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Abstract

A planar Nef polyhedron is any set that can be obtained from the open half-space by a finite number of set complement and set intersection operations. The set of Nef polyhedra is closed under the Boolean set operations. We describe a date structure that realizes two-dimensional Nef polyhedra and offers a large set of binary and unary set operations. The underlying set operations are realized by an efficient and complete algorithm for the overlay of two Nef polyhedra. The algorithm is efficient in the sense that its running time is bounded by the size of the inputs plus the size of the output times a logarithmic factor. The algorithm is complete in the sense that it can handle all inputs and requires no general position assumption. The seecond part of the algorithmic interface considers point location and ray shooting in planar subdivisions. The implementation follows the generic programming paradigm in C++ and CGAL. Several concept interfaces are defined that allow the adaptation of the software by the means of traits classes. The described project is part of the CGAL libarary version 2.3.