 Point_3;
typedef typename K::Plane_3 Plane_3;
public:
typedef Point_3 result_type;
typedef Arity_tag< 2 > Arity;
Point_3
operator()(const Plane_3& h, const Point_2& p) const
{
Point_3 hp( p.hx(), p.hy(), RT(0.0), p.hw());
return hp.transform( h.transform_to_2d().inverse() );
}
};
template <typename K>
class Construct_line_2
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
typedef typename K::Direction_2 Direction_2;
typedef typename K::Segment_2 Segment_2;
typedef typename K::Ray_2 Ray_2;
typedef typename K::Line_2 Line_2;
typedef typename K::Construct_point_on_2 Construct_point_on_2;
Construct_point_on_2 cp;
public:
typedef Line_2 result_type;
typedef Arity_tag< 2 > Arity;
Construct_line_2() {}
Construct_line_2(const Construct_point_on_2& cp_) : cp(cp_) {}
Line_2
operator()() const
{ return Line_2(); }
// #ifndef CGAL_NO_DEPRECATED_CODE
Line_2
operator()(const RT& a, const RT& b, const RT& c) const
{ return Line_2(a, b, c); }
// #endif // CGAL_NO_DEPRECATED_CODE
Line_2
operator()(const Point_2& p, const Point_2& q) const
{
return Line_2(
// a() * X + b() * Y + c() * W() == 0
// | X Y W |
// | p.hx() p.hy() p.hw() |
// | q.hx() q.hy() q.hw() |
p.hy()*q.hw() - p.hw()*q.hy(),
p.hw()*q.hx() - p.hx()*q.hw(),
p.hx()*q.hy() - p.hy()*q.hx() );
}
Line_2
operator()(const Point_2& p, const Vector_2& v) const
{
Point_2 q = p + v;
return Line_2( p.hy()*q.hw() - p.hw()*q.hy(),
p.hw()*q.hx() - p.hx()*q.hw(),
p.hx()*q.hy() - p.hy()*q.hx() );
}
Line_2
operator()(const Point_2& p, const Direction_2& d) const
{
Point_2 q = p + d.to_vector();
return Line_2( p.hy()*q.hw() - p.hw()*q.hy(),
p.hw()*q.hx() - p.hx()*q.hw(),
p.hx()*q.hy() - p.hy()*q.hx() );
}
Line_2
operator()(const Segment_2& s) const
{ return this->operator()(cp(s, 0), cp(s, 1)); }
Line_2
operator()(const Ray_2& r) const
{ return this->operator()(cp(r, 0), cp(r, 1)); }
};
template <typename K>
class Construct_midpoint_2
{
typedef typename K::FT FT;
typedef typename K::Point_2 Point_2;
public:
typedef Point_2 result_type;
typedef Arity_tag< 2 > Arity;
Point_2
operator()(const Point_2& p, const Point_2& q) const
{
typedef typename K::RT RT;
const RT& phw = p.hw();
const RT& qhw = q.hw();
return Point_2( p.hx()*qhw + q.hx()*phw,
p.hy()*qhw + q.hy()*phw,
phw * qhw * RT( 2));
}
};
template <typename K>
class Construct_midpoint_3
{
typedef typename K::FT FT;
typedef typename K::Point_3 Point_3;
public:
typedef Point_3 result_type;
typedef Arity_tag< 2 > Arity;
Point_3
operator()(const Point_3& p, const Point_3& q) const
{
typedef typename K::RT RT;
RT phw = p.hw();
RT qhw = q.hw();
return Point_3( p.hx()*qhw + q.hx()*phw,
p.hy()*qhw + q.hy()*phw,
p.hz()*qhw + q.hz()*phw,
RT(2) * phw * qhw );
}
};
// TODO ...
