Advanced programming techniques applied to Cgal's arrangement package

Abstract

Arrangements of planar curves are fundamental structures in computational geometry. Recently, the arrangement package of Cgal, the Computational Geometry Algorithms Library, has been redesigned and re-implemented exploiting several advanced programming techniques. The resulting software package, which constructs and maintains planar arrangements, is easier to use, to extend, and to adapt to a variety of applications. It is more efficient space- and time-wise, and more robust. The implementation is complete in the sense that it handles degenerate input, and it produces exact results. In this paper we describe how various programming techniques were used to accomplish specific tasks within the context of computational geometry in general and arrangements in particular. These tasks are exemplified by several applications, whose robust implementation is based on the arrangement package. Together with a set of benchmarks they assured the successful application of the various programming techniques.