// Copyright (c) 1999 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/H3/include/CGAL/Homogeneous/PlaneH3.h,v $
// $Revision: 1.14 $ $Date: 2004/02/19 20:26:40 $
// $Name: $
//
// Author(s) : Stefan Schirra
#ifndef CGAL_PLANEH3_H
#define CGAL_PLANEH3_H
#include <CGAL/Fourtuple.h>
CGAL_BEGIN_NAMESPACE
template < class R_ >
class PlaneH3
{
typedef typename R_::RT RT;
typedef typename R_::FT FT;
typedef typename R_::Point_2 Point_2;
typedef typename R_::Point_3 Point_3;
typedef typename R_::Vector_3 Vector_3;
typedef typename R_::Line_3 Line_3;
typedef typename R_::Segment_3 Segment_3;
typedef typename R_::Ray_3 Ray_3;
typedef typename R_::Direction_3 Direction_3;
typedef typename R_::Plane_3 Plane_3;
typedef typename R_::Aff_transformation_3 Aff_transformation_3;
typedef Fourtuple<RT> Rep;
typedef typename R_::template Handle<Rep>::type Base;
Base base;
public:
typedef R_ R;
PlaneH3() {}
PlaneH3(const Point_3&, const Point_3&, const Point_3& );
PlaneH3(const RT& a, const RT& b,
const RT& c, const RT& d );
PlaneH3(const Point_3&, const Ray_3& );
PlaneH3(const Point_3&, const Line_3& );
PlaneH3(const Point_3&, const Segment_3& );
PlaneH3(const Line_3&, const Point_3& );
PlaneH3(const Segment_3&, const Point_3& );
PlaneH3(const Ray_3&, const Point_3& );
PlaneH3(const Point_3&, const Direction_3& );
PlaneH3(const Point_3&, const Vector_3& );
PlaneH3(const Point_3&, const Direction_3&, const Direction_3& );
const RT & a() const;
const RT & b() const;
const RT & c() const;
const RT & d() const;
bool operator==( const PlaneH3<R>& ) const;
bool operator!=( const PlaneH3<R>& ) const;
Line_3 perpendicular_line(const Point_3& ) const;
Plane_3 opposite() const; // plane with opposite orientation
Point_3 projection(const Point_3& ) const;
Point_3 point() const; // same point on the plane
Direction_3
orthogonal_direction() const;
Vector_3
orthogonal_vector() const;
Oriented_side oriented_side(const Point_3 &p) const;
bool has_on(const Point_3 &p) const;
bool has_on(const Line_3 &p) const;
bool has_on_positive_side(const Point_3&l) const;
bool has_on_negative_side(const Point_3&l) const;
bool is_degenerate() const;
Plane_3 transform(const Aff_transformation_3& ) const;
Aff_transformation_3 transform_to_2d() const;
Point_2 to_2d(const Point_3& ) const;
Point_3 to_3d(const Point_2& ) const;
Vector_3 base1() const;
Vector_3 base2() const;
protected:
Point_3 point1() const; // same point different from point()
Point_3 point2() const; // same point different from point()
// and point1()
void new_rep(const Point_3 &p,
const Point_3 &q,
const Point_3 &r);
void new_rep(const RT &a, const RT &b,
const RT &c, const RT &d);
};
//
// a() * X + b() * Y + c() * Z() + d() * W() == 0
//
// | X Y Z W |
// | p.hx() p.hy() p.hz() p.hw() |