template <typename K>
class Construct_opposite_vector_2
{
typedef typename K::Vector_2 Vector_2;
public:
typedef Vector_2 result_type;
typedef Arity_tag< 1 > Arity;
Vector_2
operator()( const Vector_2& v) const
{ return Vector_2(-v.hx(), -v.hy(), v.hw()); }
};
template <typename K>
class Construct_opposite_vector_3
{
typedef typename K::Vector_3 Vector_3;
public:
typedef Vector_3 result_type;
typedef Arity_tag< 1 > Arity;
Vector_3
operator()( const Vector_3& v) const
{ return Vector_3(-v.hx(), -v.hy(), -v.hz(), v.hw()); }
};
template <typename K>
class Construct_orthogonal_vector_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Plane_3 Plane_3;
public:
typedef Vector_3 result_type;
typedef Arity_tag< 1 > Arity;
Vector_3
operator()( const Plane_3& p ) const
{ return p.orthogonal_vector(); }
Vector_3
operator()( const Point_3& p, const Point_3& q, const Point_3& r ) const
{
return operator()(Plane_3(p, q, r));
}
};
template <typename K>
class Construct_projected_point_3
{
typedef typename K::RT RT;
typedef typename K::Point_3 Point_3;
typedef typename K::Plane_3 Plane_3;
typedef typename K::Line_3 Line_3;
typedef typename K::Vector_3 Vector_3;
public:
typedef Point_3 result_type;
typedef Arity_tag< 2 > Arity;
Point_3
operator()( const Line_3& l, const Point_3& p ) const
{
if ( l.has_on(p) )
return p;
Vector_3 v = p - l.point();
const RT& vx = v.hx();
const RT& vy = v.hy();
const RT& vz = v.hz();
const RT& vw = v.hw();
Vector_3 dir = l.to_vector();
const RT& dx = dir.hx();
const RT& dy = dir.hy();
const RT& dz = dir.hz();
const RT& dw = dir.hw();
RT lambda_num = (vx*dx + vy*dy + vz*dz)*dw; // *dw
RT lambda_den = (dx*dx + dy*dy + dz*dz)*vw; // *dw
return l.point() + ( (lambda_num * dir)/lambda_den );
}
Point_3
operator()( const Plane_3& h, const Point_3& p ) const
{ return h.projection(p); }
};
template <typename K>
class Construct_scaled_vector_2
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Vector_2 Vector_2;
public:
typedef Vector_2 result_type;
typedef Arity_tag< 2 > Arity;
Vector_2
operator()( const Vector_2& v, const RT& c) const
{
return Vector_2(c * v.hx(), c * v.hy(), v.hw());
}
Vector_2
operator()( const Vector_2& v, const FT& c) const
{
return Vector_2( v.hx()*c.numerator(), v.hy()*c.numerator(),
v.hw()*c.denominator() ); }
};
template <typename K>
class Construct_scaled_vector_3
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Vector_3 Vector_3;
public:
typedef Vector_3 result_type;
typedef Arity_tag< 2 > Arity;
Vector_3
operator()( const Vector_3& v, const RT& c) const
{
return Vector_3(c * v.hx(), c * v.hy(), c * v.hz(), v.hw());
}
Vector_3
operator()( const Vector_3& v, const FT& c) const
{
return Vector_3( v.hx()*c.numerator(), v.hy()*c.numerator(),
v.hz()*c.numerator(), v.hw()*c.denominator() ); }
};
template <typename K>
class Construct_translated_point_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Vector_2 Vector_2;
public:
typedef Point_2 result_type;
typedef Arity_tag< 2 > Arity;
Point_2
operator()( const Point_2& p, const Vector_2& v) const
{
return Point_2( p.hx()*v.hw() + v.hx()*p.hw(),
p.hy()*v.hw() + v.hy()*p.hw(),
p.hw()*v.hw() );
}
Point_2
operator()( const Origin&, const Vector_2& v) const
{
return Point_2( v.hx(),
v.hy(),
v.hw() );
}
};
template <typename K>
class Construct_translated_point_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Vector_3 Vector_3;
public:
typedef Point_3 result_type;
typedef Arity_tag< 2 > Arity;
Point_3
operator()( const Point_3& p, const Vector_3& v) const
{
return Point_3(p.hx()*v.hw() + v.hx()*p.hw(),
p.hy()*v.hw() + v.hy()*p.hw(),
p.hz()*v.hw() + v.hz()*p.hw(),
p.hw()*v.hw() );
}
Point_3
operator()( const Origin&, const Vector_3& v) const
{
return Point_3( v.hx(),
v.hy(),
v.hz(),
v.hw() );
}
};
template <typename K>
class Construct_vector_2
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Segment_2 Segment_2;
typedef typename K::Ray_2 Ray_2;
typedef typename K::Line_2 Line_2;
typedef typename K::Vector_2 Vector_2;
typedef typename K::Point_2 Point_2;
public:
typedef Vector_2 result_type;
typedef Arity_tag< 2 > Arity;
Vector_2
operator()() const
{ return Vector_2(); }
Vector_2
operator()( const Point_2& p, const Point_2& q) const
{
return Vector_2( q.hx()*p.hw() - p.hx()*q.hw(),
q.hy()*p.hw() - p.hy()*q.hw(),
p.hw()*q.hw() );
}
Vector_2
operator()( const Origin& , const Point_2& q) const
{
return Vector_2( q.hx() ,
q.hy() ,
q.hw() );
}
Vector_2
operator()( const Point_2& p, const Origin& q) const
{
return Vector_2( - p.hx(),
- p.hy(),
p.hw() );
}
Vector_2
operator()( const Segment_2& s) const
{ return s.to_vector(); }
Vector_2
operator()( const Ray_2& r) const
{ return r.to_vector(); }
Vector_2
operator()( const Line_2& l) const
{ return l.to_vector(); }
Vector_2
operator()( Null_vector) const
{ return Vector_2(RT(0), RT(0), RT(1)); }
// #ifndef CGAL_NO_DEPRECATED_CODE
Vector_2
operator()( const RT& x, const RT& y) const
