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// Copyright (c) 2000,2001 // 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/Kernel_d/include/CGAL/Kernel_d/Segment_d.h $ // $Id: include/CGAL/Kernel_d/Segment_d.h b26b07a1242 $ // SPDX-License-Identifier: LGPL-3.0-or-later OR LicenseRef-Commercial // // // Author(s) : Michael Seel #ifndef CGAL_SEGMENT_D_H #define CGAL_SEGMENT_D_H #include #include #include #include #include #include namespace CGAL { template std::istream& operator>> (std::istream&, Segment_d&); template std::ostream& operator<< (std::ostream&, const Segment_d&); /*{\Manpage {Segment_d}{R}{Segments in d-space}{s}}*/ template class Segment_d : public Handle_for< Pair_d > { typedef Pair_d Pair; typedef Handle_for Base; typedef Segment_d Self; using Base::ptr; /*{\Mdefinition An instance $s$ of the data type |Segment_d| is a directed straight line segment in $d$-dimensional Euclidean space connecting two points $p$ and $q$. $p$ is called the source point and $q$ is called the target point of $s$, both points are called endpoints of $s$. A segment whose endpoints are equal is called \emph{degenerate}.}*/ public: typedef CGAL::Dynamic_dimension_tag Ambient_dimension; typedef CGAL::Dimension_tag<1> Feature_dimension; /*{\Mtypes 5}*/ typedef p_R R; /*{\Mtypemember the representation type.}*/ typedef typename p_R::RT RT; /*{\Mtypemember the ring type.}*/ typedef typename p_R::FT FT; /*{\Mtypemember the field type.}*/ typedef typename p_R::LA LA; /*{\Mtypemember the linear algebra layer.}*/ friend class Line_d; friend class Ray_d; private: Segment_d(const Base& b) : Base(b) {} public: /*{\Mcreation 3}*/ Segment_d() : Base( Pair() ) {} /*{\Mcreate introduces a variable |\Mvar| of type |\Mname|.}*/ Segment_d(const Point_d& p, const Point_d& q) /*{\Mcreate introduces a variable |\Mvar| of type |\Mname| which is initialized to the segment $(p,q)$. }*/ : Base( Pair(p,q) ) {} Segment_d(const Point_d& p, const Vector_d& v) /*{\Mcreate introduces a variable |\Mvar| of type |\Mname| which is initialized to the segment |(p,p+v)|. }*/ : Base( Pair(p,p+v) ) {} /*{\Moperations 3 3}*/ int dimension() const { return (ptr()->_p[0].dimension()); } /*{\Mop returns the dimension of the underlying space. }*/ Point_d source() const { return ptr()->_p[0]; } /*{\Mop returns the source point of segment |\Mvar|. }*/ Point_d target() const { return ptr()->_p[1]; } /*{\Mop returns the target point of segment |\Mvar|. }*/ // defined for historical reasons Point_d vertex(int i) const /*{\Mop returns source or target of |\Mvar|: |vertex(0)| returns the source, |vertex(1)| returns the target. The parameter $i$ is taken modulo $2$, which gives easy access to the other vertex. \precond $i \geq 0$.}*/ { CGAL_assertion(i>=0); return ptr()->_p[i%2]; } Point_d point(int i) const { return vertex(i); } /*{\Mop returns |vertex(i)|.}*/ Point_d operator[](int i) const { return vertex(i); } /*{\Marrop returns |vertex(i)|.}*/ Point_d min BOOST_PREVENT_MACRO_SUBSTITUTION () const /*{\Mop returns the lexicographically smaller vertex.}*/ { typename R::Compare_lexicographically_d cmp; if (cmp(source(),target()) == CGAL::SMALLER) return source(); else return target(); } Point_d max BOOST_PREVENT_MACRO_SUBSTITUTION () const /*{\Mop returns the lexicographically larger vertex.}*/ { typename R::Compare_lexicographically_d cmp; if (cmp(source(),target()) == SMALLER) return target(); else return source(); } Segment_d opposite() const /*{\Mop returns the segment |(target(),source())|.}*/ { return Segment_d(target(),source()); } Direction_d direction() const /*{\Mop returns the direction from source to target.