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CGAL 5.6 - 2D and 3D Linear Geometry Kernel
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CGAL 5.6 - 2D and 3D Linear Geometry Kernel
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#include <CGAL/Segment_3.h>
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.
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. More... | |
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. More... | |
| 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. More... | |
| 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. More... | |
| 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. | |
| 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.
| 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.
| Vector_3<Kernel> CGAL::Segment_3< Kernel >::to_vector | ( | ) | const |
returns the vector s.target() - s.
| 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.
1.8.13