Two-Dimensional Arrangements in CGAL and Adaptive Point Location for Parametric Curves

Given a collection C of curves in the plane, the arrangement of C is the subdivision of the plane into vertices, edges and faces induced by the curves in C. Constructing arrangements of curves in the plane is a basic problem in computational geometry. Applications relying on arrangements arise in elds such as robotics, computer vision and computer graphics. Many algorithms for constructing and maintaining arrangements under various conditions have been published in papers. However, there are not many implementations of (general) arrangements packages available. We present an implementation of a generic and robust package for arrangements of curves that is part of the CGAL1 library. We also present an application based on this package for adaptive point location in arrangements of parametric curves.

• Type: Conference
• Year: 2000
• Where: WAE
• Authors: Iddo Hanniel, Dan Halperin
• Keywords: Arrangements, Arrangements Packages, Computational Geometry, WAE 2000, WAE 2001