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// Copyright (c) 1999 // Utrecht University (The Netherlands), // ETH Zurich (Switzerland), // INRIA Sophia-Antipolis (France), // Max-Planck-Institute Saarbruecken (Germany), // and Tel-Aviv University (Israel). All rights reserved. // // This file is part of CGAL (www.cgal.org) // // $URL: https://github.com/CGAL/cgal/blob/v6.1/Homogeneous_kernel/include/CGAL/Homogeneous/VectorH3.h $ // $Id: include/CGAL/Homogeneous/VectorH3.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Stefan Schirra #ifndef CGAL_HOMOGENEOUS_VECTOR_3_H #define CGAL_HOMOGENEOUS_VECTOR_3_H #include #include #include namespace CGAL { template < class R_ > class VectorH3 { typedef typename R_::RT RT; typedef typename R_::FT FT; typedef typename R_::Point_3 Point_3; typedef typename R_::Vector_3 Vector_3; typedef typename R_::Segment_3 Segment_3; typedef typename R_::Ray_3 Ray_3; typedef typename R_::Line_3 Line_3; typedef typename R_::Direction_3 Direction_3; typedef std::array Rep; typedef typename R_::template Handle::type Base; typedef Rational_traits Rat_traits; Base base; public: typedef Cartesian_const_iterator_d Cartesian_const_iterator; typedef R_ R; VectorH3() {} VectorH3(const Point_3& a, const Point_3& b) { *this = R().construct_vector_3_object()(a, b); } VectorH3(const Segment_3& s) { *this = R().construct_vector_3_object()(s); } VectorH3(const Ray_3& r) { *this = R().construct_vector_3_object()(r); } VectorH3(const Line_3& l) { *this = R().construct_vector_3_object()(l); } VectorH3(const Null_vector&) : base{RT(0), RT(0), RT(0), RT(1)} {} template < typename Tx, typename Ty, typename Tz > VectorH3(const Tx & x, const Ty & y, const Tz & z, std::enable_if_t< std::is_convertible_v && std::is_convertible_v && std::is_convertible_v>* = 0) : base(CGAL::make_array(x, y, z, RT(1))) {} VectorH3(const FT& x, const FT& y, const FT& z) : base(Rat_traits().denominator(x) * Rat_traits().denominator(y) * Rat_traits().denominator(z) >= 0 ? CGAL::make_array( Rat_traits().numerator(x) * Rat_traits().denominator(y) * Rat_traits().denominator(z), Rat_traits().numerator(y) * Rat_traits().denominator(x) * Rat_traits().denominator(z), Rat_traits().numerator(z) * Rat_traits().denominator(x) * Rat_traits().denominator(y), Rat_traits().denominator(x) * Rat_traits().denominator(y) * Rat_traits().denominator(z)) : CGAL::make_array( - Rat_traits().numerator(x) * Rat_traits().denominator(y) * Rat_traits().denominator(z), - Rat_traits().numerator(y) * Rat_traits().denominator(x) * Rat_traits().denominator(z), - Rat_traits().numerator(z) * Rat_traits().denominator(x) * Rat_traits().denominator(y), - Rat_traits().denominator(x) * Rat_traits().denominator(y) * Rat_traits().denominator(z))) { CGAL_kernel_assertion(hw() > 0); } VectorH3(const RT& x, const RT& y, const RT& z, const RT& w) : base( w >= RT(0) ? CGAL::make_array(x, y, z, w) : CGAL::make_array(-x, -y, -z, -w) ) {} const RT & hx() const { return get_pointee_or_identity(base)[0]; } const RT & hy() const { return get_pointee_or_identity(base)[1]; } const RT & hz() const { return get_pointee_or_identity(base)[2]; } const RT & hw() const { return get_pointee_or_identity(base)[3]; } FT x() const { return FT(hx())/FT(hw()); } FT y() const { return FT(hy())/FT(hw()); } FT z() const { return FT(hz())/FT(hw()); } const RT & homogeneous(int i) const; FT cartesian(int i) const; FT operator[](int i) const; Cartesian_const_iterator cartesian_begin() const { return make_cartesian_const_iterator_begin(get_pointee_or_identity(base).begin(), std::prev(get_pointee_or_identity(base).end())); } Cartesian_const_iterator cartesian_end() const { return make_cartesian_const_iterator_end(std::prev(get_pointee_or_identity(base).end())); } int dimension() const { return 3; }; Direction_3 direction() const; Vector_3 operator-() const; typename R::Boolean operator==( const VectorH3& v) const; typename R::Boolean operator!=( const VectorH3& v) const; Vector_3 operator+( const VectorH3 &v) const; Vector_3 operator-( const VectorH3 &v) const; FT squared_length() const; Vector_3 operator/( const RT &f) const; Vector_3 operator/( const FT &f) const; }; template < class R > CGAL_KERNEL_INLINE typename VectorH3::FT VectorH3::cartesian(int i) const { CGAL_kernel_precondition(i == 0 || i == 1 || i == 2); switch (i) { case 0: return x(); case 1: return y(); } return z(); } template < class R > CGAL_KERNEL_INLINE const typename VectorH3::RT & VectorH3::homogeneous(int i) const { CGAL_kernel_precondition(i == 0 || i == 1 || i == 2 || i == 3); return get_pointee_or_identity(base)[i]; } template < class R > inline typename VectorH3::Direction_3 VectorH3::direction() const { return Direction_3(hx(), hy(), hz()); } template < class R > CGAL_KERNEL_INLINE typename R::Boolean VectorH3::operator==( const VectorH3& v) const { return ( (hx() * v.hw() == v.hx() * hw() ) &&(hy() * v.hw() == v.hy() * hw() ) &&(hz() * v.hw() == v.hz() * hw() ) ); } template < class R > inline typename R::Boolean VectorH3::operator!=( const VectorH3& v) const { return !(*this == v); } template < class R > inline typename VectorH3::FT VectorH3::operator[](int i) const { return cartesian(i); } template < class R > CGAL_KERNEL_INLINE typename VectorH3::Vector_3 VectorH3::operator-() const { return Vector_3( - hx(), - hy(), -hz(), hw() ); } template CGAL_KERNEL_INLINE typename R::Vector_3 VectorH3::operator+(const VectorH3& v) const { return typename R::Vector_3(hx()*v.hw() + v.hx()*hw(), hy()*v.hw() + v.hy()*hw(), hz()*v.hw() + v.hz()*hw(), hw()*v.hw() ); } template CGAL_KERNEL_INLINE typename R::Vector_3 VectorH3::operator-(const VectorH3& v) const { return typename R::Vector_3(hx()*v.hw() - v.hx()*hw(), hy()*v.hw() - v.hy()*hw(), hz()*v.hw() - v.hz()*hw(), hw()*v.hw() ); } template CGAL_KERNEL_INLINE typename VectorH3::FT VectorH3::squared_length() const { typedef typename R::FT FT; return FT( CGAL_NTS square(hx()) + CGAL_NTS square(hy()) + CGAL_NTS square(hz()) ) / FT( CGAL_NTS square(hw()) ); } template CGAL_KERNEL_INLINE typename R::Vector_3 VectorH3::operator/(const typename VectorH3::RT& f) const { return typename R::Vector_3( hx(), hy(), hz(), hw()*f ); } template CGAL_KERNEL_INLINE typename R::Vector_3 VectorH3::operator/(const typename VectorH3::FT& f) const { return typename R::Vector_3(hx()*f.denominator(), hy()*f.denominator(), hz()*f.denominator(), hw()*f.numerator() ); } } //namespace CGAL #endif // CGAL_HOMOGENEOUS_VECTOR_3_H