\\ \precond |\Mvar| is non-degenerate. }*/ { CGAL_assertion_msg((!is_degenerate()), "Segment_d::direction(): degenerate segment cannot be converted."); return ptr()->direction(); } Vector_d vector() const /*{\Mop returns the vector from source to target.}*/ { return ptr()->vector(); } FT squared_length() const /*{\Mop returns the square of the length of |\Mvar|.}*/ { return (target()-source()).squared_length(); } bool has_on(const Point_d& p) const /*{\Mop returns true if $p$ lies on |\Mvar| and false otherwise. }*/ { if (is_degenerate()) return (source() == p); typename R::Position_on_line_d pos; FT l; if ( pos(p,source(),target(),l) ) return (FT(0)<=l && l<=FT(1)); return false; } inline Line_d supporting_line() const; /*{\Mop returns the supporting line of |\Mvar|. \precond |\Mvar| is non-degenerate. }*/ Segment_d transform(const Aff_transformation_d& t) const /*{\Mop returns $t(s)$.}*/ { return Segment_d(source().transform(t), target().transform(t)); } Segment_d operator+(const Vector_d& v) const /*{\Mbinop returns $s+v$, i.e., |\Mvar| translated by vector $v$.}*/ { return Segment_d(source()+v,target()+v); } bool is_degenerate() const /*{\Mop returns true if |\Mvar| is degenerate i.e. |\Mvar.source()=\Mvar.target()|. }*/ { return ptr()->is_degenerate(); } bool operator==(const Segment_d& t) const { if (this->identical(t)) return true; return ((source() == t.source() && target() == t.target())); } bool operator!=(const Segment_d& t) const { return !operator==(t); } friend std::istream& operator>> <> (std::istream&, Segment_d&); friend std::ostream& operator<< <> (std::ostream&, const Segment_d&); }; // end of class /*{\Mtext \headerline{Non-Member Functions} }*/ template bool weak_equality(const Segment_d& s, const Segment_d& t) /*{\Mfunc Test for equality as unoriented segments.}*/ { return (s==t || s==t.opposite()); } template bool parallel(const Segment_d& s1, const Segment_d& s2) /*{\Mfunc return true if one of the segments is trivial or if the unoriented supporting lines are parallel. }*/ { return s1.is_degenerate() || s2.is_degenerate() || s1.direction() == s2.direction() || s1.direction() == -s2.direction(); } template bool common_endpoint(const Segment_d& s1, const Segment_d& s2, Point_d& common) /*{\Mfunc if |s1| and |s2| touch in a common end point, this point is assigned to |common| and the result is |true|, otherwise the result is |false|. }*/ { if (s1.source() == s2.source()) { common = s1.source(); return true; } if (s1.source() == s2.target()) { common = s1.source(); return true; } if (s1.target() == s2.source()) { common = s1.target(); return true; } if (s1.target() == s2.target()) { common = s1.target(); return true; } return false; } template std::istream& operator>>(std::istream& I, Segment_d& s) { s.copy_on_write(); s.ptr()->read(I); CGAL_assertion_msg(s.source().dimension()==s.target().dimension(), "Segment_d::operator>>: dimensions disagree."); return I; } template std::ostream& operator<<(std::ostream& O, const Segment_d& s) { s.ptr()->print(O,"Segment_d"); return O; } /*{\Mimplementation Segments are implemented by a pair of points as an item type. All operations like creation, initialization, tests, the calculation of the direction and source - target vector, input and output on a segment $s$ take time $O(|s.dimension()|)$. |dimension()|, coordinate and end point access, and identity test take constant time. The operations for intersection calculation also take time $O(|s.dimension()|)$. The space requirement is $O(|s.dimension()|)$. }*/ } //namespace CGAL #endif // CGAL_SEGMENT_D_H //----------------------- end of file ----------------------------------