Segment_3<Kernel>

Navigation: Up, Table of Contents, Short Table of Contents, Package Overview, Bibliography, Index, Title Page

CGAL::Segment_3<Kernel>

Definition

An object

s of the data type Segment_3<Kernel> is a directed straight line segment in the three-dimensional Euclidean space

³, i.e. a straight line segment

[p,q] connecting two points

p,q 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.

Creation

Segment_3<Kernel> s ( Point_3<Kernel> p, Point_3<Kernel> q);
introduces a segment s with source p and target q. It is directed from the source towards the target.

Operations

bool s.operator== ( q)
Test for equality: Two segments are equal, iff their sources and targets are equal.

bool s.operator!= ( q)
Test for inequality.

Point_3<Kernel> s.source () returns the source of s.

Point_3<Kernel> s.target () returns the target of s.

Point_3<Kernel> s.min () returns the point of s with smallest coordinate (lexicographically).

Point_3<Kernel> s.max () returns the point of s with largest coordinate (lexicographically).

Point_3<Kernel> s.vertex ( int i) 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.

Point_3<Kernel> s.point ( int i) returns vertex(i).

Point_3<Kernel> s.operator[] ( int i)
returns vertex(i).

Kernel::FT s.squared_length ()
returns the squared length of s.

Vector_3<Kernel> s.to_vector () returns the vector s.target() - s.source().

Direction_3<Kernel>
s.direction () returns the direction from source to target.

Segment_3<Kernel> s.opposite () returns a segment with source and target interchanged.

Line_3<Kernel> s.supporting_line ()
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.

bool s.is_degenerate () segment s is degenerate, if source and target fall together.

bool s.has_on ( Point_3<Kernel> p)
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 s.bbox () returns a bounding box containing s.

Segment_3<Kernel> s.transform ( Aff_transformation_3<Kernel> t)
returns the segment obtained by applying t on the source and the target of s.

Segment_3<Kernel> s ( Point_3<Kernel> p, Point_3<Kernel> q);
	introduces a segment s with source p and target q. It is directed from the source towards the target.

bool	s.operator== ( q)
		Test for equality: Two segments are equal, iff their sources and targets are equal.

bool	s.operator!= ( q)
		Test for inequality.

Point_3<Kernel>	s.source ()	returns the source of s.
Point_3<Kernel>	s.target ()	returns the target of s.

Point_3<Kernel>	s.min ()	returns the point of s with smallest coordinate (lexicographically).

Point_3<Kernel>	s.max ()	returns the point of s with largest coordinate (lexicographically).

Point_3<Kernel>	s.vertex ( int i)	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.

Point_3<Kernel>	s.point ( int i)	returns vertex(i).
Point_3<Kernel>	s.operator[] ( int i)
		returns vertex(i).

Kernel::FT	s.squared_length ()
		returns the squared length of s.

Vector_3<Kernel>	s.to_vector ()	returns the vector s.target() - s.source().

Direction_3<Kernel>
	s.direction ()	returns the direction from source to target.

Segment_3<Kernel>	s.opposite ()	returns a segment with source and target interchanged.

Line_3<Kernel>	s.supporting_line ()
		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.

bool	s.is_degenerate ()	segment s is degenerate, if source and target fall together.

bool	s.has_on ( Point_3<Kernel> p)
		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	s.bbox ()	returns a bounding box containing s.

Segment_3<Kernel>	s.transform ( Aff_transformation_3<Kernel> t)
		returns the segment obtained by applying t on the source and the target of s.

CGAL::Segment_3<Kernel>

Definition

Creation

Operations

See Also