Reference Manual

Efi Fogel

This package can be used to construct, maintain, alter, and display arrangements on a curve. Once an arrangement is constructed, the package can be used to obtain results of various queries on the arrangement, such as point location. The package also supports operations on arrangements, such as computing the overlay of two arrangements. Arrangements and arrangement components can also be extended to store additional data.

Introduced in: CGAL 6.2
BibTeX: cgal:f-a1-26b
License: GPL

Given a set \(\mathcal{P}\) of points on a curve, the arrangement \( {\mathcal A}({\mathcal P})\) is the subdivision of the curve induced by the points in \(\mathcal{P}\) into maximally connected cells. The cells can be \(0\)-dimensional (vertices) or \(1\)-dimensional (edges).

The class Arrangement_on_curve_1<Traits> encapsulates a data structure that maintains arrangements of points. It comes with a variety of algorithms that operate on 1D arrangements, such as point-location queries and overlay computations, which are implemented as peripheral classes or as free (global) functions.

Classified Reference Pages

Enumerations

Tags

Concepts

• ArrangementOnCurve_1
• AocTraits_1
• AocTopologyTraits

Geometric Object Concepts

• AocTraits::Point_1

Function Object Concepts

• AocTraits::CompareX_1

Classes

• CGAL::Arrangement_on_curves_1::Arrangement_on_curves_1<GeometryTraits_1,TopologyTraits>
• CGAL::Arrangement_on_curves_1::Unbounded_topology_traits<Point_1, VertexData, EdgeData, UseVector, Allocator>

Functions

• CGAL::insert()
• CGAL::locate()
• CGAL::overlay()
• CGAL::IO::read()
• CGAL::IO::write()
• CGAL::operator<<
• CGAL::operator<<

Topics
	Concepts
	I/O
	Free Functions
	Geometry Traits Classes

Classes
class	CGAL::Arrangement_on_curve_1::Arrangement_on_curve_1< GeometryTraits_1, TopologyTraits, BinarySearch >
class	CGAL::Arrangement_on_curve_1::Unbounded_topology_traits< Point_1, VertexData, EdgeData, UseVector, Allocator >
	The class template Unbounded_topology_traits provides a model of the AocTopologyTraits concept for 1D arrangements embedded on an unbounded carrier curve. More...