// | q.hx() q.hy() q.hz() q.hw() |
// | r.hx() r.hy() r.hz() r.hw() |
//
// Fourtuple<RT> ( a(), b(), c(), d() )
template < class R >
inline
void
PlaneH3<R>::new_rep(const typename PlaneH3<R>::Point_3 &p,
const typename PlaneH3<R>::Point_3 &q,
const typename PlaneH3<R>::Point_3 &r)
{
RT phx = p.hx();
RT phy = p.hy();
RT phz = p.hz();
RT phw = p.hw();
RT qhx = q.hx();
RT qhy = q.hy();
RT qhz = q.hz();
RT qhw = q.hw();
RT rhx = r.hx();
RT rhy = r.hy();
RT rhz = r.hz();
RT rhw = r.hw();
base = Rep (
phy*( qhz*rhw - qhw*rhz )
- qhy*( phz*rhw - phw*rhz ) // * X
+ rhy*( phz*qhw - phw*qhz ),
- phx*( qhz*rhw - qhw*rhz )
+ qhx*( phz*rhw - phw*rhz ) // * Y
- rhx*( phz*qhw - phw*qhz ),
phx*( qhy*rhw - qhw*rhy )
- qhx*( phy*rhw - phw*rhy ) // * Z
+ rhx*( phy*qhw - phw*qhy ),
- phx*( qhy*rhz - qhz*rhy )
+ qhx*( phy*rhz - phz*rhy ) // * W
- rhx*( phy*qhz - phz*qhy ) );
}
template < class R >
inline
void
PlaneH3<R>::new_rep(const RT &a, const RT &b, const RT &c, const RT &d)
{ base = Rep(a, b, c, d); }
template < class R >
inline
bool
PlaneH3<R>::operator!=(const PlaneH3<R>& l) const
{
return !(*this == l);
}
template < class R >
CGAL_KERNEL_INLINE
PlaneH3<R>::PlaneH3(const typename PlaneH3<R>::Point_3& p,
const typename PlaneH3<R>::Point_3& q,
const typename PlaneH3<R>::Point_3& r)
{ new_rep(p,q,r); }
template < class R >
CGAL_KERNEL_INLINE
PlaneH3<R>::PlaneH3(const RT& a, const RT& b,
const RT& c, const RT& d)
{ new_rep(a,b,c,d); }
template < class R >
CGAL_KERNEL_INLINE
PlaneH3<R>::PlaneH3(const typename PlaneH3<R>::Point_3& p ,
const typename PlaneH3<R>::Line_3& l)
{ new_rep(p, l.point(0), l.point(1) ); }
template < class R >
CGAL_KERNEL_INLINE
PlaneH3<R>::PlaneH3(const typename PlaneH3<R>::Point_3& p,
const typename PlaneH3<R>::Segment_3& s)
{ new_rep(p, s.source(), s.target() ); }
template < class R >
CGAL_KERNEL_INLINE
PlaneH3<R>::PlaneH3(const typename PlaneH3<R>::Point_3& p ,
const typename PlaneH3<R>::Ray_3& r)
{ new_rep(p, r.start(), r.start() + r.direction().to_vector() ); }
template < class R >
CGAL_KERNEL_INLINE
PlaneH3<R>::PlaneH3(const typename PlaneH3<R>::Line_3& l ,
const typename PlaneH3<R>::Point_3& p)
{ new_rep(l.point(0), p, l.point(1) ); }
template < class R >
CGAL_KERNEL_INLINE
PlaneH3<R>::PlaneH3(const typename PlaneH3<R>::Segment_3& s,
const typename PlaneH3<R>::Point_3& p)
{ new_rep(s.source(), p, s.target() ); }
template < class R >
CGAL_KERNEL_INLINE
PlaneH3<R>::PlaneH3(const typename PlaneH3<R>::Ray_3& r,
const typename PlaneH3<R>::Point_3& p)
{ new_rep(r.start(), p, r.start() + r.direction().to_vector() ); }
template < class R >
CGAL_KERNEL_INLINE
PlaneH3<R>::PlaneH3(const typename PlaneH3<R>::Point_3& p,
const typename PlaneH3<R>::Direction_3& d)
{
Vector_3 ov = d.to_vector();