{ return Vector_2(x, y); }
Vector_2
operator()( const RT& x, const RT& y, const RT& w) const
{ return Vector_2(x, y, w); }
// #endif // CGAL_NO_DEPRECATED_CODE
};
template <typename K>
class Construct_vector_3
{
typedef typename K::RT RT;
typedef typename K::FT FT;
typedef typename K::Segment_3 Segment_3;
typedef typename K::Ray_3 Ray_3;
typedef typename K::Line_3 Line_3;
typedef typename K::Vector_3 Vector_3;
typedef typename K::Point_3 Point_3;
public:
typedef Vector_3 result_type;
typedef Arity_tag< 2 > Arity;
Vector_3
operator()() const
{ return Vector_3(); }
Vector_3
operator()( const Point_3& p, const Point_3& q) const
{
return Vector_3(q.hx()*p.hw() - p.hx()*q.hw(),
q.hy()*p.hw() - p.hy()*q.hw(),
q.hz()*p.hw() - p.hz()*q.hw(),
q.hw()*p.hw() );
}
Vector_3
operator()( const Origin& , const Point_3& q) const
{
return Vector_3( q.hx() ,
q.hy() ,
q.hz() ,
q.hw() );
}
Vector_3
operator()( const Point_3& p, const Origin& q) const
{
return Vector_3( - p.hx(),
- p.hy(),
- p.hz(),
p.hw() );
}
Vector_3
operator()( const Segment_3& s) const
{ return this->operator()(s.start(), s.end()); }
Vector_3
operator()( const Ray_3& r) const
{ return r.to_vector(); }
Vector_3
operator()( const Line_3& l) const
{ return l.to_vector(); }
Vector_3
operator()( const Null_vector&) const
{ return Vector_3(RT(0), RT(0), RT(0), RT(1)); }
// #ifndef CGAL_NO_DEPRECATED_CODE
Vector_3
operator()( const RT& x, const RT& y, const RT& z) const
{ return Vector_3(x, y, z); }
Vector_3
operator()( const RT& x, const RT& y, const RT& z, const RT& w) const
{ return Vector_3(x, y, z, w); }
// #endif // CGAL_NO_DEPRECATED_CODE
};
template <typename K>
class Coplanar_orientation_3
{
typedef typename K::Point_3 Point_3;
#ifdef CGAL_kernel_exactness_preconditions
typedef typename K::Coplanar_3 Coplanar_3;
typedef typename K::Collinear_3 Collinear_3;
Coplanar_3 cp;
Collinear_3 cl;
#endif // CGAL_kernel_exactness_preconditions
public:
typedef Orientation result_type;
typedef Arity_tag< 4 > Arity;
#ifdef CGAL_kernel_exactness_preconditions
Coplanar_orientation_3() {}
Coplanar_orientation_3(const Coplanar_3& cp_, const Collinear_3& cl_)
: cp(cp_), cl(cl_)
{}
#endif // CGAL_kernel_exactness_preconditions
Orientation
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
Orientation oxy_pqr = orientationH2(p.hx(), p.hy(), p.hw(),
q.hx(), q.hy(), q.hw(),
r.hx(), r.hy(), r.hw());
if (oxy_pqr != COLLINEAR)
return oxy_pqr;
Orientation oyz_pqr = orientationH2(p.hy(), p.hz(), p.hw(),
q.hy(), q.hz(), q.hw(),
r.hy(), r.hz(), r.hw());
if (oyz_pqr != COLLINEAR)
return oyz_pqr;
return orientationH2(p.hx(), p.hz(), p.hw(),
q.hx(), q.hz(), q.hw(),
r.hx(), r.hz(), r.hw());
}
Orientation
operator()( const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& s) const
{
// p,q,r,s supposed to be coplanar
// p,q,r supposed to be non collinear
// tests whether s is on the same side of p,q as r
// returns :
// COLLINEAR if pqr collinear
// POSITIVE if qrp and qrs have the same orientation
// NEGATIVE if qrp and qrs have opposite orientations
CGAL_kernel_exactness_precondition( ! cl(p, q, r) );
CGAL_kernel_exactness_precondition( cp(p, q, r, s) );
// compute orientation of p,q,s in this plane P:
Orientation save;
if ( (save = orientationH2( p.hy(), p.hz(), p.hw(),
q.hy(), q.hz(), q.hw(),
r.hy(), r.hz(), r.hw())) != COLLINEAR)
{ return
static_cast<Orientation>(
static_cast<int>( save)
* static_cast<int>( orientationH2( p.hy(), p.hz(), p.hw(),
q.hy(), q.hz(), q.hw(),
s.hy(), s.hz(), s.hw())) );
}
if ( (save = orientationH2( p.hx(), p.hz(), p.hw(),
q.hx(), q.hz(), q.hw(),
r.hx(), r.hz(), r.hw())) != COLLINEAR)
{ return
static_cast<Orientation>(
static_cast<int>( save)
* static_cast<int>( orientationH2( p.hx(), p.hz(), p.hw(),
q.hx(), q.hz(), q.hw(),
s.hx(), s.hz(), s.hw())) );
}
if ( (save = orientationH2( p.hx(), p.hy(), p.hw(),
q.hx(), q.hy(), q.hw(),
r.hx(), r.hy(), r.hw())) != COLLINEAR)
{ return
static_cast<Orientation>(
static_cast<int>( save)
* static_cast<int>( orientationH2( p.hx(), p.hy(), p.hw(),
q.hx(), q.hy(), q.hw(),
s.hx(), s.hy(), s.hw())) );
}
CGAL_kernel_assertion( false);
return COLLINEAR;
}
};
template <typename K>
class Coplanar_side_of_bounded_circle_3
{
typedef typename K::Point_3 Point_3;
#ifdef CGAL_kernel_exactness_preconditions
typedef typename K::Coplanar_3 Coplanar_3;
typedef typename K::Collinear_3 Collinear_3;
Coplanar_3 cp;
Collinear_3 cl;
#endif // CGAL_kernel_exactness_preconditions
public:
typedef Bounded_side result_type;
typedef Arity_tag< 4 > Arity;
#ifdef CGAL_kernel_exactness_preconditions
Coplanar_side_of_bounded_circle_3() {}
Coplanar_side_of_bounded_circle_3(const Coplanar_3& cp_,
const Collinear_3& cl_)
: cp(cp_), cl(cl_)
{}
#endif // CGAL_kernel_exactness_preconditions
Bounded_side
operator()( const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& t) const
{
// p,q,r,t are supposed to be coplanar.
