CGAL::Segment_d<Kernel>

Definition

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 degenerate.

Types

Creation

Operations

int	s.dimension ()	returns the dimension of the ambient space.
Point_d<Kernel>	s.source ()	returns the source point of segment s.
Point_d<Kernel>	s.target ()	returns the target point of segment s.
Point_d<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. Precondition:  $$i 0.
Point_d<Kernel>	s.point ( int i)	returns vertex(i).
Point_d<Kernel>	s [ int i ]	returns vertex(i).
Point_d<Kernel>	s.min ()	returns the lexicographically smaller vertex.
Point_d<Kernel>	s.max ()	returns the lexicographically larger vertex.
Segment_d<Kernel>	s.opposite ()	returns the segment (target(),source()).
Direction_d<Kernel>	s.direction ()	returns the direction from source to target. Precondition:  s is non-degenerate.
Vector_d<Kernel>	s.vector ()	returns the vector from source to target.
FT	s.squared_length ()	returns the square of the length of s.
bool	s.has_on ( Point_d<Kernel> p)	returns true if $$p lies on s and false otherwise. Precondition:  s.dimension()==p.dimension().
Line_d<Kernel>	s.supporting_line ()	returns the supporting line of s. Precondition:  s is non-degenerate.
Segment_d<Kernel>	s.transform ( Aff_transformation_d<Kernel> t)
		returns $$t(s). Precondition:  s.dimension()==t.dimension().
Segment_d<Kernel>	s + Vector_d<Kernel> v	returns $$s+v, i.e., s translated by vector $$v. Precondition:  s.dimension()==v.dimension().
bool	s.is_degenerate ()	returns true if s is degenerate i.e. s.source()=s.target().

Non-Member Functions

Implementation

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()).