\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Arrangements

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
List of all members
ArrangementPointLocation_2 Concept Reference
Concepts

## Definition

A model of the `ArrangementPointLocation_2` concept can answer point-location queries on an arrangement attached to it. Namely, given a `Arrangement_2::Point_2` object, representing a point in the plane, it returns the arrangement cell containing it. In the general case, the query point is contained inside an arrangement face, but in degenerate situations it may lie on an edge or coincide with an arrangement vertex.

A note on Backwards compatibility
The `locate` member function used to return `CGAL::Object` up to CGAL version 4.2. Starting with CGAL version 4.3 the return type is determined by a metafunction. To preserve backwards compatibility `CGAL::Object` can be constructed from the new return types implicitly, but switching to the new style is recommended. To enable the old style without any overhead, the macro `CGAL_ARR_POINT_LOCATION_VERSION` can be defined to 1 before any CGAL header is included.

Has Models:

  `CGAL::Arr_naive_point_location<Arrangement>`

  `CGAL::Arr_walk_along_line_point_location<Arrangement>`

  `CGAL::Arr_trapezoid_ric_point_location<Arrangement>`

  `CGAL::Arr_landmarks_point_location<Arrangement,Generator>`

See Also
  `CGAL::Arr_naive_point_location<Arrangement>`
  `CGAL::Arr_walk_along_line_point_location<Arrangement>`
  `CGAL::Arr_trapezoid_ric_point_location<Arrangement>`
  `CGAL::Arr_landmarks_point_location<Arrangement,Generator>`
  `CGAL::Arr_point_location_result<Arrangement>`
  `CGAL_ARR_POINT_LOCATION_VERSION`

## Types
typedef unspecified_type | Arrangement_2
| the associated arrangement type.
typedef unspecified_type | Point_2
| equivalent to `Arrangement_2::Point_2`.

## Creation
| ArrangementPointLocation_2 ()
| default constructor.
| ArrangementPointLocation_2 (const Arrangement_2 &arr)
| constructs a point-location object `pl` attached to the given arrangement `arr`.

## Query Functions
Arr_point_location_result < Arrangement_2 >::Type | locate (const Point_2 &q) const
| locates the arrangement cell that contains the query point `q` and returns a discriminated union container of the following bounded types: More...

## Operations
void | attach (const Arrangement_2 &arr)
| attaches `pl` to the given arrangement `arr`.
void | detach ()
| detaches `pl` from the arrangement it is currently attached to.

## Member Function Documentation

Arr_point_location_result<Arrangement_2>::Type ArrangementPointLocation_2::locate | ( | const Point_2 & | q) |  | const

locates the arrangement cell that contains the query point `q` and returns a discriminated union container of the following bounded types:

- `Arrangement_2::Face_const_handle`, in case `q` is contained inside an arrangement face;
- `Arrangement_2::Halfedge_const_handle`, in case `q` lies on an arrangement edge;
- `Arrangement_2::Vertex_const_handle`, in case `q` coincides with an arrangement vertex.

Precondition
  `pl` is attached to a valid arrangement object.