// p,q,r determine an orientation of this plane (not collinear).
// returns the equivalent of side_of_bounded_circle(p,q,r,t)
// in this plane
CGAL_kernel_exactness_precondition( cp(p,q,r,t) );
CGAL_kernel_exactness_precondition( !cl(p,q,r) );
return (Bounded_side)
side_of_oriented_sphere(p, q, r, t+cross_product(q-p, r-p), t);
} // FIXME
};
template <typename K>
class Equal_xy_3
{
typedef typename K::Point_3 Point_3;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Point_3& p, const Point_3& q) const
{
return (p.hx() * q.hw() == q.hx() * p.hw() )
&& (p.hy() * q.hw() == q.hy() * p.hw() );
}
};
template <typename K>
class Equal_x_2
{
typedef typename K::Point_2 Point_2;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Point_2& p, const Point_2& q) const
{ return p.hx()*q.hw() == q.hx()*p.hw(); }
};
template <typename K>
class Equal_x_3
{
typedef typename K::Point_3 Point_3;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Point_3& p, const Point_3& q) const
{ return p.hx()*q.hw() == q.hx()*p.hw(); }
};
template <typename K>
class Equal_y_2
{
typedef typename K::Point_2 Point_2;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Point_2& p, const Point_2& q) const
{ return p.hy()*q.hw() == q.hy()*p.hw(); }
};
template <typename K>
class Equal_y_3
{
typedef typename K::Point_3 Point_3;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Point_3& p, const Point_3& q) const
{ return p.hy()*q.hw() == q.hy()*p.hw(); }
};
template <typename K>
class Equal_z_3
{
typedef typename K::Point_3 Point_3;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Point_3& p, const Point_3& q) const
{ return p.hz()*q.hw() == q.hz()*p.hw(); }
};
template <typename K>
class Has_on_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Line_3 Line_3;
typedef typename K::Ray_3 Ray_3;
typedef typename K::Segment_3 Segment_3;
typedef typename K::Plane_3 Plane_3;
typedef typename K::Triangle_3 Triangle_3;
typedef typename K::Tetrahedron_3 Tetrahedron_3;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Line_3& l, const Point_3& p) const
{ return l.has_on(p); }
bool
operator()( const Ray_3& r, const Point_3& p) const
{ return r.has_on(p); }
bool
operator()( const Segment_3& s, const Point_3& p) const
{ return s.has_on(p); }
bool
operator()( const Plane_3& pl, const Point_3& p) const
{ return pl.has_on(p); }
bool
operator()( const Triangle_3& t, const Point_3& p) const
{
if (!t.is_degenerate() )
{
Plane_3 sup_pl = t.supporting_plane();
if ( !sup_pl.has_on(p) )
{
return false;
}
Tetrahedron_3 tetrapak( t.vertex(0),
t.vertex(1),
t.vertex(2),
t.vertex(0) + sup_pl.orthogonal_vector());
return tetrapak.has_on_boundary(p);
}
Point_3 minp( t.vertex(0) );
Point_3 maxp( t.vertex(1) );
if (lexicographically_xyz_smaller(t.vertex(1),t.vertex(0)) )
{
minp = t.vertex(1);
maxp = t.vertex(0);
}
if (lexicographically_xyz_smaller(t.vertex(2),minp ) )
{
minp = t.vertex(2);
}
if (lexicographically_xyz_smaller(maxp, t.vertex(2)) )
{
maxp = t.vertex(2);
}
if (minp == maxp)
{
return (p == maxp);
}
Segment_3 s(minp,maxp);
return s.has_on(p);
}
};
template <typename K>
class Less_distance_to_point_2
{
typedef typename K::Point_2 Point_2;
public:
typedef bool result_type;
typedef Arity_tag< 3 > Arity;
bool
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
typedef typename K::RT RT;
const RT phx = p.hx();
const RT phy = p.hy();
const RT phw = p.hw();
const RT qhx = q.hx();
const RT qhy = q.hy();
const RT qhw = q.hw();
const RT rhx = r.hx();
const RT rhy = r.hy();
const RT rhw = r.hw();
const RT RT0 = RT(0);
const RT RT2 = RT(2);
RT dosd = // difference of squared distances
// phx * phx * qhw * qhw * rhw * rhw
// -RT(2) * phx * qhx * phw * qhw * rhw * rhw
