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## 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.

### See Also

Kernel::Segment_3

Next: Sphere_3<Kernel>

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The CGAL Project . Tue, December 21, 2004 .