CGAL::Segment_3< Kernel > Class Template Reference

#include <CGAL/Segment_3.h>

Definition

template<typename Kernel>
class CGAL::Segment_3< Kernel >

An object s of the data type Segment_3 is a directed straight line segment in the three-dimensional Euclidean space \( \E^3\), that is a straight line segment \( [p,q]\) connecting two points \( p,q \in \R^3\).

The segment is topologically closed, i.e. the end points belong to it. Point p is called the source and q is called the target of s. The length of s is the Euclidean distance between p and q. Note that there is only a function to compute the square of the length, because otherwise we had to perform a square root operation which is not defined for all number types, which is expensive, and may not be exact.

Is model of

Kernel::Segment_3

Hashable if Kernel is a cartesian kernel and if Kernel::FT is Hashable

Creation
	Segment_3 (const Point_3< Kernel > &p, const Point_3< Kernel > &q)
	introduces a segment s with source p and target q.

Operations
bool	operator== (const Segment_3< Kernel > &q) const
	Test for equality: Two segments are equal, iff their sources and targets are equal.
bool	operator!= (const Segment_3< Kernel > &q) const
	Test for inequality.
Point_3< Kernel >	source () const
	returns the source of s.
Point_3< Kernel >	target () const
	returns the target of s.
Point_3< Kernel >	min () const
	returns the point of s with smallest coordinate (lexicographically).
Point_3< Kernel >	max () const
	returns the point of s with largest coordinate (lexicographically).
Point_3< Kernel >	vertex (int i) const
	returns source or target of s: vertex(0) returns the source, vertex(1) returns the target.
Point_3< Kernel >	point (int i) const
	returns vertex(i).
Point_3< Kernel >	operator[] (int i) const
	returns vertex(i).
Kernel::FT	squared_length () const
	returns the squared length of s.
Vector_3< Kernel >	to_vector () const
	returns the vector s.target() - s.
Direction_3< Kernel >	direction () const
	returns the direction from source to target.
Segment_3< Kernel >	opposite () const
	returns a segment with source and target interchanged.
Line_3< Kernel >	supporting_line () const
	returns the line l passing through s.
bool	is_degenerate () const
	segment s is degenerate, if source and target fall together.
bool	has_on (const Point_3< Kernel > &p) const
	A point is on s, iff it is equal to the source or target of s, or if it is in the interior of s.
Bbox_3	bbox () const
	returns a bounding box containing s.
Segment_3< Kernel >	transform (const Aff_transformation_3< Kernel > &t) const
	returns the segment obtained by applying t on the source and the target of s.

Constructor & Destructor Documentation

Segment_3()

template<typename Kernel >

CGAL::Segment_3< Kernel >::Segment_3	(	const Point_3< Kernel > &	p,
		const Point_3< Kernel > &	q
	)

introduces a segment s with source p and target q.

It is directed from the source towards the target.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

Member Function Documentation

bbox()

template<typename Kernel >

Bbox_3 CGAL::Segment_3< Kernel >::bbox

(

)

const

returns a bounding box containing s.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

max()

template<typename Kernel >

Point_3< Kernel > CGAL::Segment_3< Kernel >::max

(

)

const

returns the point of s with largest coordinate (lexicographically).

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

min()

template<typename Kernel >

Point_3< Kernel > CGAL::Segment_3< Kernel >::min

(

)

const

returns the point of s with smallest coordinate (lexicographically).

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

operator[]()

template<typename Kernel >

Point_3< Kernel > CGAL::Segment_3< Kernel >::operator[]

(

int

i

)

const

returns vertex(i).

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

opposite()

template<typename Kernel >

Segment_3< Kernel > CGAL::Segment_3< Kernel >::opposite

(

)

const

returns a segment with source and target interchanged.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

point()

template<typename Kernel >

Point_3< Kernel > CGAL::Segment_3< Kernel >::point

(

int

i

)

const

returns vertex(i).

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

source()

template<typename Kernel >

Point_3< Kernel > CGAL::Segment_3< Kernel >::source

(

)

const

returns the source of s.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

supporting_line()

template<typename Kernel >

Line_3< Kernel > CGAL::Segment_3< Kernel >::supporting_line

(

)

const

returns the line l passing through s.

Line l has the same orientation as segment s, that is from the source to the target of s.

target()

template<typename Kernel >

Point_3< Kernel > CGAL::Segment_3< Kernel >::target

(

)

const

returns the target of s.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.

to_vector()

template<typename Kernel >

Vector_3< Kernel > CGAL::Segment_3< Kernel >::to_vector

(

)

const

returns the vector s.target() - s.

source().

vertex()

template<typename Kernel >

Point_3< Kernel > CGAL::Segment_3< Kernel >::vertex

(

int

i

)

const

returns source or target of s: 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.

Exactness

This construction is trivial and therefore always exact in Exact_predicates_inexact_constructions_kernel.