new_rep( ov.hx()*p.hw(),
ov.hy()*p.hw(),
ov.hz()*p.hw(),
-(ov.hx()*p.hx() + ov.hy()*p.hy() + ov.hz()*p.hz() ) );
}
template < class R >
CGAL_KERNEL_INLINE
PlaneH3<R>::PlaneH3(const typename PlaneH3<R>::Point_3& p,
const typename PlaneH3<R>::Vector_3& ov)
{
new_rep( ov.hx()*p.hw(),
ov.hy()*p.hw(),
ov.hz()*p.hw(),
-(ov.hx()*p.hx() + ov.hy()*p.hy() + ov.hz()*p.hz() ) );
}
template < class R >
CGAL_KERNEL_INLINE
PlaneH3<R>::PlaneH3(const typename PlaneH3<R>::Point_3& p,
const typename PlaneH3<R>::Direction_3& d1,
const typename PlaneH3<R>::Direction_3& d2)
{ new_rep( p, p + d1.to_vector(), p + d2.to_vector() ); }
template < class R >
inline
const typename PlaneH3<R>::RT &
PlaneH3<R>::a() const
{ return get(base).e0; }
template < class R >
inline
const typename PlaneH3<R>::RT &
PlaneH3<R>::b() const
{ return get(base).e1; }
template < class R >
inline
const typename PlaneH3<R>::RT &
PlaneH3<R>::c() const
{ return get(base).e2; }
template < class R >
inline
const typename PlaneH3<R>::RT &
PlaneH3<R>::d() const
{ return get(base).e3; }
template < class R >
CGAL_KERNEL_INLINE
typename PlaneH3<R>::Line_3
PlaneH3<R>::perpendicular_line(const typename PlaneH3<R>::Point_3& p) const
{ return Line_3( p, orthogonal_direction() ); }
template < class R >
CGAL_KERNEL_INLINE
typename PlaneH3<R>::Plane_3
PlaneH3<R>::opposite() const
{ return PlaneH3<R>(-a(), -b(), -c(), -d() ); }
template < class R >
CGAL_KERNEL_INLINE
typename PlaneH3<R>::Point_3
PlaneH3<R>::projection(const typename PlaneH3<R>::Point_3& p) const
{ return _projection( p, *this ); }
template < class R >
CGAL_KERNEL_INLINE
typename PlaneH3<R>::Point_3
PlaneH3<R>::point() const
{
const RT RT0(0);
if ( a() != RT0 )
{
return Point_3( -d(), RT0, RT0, a() );
}
if ( b() != RT0 )
{
return Point_3( RT0, -d(), RT0, b() );
}
CGAL_kernel_assertion ( c() != RT0);
return Point_3( RT0, RT0, -d(), c() );
}
template < class R >
CGAL_KERNEL_INLINE
typename PlaneH3<R>::Vector_3
PlaneH3<R>::base1() const
{
// 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 ( a() != RT0 )
{
return Vector_3( -b(), a(), RT0, a() );
}
if ( b() != RT0 )
{
return Vector_3( RT0, -c(), b(), b() );
}
CGAL_kernel_assertion ( c() != RT(0) );
return Vector_3( c(), RT0, -a(), c() );
}
template < class R >
inline
typename PlaneH3<R>::Vector_3
PlaneH3<R>::base2() const
{
Vector_3 a = orthogonal_vector();
Vector_3 b = base1();
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() );
}
// Actually, the following should work, but bcc doesn't like it:
// { return cross_product( orthogonal_vector(), base1() ); }
template < class R >
inline
typename PlaneH3<R>::Point_3
PlaneH3<R>::point1() const
{ return point() + base1(); }
template < class R >
inline
typename PlaneH3<R>::Point_3