// + qhx * qhx * phw * phw * rhw * rhw
//
// + phy * phy * qhw * qhw * rhw * rhw
// -RT(2) * phy * qhy * phw * qhw * rhw * rhw
// + qhy * qhy * phw * phw * rhw * rhw
//
// - ( phx * phx * qhw * qhw * rhw * rhw
// -RT(2) * phx * rhx * phw * qhw * qhw * rhw
// + rhx * rhx * phw * phw * qhw * qhw
//
// + phy * phy * qhw * qhw * rhw * rhw
// -RT(2) * phy * rhy * phw * qhw * qhw * rhw
// + rhy * rhy * phw * phw * qhw * qhw
rhw*rhw * ( phw * ( qhx*qhx + qhy*qhy )
- RT2 * qhw * ( phx*qhx + phy*qhy )
)
- qhw*qhw * ( phw * ( rhx*rhx + rhy*rhy )
- RT2 * rhw * ( phx*rhx + phy*rhy )
);
return ( dosd < RT0 );
}
};
template <typename K>
class Less_distance_to_point_3
{
typedef typename K::Point_3 Point_3;
public:
typedef bool result_type;
typedef Arity_tag< 3 > Arity;
bool
operator()(const Point_3& p, const Point_3& q, const Point_3& r) const
{
typedef typename K::RT RT;
const RT phx = p.hx();
const RT phy = p.hy();
const RT phz = p.hz();
const RT phw = p.hw();
const RT qhx = q.hx();
const RT qhy = q.hy();
const RT qhz = q.hz();
const RT qhw = q.hw();
const RT rhx = r.hx();
const RT rhy = r.hy();
const RT rhz = r.hz();
const RT rhw = r.hw();
const RT RT0 = RT(0);
const RT RT2 = RT(2);
RT dosd = // difference of squared distances
rhw*rhw * ( phw * ( qhx*qhx + qhy*qhy + qhz*qhz )
- RT2 * qhw * ( phx*qhx + phy*qhy + phz*qhz )
)
- qhw*qhw * ( phw * ( rhx*rhx + rhy*rhy + rhz*rhz )
- RT2 * rhw * ( phx*rhx + phy*rhy + phz*rhz )
);
return ( dosd < RT0 );
}
};
template <typename K>
class Less_signed_distance_to_line_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Line_2 Line_2;
public:
typedef bool result_type;
typedef Arity_tag< 4 > Arity;
bool
operator()(const Point_2& p, const Point_2& q,
const Point_2& r, const Point_2& s) const
{
typedef typename K::RT RT;
const RT phx= p.hx();
const RT phy= p.hy();
const RT phw= p.hw();
const RT qhx= q.hx();
const RT qhy= q.hy();
const RT qhw= q.hw();
const RT rhx= r.hx();
const RT rhy= r.hy();
const RT rhw= r.hw();
const RT shx= s.hx();
const RT shy= s.hy();
const RT shw= s.hw();
const RT RT0 = RT(0);
RT scaled_dist_r_minus_scaled_dist_s =
( rhx*shw - shx*rhw ) * (phy*qhw - qhy*phw)
- ( rhy*shw - shy*rhw ) * (phx*qhw - qhx*phw);
return ( scaled_dist_r_minus_scaled_dist_s < RT0 );
}
bool
operator()(const Line_2& l, const Point_2& p,
const Point_2& q) const
{
typedef typename K::RT RT;
const RT la = l.a();
const RT lb = l.b();
const RT phx= p.hx();
const RT phy= p.hy();
const RT phw= p.hw();
const RT qhx= q.hx();
const RT qhy= q.hy();
const RT qhw= q.hw();
const RT RT0 = RT(0);
RT scaled_dist_p_minus_scaled_dist_q =
la*( phx*qhw - qhx*phw )
+ lb*( phy*qhw - qhy*phw );
return ( scaled_dist_p_minus_scaled_dist_q < RT0 );
}
};
template <typename K>
class Less_signed_distance_to_plane_3
{
typedef typename K::RT RT;
typedef typename K::Point_3 Point_3;
typedef typename K::Plane_3 Plane_3;
typedef typename K::Construct_plane_3 Construct_plane_3;
public:
typedef bool result_type;
typedef Arity_tag< 3 > Arity;
bool
operator()( const Plane_3& pl, const Point_3& p, const Point_3& q) const
{
const RT pla = pl.a();
const RT plb = pl.b();
const RT plc = pl.c();
const RT phx = p.hx();
const RT phy = p.hy();
const RT phz = p.hz();
const RT phw = p.hw();
const RT qhx = q.hx();
const RT qhy = q.hy();
const RT qhz = q.hz();
const RT qhw = q.hw();
const RT RT0 = RT(0);
RT scaled_dist_p_minus_scaled_dist_q =
pla*( phx*qhw - qhx*phw )
+ plb*( phy*qhw - qhy*phw )
+ plc*( phz*qhw - qhz*phw );
return ( scaled_dist_p_minus_scaled_dist_q < RT0 );
}
bool
operator()(const Point_3& plp, const Point_3& plq,const Point_3& plr,
const Point_3& p, const Point_3& q) const
{
Construct_plane_3 construct_plane_3;