PlaneH3<R>::point2() const
{ return point() + base2(); }
template < class R >
inline
typename PlaneH3<R>::Direction_3
PlaneH3<R>::orthogonal_direction() const
{ return Direction_3(a(), b(), c() ); }
template < class R >
inline
typename PlaneH3<R>::Vector_3
PlaneH3<R>::orthogonal_vector() const
{ return Vector_3(a(), b(), c() ); }
template < class R >
typename PlaneH3<R>::Plane_3
PlaneH3<R>::transform(const typename PlaneH3<R>::Aff_transformation_3& t) const
{
return t.transform(*this);
}
#ifndef CGAL_NO_OSTREAM_INSERT_PLANE3
template < class R >
std::ostream &operator<<(std::ostream &os, const PlaneH3<R> &p)
{
switch(os.iword(IO::mode)) {
case IO::ASCII :
return os << p.a() << ' ' << p.b() << ' ' << p.c() << ' ' << p.d();
case IO::BINARY :
write(os, p.a());
write(os, p.b());
write(os, p.c());
write(os, p.d());
return os;
default:
os << "PlaneC3(" << p.a() << ", " << p.b() << ", ";
os << p.c() << ", " << p.d() <<")";
return os;
}
}
#endif // CGAL_NO_OSTREAM_INSERT_PLANE3
#ifndef CGAL_NO_ISTREAM_EXTRACT_PLANE3
template < class R >
std::istream &operator>>(std::istream &is, PlaneH3<R> &p)
{
typename R::RT a, b, c, d;
switch(is.iword(IO::mode)) {
case IO::ASCII :
is >> a >> b >> c >> d;
break;
case IO::BINARY :
read(is, a);
read(is, b);
read(is, c);
read(is, d);
break;
default:
std::cerr << "" << std::endl;
std::cerr << "Stream must be in ascii or binary mode" << std::endl;
break;
}
p = PlaneH3<R>(a, b, c, d);
return is;
}
#endif // CGAL_NO_ISTREAM_EXTRACT_PLANE3
template < class R >
bool
PlaneH3<R>::is_degenerate() const
{
const RT RT0(0);
return ( (a() == RT0 ) && (b() == RT0 ) && (c() == RT0 ) );
}
template < class R >
bool
PlaneH3<R>::has_on_positive_side( const typename PlaneH3<R>::Point_3& p) const
{
return (a()*p.hx() + b()*p.hy() + c()*p.hz() + d()*p.hw() > RT(0) );
}
template < class R >
bool
PlaneH3<R>::has_on_negative_side( const typename PlaneH3<R>::Point_3& p) const
{
return (a()*p.hx() + b()*p.hy() + c()*p.hz() + d()*p.hw() < RT(0) );
}
template < class R >
bool
PlaneH3<R>::has_on( const typename PlaneH3<R>::Point_3& p) const
{
return (a()*p.hx() + b()*p.hy() + c()*p.hz() + d()*p.hw() == RT(0) );
}
template < class R >
bool
PlaneH3<R>::has_on( const typename PlaneH3<R>::Line_3& l) const
{
Point_3 p = l.point();
Vector_3 ld = l.direction().to_vector();
Vector_3 ov = orthogonal_vector();
return ( ( a()*p.hx() + b()*p.hy() + c()*p.hz() + d()*p.hw() == RT(0) )
&&( ld.hx()*ov.hx() + ld.hy()*ov.hy() + ld.hz()*ov.hz() == RT(0) ) );
}
template < class R >
Oriented_side
PlaneH3<R>::oriented_side( const typename PlaneH3<R>::Point_3& p) const
{
RT value = a()*p.hx() + b()*p.hy() + c()*p.hz() + d()*p.hw() ;
if (value > RT(0) )
{
return ON_POSITIVE_SIDE;
}
else
{
return
(value < RT(0) ) ? ON_NEGATIVE_SIDE : ON_ORIENTED_BOUNDARY;
}
}
template < class R >
bool
PlaneH3<R>::operator==(const PlaneH3<R>& l) const
{
if ( (a() * l.d() != l.a() * d() )
||(b() * l.d() != l.b() * d() )
||(c() * l.d() != l.c() * d() ) )
{
return false;
}
int sd = static_cast<int>(CGAL_NTS sign(d()));
int sld = static_cast<int>(CGAL_NTS sign(l.d()));
if ( sd == sld )
{
if (sd == 0)
{
return ( (a()*l.b() == b()*l.a() )
&&(a()*l.c() == c()*l.a() )
&&(b()*l.c() == c()*l.b() )
&&(CGAL_NTS sign(a() )== CGAL_NTS sign( l.a() ))
&&(CGAL_NTS sign(b() )== CGAL_NTS sign( l.b() ))
&&(CGAL_NTS sign(c() )== CGAL_NTS sign( l.c() )) );
}
else
{
return true;
}
}
else
{
return false;
}
}
template < class R >
typename PlaneH3<R>::Aff_transformation_3
PlaneH3<R>::transform_to_2d() const
{
const RT RT0(0);
const RT RT1(1);
Vector_3 nov = orthogonal_vector();
Vector_3 e1v = point1()-point() ;
Vector_3 e2v = point2()-point() ;
RT orthohx = nov.hx();
RT orthohy = nov.hy();
RT orthohz = nov.hz();
RT e1phx = e1v.hx();
RT e1phy = e1v.hy();
RT e1phz = e1v.hz();
RT e2phx = e2v.hx();
RT e2phy = e2v.hy();
RT e2phz = e2v.hz();
RT t11 = -( orthohy*e2phz - orthohz*e2phy );
RT t12 = ( orthohx*e2phz - orthohz*e2phx );
RT t13 = -( orthohx*e2phy - orthohy*e2phx );
RT t21 = ( orthohy*e1phz - orthohz*e1phy );
RT t22 = -( orthohx*e1phz - orthohz*e1phx );
RT t23 = ( orthohx*e1phy - orthohy*e1phx );
RT t31 = ( e1phy*e2phz - e1phz*e2phy );
RT t32 = -( e1phx*e2phz - e1phz*e2phx );
RT t33 = ( e1phx*e2phy - e1phy*e2phx );
RT scale = det3x3_by_formula( orthohx, orthohy, orthohz,
e1phx, e1phy, e1phz,
e2phx, e2phy, e2phz );
Aff_transformation_3
point_to_origin(TRANSLATION, - ( point() - ORIGIN ) );
Aff_transformation_3
rotate_and_more( t11, t12, t13, RT0,
t21, t22, t23, RT0,
t31, t32, t33, RT0,
scale);
Point_3 ortho( orthohx, orthohy, orthohz );
Point_3 e1p( e1phx, e1phy, e1phz );
Point_3 e2p( e2phx, e2phy, e2phz );
CGAL_kernel_assertion(( ortho.transform(rotate_and_more)
== Point_3( RT(0), RT(0), RT(1)) ));
CGAL_kernel_assertion(( e1p.transform(rotate_and_more)
== Point_3( RT(1), RT(0), RT(0)) ));
CGAL_kernel_assertion(( e2p.transform(rotate_and_more)
== Point_3( RT(0), RT(1), RT(0)) ));
return rotate_and_more * point_to_origin;
}
template < class R >
CGAL_KERNEL_INLINE
typename PlaneH3<R>::Point_2
PlaneH3<R>::to_2d(const typename PlaneH3<R>::Point_3& p) const
{
Point_3 tp = p.transform( transform_to_2d() );
return Point_2( tp.hx(), tp.hy(), tp.hw());
}
template < class R >
CGAL_KERNEL_INLINE
typename PlaneH3<R>::Point_3
PlaneH3<R>::to_3d(const typename PlaneH3<R>::Point_2& p) const
{
Point_3 hp( p.hx(), p.hy(), RT(0.0), p.hw());
return hp.transform( transform_to_2d().inverse() );
}
CGAL_END_NAMESPACE
#endif // CGAL_PLANEH3_H
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