return operator()(construct_plane_3(plp, plq, plr), p, q);
}
};
template <typename K>
class Less_xyz_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Compare_xyz_3 Compare_xyz_3;
Compare_xyz_3 c;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
Less_xyz_3() {}
Less_xyz_3(const Compare_xyz_3& c_) : c(c_) {}
bool
operator()( const Point_3& p, const Point_3& q) const
{ return c(p, q) == SMALLER; }
};
template <typename K>
class Less_xy_2
{
typedef typename K::Point_2 Point_2;
typedef typename K::Compare_xy_2 Compare_xy_2;
Compare_xy_2 c;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
Less_xy_2() {}
Less_xy_2(const Compare_xy_2& c_) : c(c_) {}
bool
operator()( const Point_2& p, const Point_2& q) const
{ return c(p, q) == SMALLER; }
};
template <typename K>
class Less_xy_3
{
typedef typename K::Point_3 Point_3;
typedef typename K::Compare_xy_3 Compare_xy_3;
Compare_xy_3 c;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
Less_xy_3() {}
Less_xy_3(const Compare_xy_3& c_) : c(c_) {}
bool
operator()( const Point_3& p, const Point_3& q) const
{ return c(p, q) == SMALLER; }
};
template <typename K>
class Less_x_2
{
typedef typename K::Point_2 Point_2;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Point_2& p, const Point_2& q) const
{ return ( p.hx()*q.hw() < q.hx()*p.hw() ); }
};
template <typename K>
class Less_x_3
{
typedef typename K::Point_3 Point_3;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Point_3& p, const Point_3& q) const
{ return ( p.hx()*q.hw() < q.hx()*p.hw() ); }
};
template <typename K>
class Less_yx_2
{
typedef typename K::Point_2 Point_2;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Point_2& p, const Point_2& q) const
{
typedef typename K::RT RT;
const RT& phx = p.hx();
const RT& phy = p.hy();
const RT& phw = p.hw();
const RT& qhx = q.hx();
const RT& qhy = q.hy();
const RT& qhw = q.hw();
RT pV = phy * qhw;
RT qV = qhy * phw;
if ( qV < pV )
{
return false;
}
else if ( pV < qV )
{
return true;
}
pV = phx * qhw;
qV = qhx * phw;
return ( pV < qV );
}
};
template <typename K>
class Less_y_2
{
typedef typename K::Point_2 Point_2;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Point_2& p, const Point_2& q) const
{ return ( p.hy()*q.hw() < q.hy()*p.hw() ); }
};
template <typename K>
class Less_y_3
{
typedef typename K::Point_3 Point_3;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Point_3& p, const Point_3& q) const
{ return ( p.hy()*q.hw() < q.hy()*p.hw() ); }
};
template <typename K>
class Less_z_3
{
typedef typename K::Point_3 Point_3;
public:
typedef bool result_type;
typedef Arity_tag< 2 > Arity;
bool
operator()( const Point_3& p, const Point_3& q) const
{ return (p.hz() * q.hw() < q.hz() * p.hw() ); }
};
template <typename K>
class Orientation_2
{
typedef typename K::Point_2 Point_2;
public:
typedef Orientation result_type;
typedef Arity_tag< 3 > Arity;
Orientation
operator()(const Point_2& p, const Point_2& q, const Point_2& r) const
{
typedef typename K::RT RT;
const RT& phx = p.hx();
const RT& phy = p.hy();
const RT& phw = p.hw();
const RT& qhx = q.hx();
const RT& qhy = q.hy();
const RT& qhw = q.hw();
const RT& rhx = r.hx();
const RT& rhy = r.hy();
const RT& rhw = r.hw();
// | A B |
// | C D |
RT A = phx*rhw - phw*rhx;
RT B = phy*rhw - phw*rhy;
RT C = qhx*rhw - qhw*rhx;
RT D = qhy*rhw - qhw*rhy;
return static_cast<Orientation>((int) CGAL_NTS compare(A*D, B*C));
}
};
template <typename K>
class Orientation_3
{
typedef typename K::Point_3 Point_3;
public:
typedef Orientation result_type;
typedef Arity_tag< 4 > Arity;
Orientation
operator()( const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& s) const
{
// Two rows are switched, because of the homogeneous column.
return (Orientation)
sign_of_determinant4x4( p.hx(), p.hy(), p.hz(), p.hw(),
r.hx(), r.hy(), r.hz(), r.hw(),
q.hx(), q.hy(), q.hz(), q.hw(),
s.hx(), s.hy(), s.hz(), s.hw());
}
};
template <typename K>
class Side_of_bounded_circle_2
{
typedef typename K::Point_2 Point_2;
public:
typedef Bounded_side result_type;
typedef Arity_tag< 4 > Arity;
Bounded_side
operator()( const Point_2& p, const Point_2& q, const Point_2& t) const
{
typedef typename K::RT RT;
const RT& phx = p.hx();
const RT& phy = p.hy();
const RT& phw = p.hw();
const RT& qhx = q.hx();
const RT& qhy = q.hy();
const RT& qhw = q.hw();
const RT& thx = t.hx();
const RT& thy = t.hy();
const RT& thw = t.hw();
return Bounded_side(
CGAL_NTS compare((thx*phw-phx*thw)*(qhx*thw-thx*qhw),
(thy*phw-phy*thw)*(thy*qhw-qhy*thw)) );
}
Bounded_side
operator()( const Point_2& q, const Point_2& r,
const Point_2& s, const Point_2& t) const
{
typedef typename K::RT RT;
const RT& qhx = q.hx();
const RT& qhy = q.hy();
const RT& qhw = q.hw();
const RT& rhx = r.hx();
const RT& rhy = r.hy();
const RT& rhw = r.hw();
const RT& shx = s.hx();
const RT& shy = s.hy();
const RT& shw = s.hw();
const RT& thx = t.hx();
const RT& thy = t.hy();
const RT& thw = t.hw();
const RT RT0 = RT(0);
CGAL_kernel_precondition( ! collinear(q,r,s) );
// compute sign of |qx qy qx^2+qy^2 1 | | a b c d |
// | -- r -- | = | e f g h |
// determinant | -- s -- | = | i j k l |
// | -- t -- | | m n o p |
// where
RT a = qhx*qhw;
RT b = qhy*qhw;
RT c = qhx*qhx + qhy*qhy;
RT d = qhw*qhw;
RT e = rhx*rhw;
RT f = rhy*rhw;
RT g = rhx*rhx + rhy*rhy;
RT h = rhw*rhw;
RT i = shx*shw;
RT j = shy*shw;
RT k = shx*shx + shy*shy;
RT l = shw*shw;
RT m = thx*thw;
RT n = thy*thw;
RT o = thx*thx + thy*thy;
RT p = thw*thw;
RT det = a * ( f*(k*p - l*o) + j*(h*o - g*p) + n*(g*l - h*k) )
- e * ( b*(k*p - l*o) + j*(d*o - c*p) + n*(c*l - d*k) )
+ i * ( b*(g*p - h*o) + f*(d*o - c*p) + n*(c*h - d*g) )
- m * ( b*(g*l - h*k) + f*(d*k - c*l) + j*(c*h - d*g) );
if ( det == RT0 )
return ON_BOUNDARY;
else
{
if (orientation(q,r,s) == CLOCKWISE)
det = -det;
return (RT0 < det ) ? ON_BOUNDED_SIDE : ON_UNBOUNDED_SIDE;
}
}
};
template <typename K>
class Side_of_bounded_sphere_3
{
typedef typename K::Point_3 Point_3;
public:
typedef Bounded_side result_type;
typedef Arity_tag< 5 > Arity;
Bounded_side
operator()( const Point_3& p, const Point_3& q, const Point_3& t) const
{
typedef typename K::RT RT;
const RT& phx = p.hx();
const RT& phy = p.hy();
const RT& phz = p.hz();
const RT& phw = p.hw();
const RT& qhx = q.hx();
const RT& qhy = q.hy();
const RT& qhz = q.hz();
const RT& qhw = q.hw();
const RT& thx = t.hx();
const RT& thy = t.hy();
const RT& thz = t.hz();
const RT& thw = t.hw();
return Bounded_side(
CGAL_NTS sign<RT>((thx*phw-phx*thw)*(qhx*thw-thx*qhw)
+ (thy*phw-phy*thw)*(qhy*thw-thy*qhw)
+ (thz*phw-phz*thw)*(qhz*thw-thz*qhw)));
}
Bounded_side
operator()( const Point_3& p, const Point_3& q,
const Point_3& r, const Point_3& t) const
{
Point_3 center = circumcenter(p, q, r);
return Bounded_side( compare_distance_to_point(center, p, t) );
} // FIXME
Bounded_side
operator()( const Point_3& p, const Point_3& q, const Point_3& r,
const Point_3& s, const Point_3& test) const
{
Oriented_side oside = side_of_oriented_sphere(p,q,r,s,test);
if ( are_positive_oriented( p,q,r,s) )
{
switch (oside)
{
case ON_POSITIVE_SIDE : return ON_BOUNDED_SIDE;
case ON_ORIENTED_BOUNDARY: return ON_BOUNDARY;
case ON_NEGATIVE_SIDE : return ON_UNBOUNDED_SIDE;
}
}
else
{
switch (oside)
{
case ON_POSITIVE_SIDE : return ON_UNBOUNDED_SIDE;
case ON_ORIENTED_BOUNDARY: return ON_BOUNDARY;
case ON_NEGATIVE_SIDE : return ON_BOUNDED_SIDE;
}
}
return ON_BOUNDARY; // Pls, no warnings anylonger
} // FIXME
};
template <typename K>
class Side_of_oriented_circle_2
{
typedef typename K::Point_2 Point_2;
public:
typedef Oriented_side result_type;
typedef Arity_tag< 4 > Arity;
Oriented_side
operator()( const Point_2& q, const Point_2& r,
const Point_2& s, const Point_2& t) const
{
typedef typename K::RT RT;
const RT& qhx = q.hx();
const RT& qhy = q.hy();
const RT& qhw = q.hw();
const RT& rhx = r.hx();
const RT& rhy = r.hy();
const RT& rhw = r.hw();
const RT& shx = s.hx();
const RT& shy = s.hy();
const RT& shw = s.hw();
const RT& thx = t.hx();
const RT& thy = t.hy();
const RT& thw = t.hw();
CGAL_kernel_precondition( ! collinear(q,r,s) );
// compute sign of |qx qy qx^2+qy^2 1 | | a b c d |
// | -- r -- | = | e f g h |
// determinant | -- s -- | = | i j k l |
// | -- t -- | | m n o p |
// where
RT a = qhx*qhw;
RT b = qhy*qhw;
RT c = qhx*qhx + qhy*qhy;
RT d = qhw*qhw;
RT e = rhx*rhw;
RT f = rhy*rhw;
RT g = rhx*rhx + rhy*rhy;
RT h = rhw*rhw;
RT i = shx*shw;
RT j = shy*shw;
RT k = shx*shx + shy*shy;
RT l = shw*shw;
RT m = thx*thw;
RT n = thy*thw;
RT o = thx*thx + thy*thy;
RT p = thw*thw;
RT det = a * ( f*(k*p - l*o) + j*(h*o - g*p) + n*(g*l - h*k) )
- e * ( b*(k*p - l*o) + j*(d*o - c*p) + n*(c*l - d*k) )
+ i * ( b*(g*p - h*o) + f*(d*o - c*p) + n*(c*h - d*g) )
- m * ( b*(g*l - h*k) + f*(d*k - c*l) + j*(c*h - d*g) );
return static_cast<Oriented_side>((int) CGAL_NTS sign(det));
}
};
template <typename K>
class Side_of_oriented_sphere_3
{
typedef typename K::Point_3 Point_3;
public:
typedef Oriented_side result_type;
typedef Arity_tag< 5 > Arity;
Oriented_side
operator()( const Point_3& p, const Point_3& q, const Point_3& r,
const Point_3& s, const Point_3& t) const
{
typedef typename K::RT RT;
CGAL_kernel_precondition( !coplanar(p,q,r,s) );
const RT phx = p.hx();
const RT phy = p.hy();
const RT phz = p.hz();
const RT phw = p.hw();
const RT phw2 = phw*phw;
const RT qhx = q.hx();
const RT qhy = q.hy();
const RT qhz = q.hz();
const RT qhw = q.hw();
const RT qhw2 = qhw*qhw;
const RT rhx = r.hx();
const RT rhy = r.hy();
const RT rhz = r.hz();
const RT rhw = r.hw();
const RT rhw2 = rhw*rhw;
const RT shx = s.hx();
const RT shy = s.hy();
const RT shz = s.hz();
const RT shw = s.hw();
const RT shw2 = shw*shw;
const RT thx = t.hx();
const RT thy = t.hy();
const RT thz = t.hz();
const RT thw = t.hw();
const RT thw2 = thw*thw;
const RT det = det5x5_by_formula<RT>(
phx*phw, phy*phw, phz*phw, phx*phx + phy*phy + phz*phz, phw2,
qhx*qhw, qhy*qhw, qhz*qhw, qhx*qhx + qhy*qhy + qhz*qhz, qhw2,
rhx*rhw, rhy*rhw, rhz*rhw, rhx*rhx + rhy*rhy + rhz*rhz, rhw2,
shx*shw, shy*shw, shz*shw, shx*shx + shy*shy + shz*shz, shw2,
thx*thw, thy*thw, thz*thw, thx*thx + thy*thy + thz*thz, thw2);
if (det < RT(0))
{
return ON_POSITIVE_SIDE;
}
else
{
return (RT(0) < det) ? ON_NEGATIVE_SIDE : ON_ORIENTED_BOUNDARY;
}
}
};
} // namespace HomogeneousKernelFunctors
CGAL_END_NAMESPACE
#endif // CGAL_HOMOGENEOUS_FUNCTION_OBJECTS_H
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