CGAL is a Computational Geometry Algorithms Library written in C++, which is being developed by research groups in Europe and Israel. The goal is to make the large body of geometric algorithms developed in the field of computational geometry available for industrial application. We discuss the major design goals for CGAL, which are correctness, flexibility, ease‐of‐use, efficiency, and robustness, and present our approach to reach these goals. Generic programming using templates in C++ plays a central role in the architecture of CGAL. We give a short introduction to generic programming in C++, compare it to the object‐oriented programming paradigm, and present examples where both paradigms are used effectively in CGAL. Moreover, we give an overview of the current structure of the CGAL‐library and consider software engineering aspects in the CGAL‐project. Copyright © 2000 John Wiley & Sons, Ltd.

We present a software library Stxxl, that enables practice-oriented experimentation with huge data sets. Stxxl is an implementation of the C++ standard template library STL for external memory computations. It supports parallel disks, overlapping between I/O and computation and is the first external memory algorithm library that supports the pipelining technique that can save more than half of the I/Os. Stxxl has already been used for the following applications: implementations of external memory algorithms for computing minimum spanning trees, connected components, breadth-first search decompositions, constructing suffix arrays, and computing social network analysis metrics for huge graphs.

Nef polyhedra in d-dimensional space are the closure of half-spaces under boolean set operations. In consequence, they can represent non-manifold situations, open and closed sets, mixed-dimensional complexes, and they are closed under all boolean and topological operations, such as complement and boundary. They were introduced by W. Nef in his seminal 1978 book on polyhedra. The generality of Nef complexes is essential for some applications.In this paper, we present a new data structure for the boundary representation of three-dimensional Nef polyhedra and efficient algorithms for boolean operations. We use exact arithmetic to avoid well-known problems with floating-point arithmetic and handle all degeneracies. Furthermore, we present important optimizations for the algorithms, and evaluate this optimized implementation with extensive experiments. The experiments supplement the theoretical runtime analysis and illustrate the effectiveness of our optimizations. We compare our implementation with the ACIS CAD kernel. ACIS is mostly faster, by a factor up to six. There are examples on which ACIS fails.The implementation was released as Open Source in the Computational Geometry Algorithm Library (CGAL) release 3.1 in December 2004.

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Abstract. The Descartes method is an algorithm for isolating the real roots of square-free polynomials with real coefficients. We assume that coefficients are given as (potentially infinite) bit-streams. In other words, coefficients can be approximated to any desired accuracy, but are not known exactly. We show that a variant of the Descartes algorithm can cope with bit-stream coefficients. To isolate the real roots of a square-free real polynomial q(x) = q n x n + . . . + q 0 with root separation ρ, coefficients |q n | ≥ 1 and |q i | ≤ 2 τ , it needs coefficient approximations to O(n(log(1/ρ) + τ)) bits after the binary point and has an expected cost of O(n 4 (log(1/ρ) + τ) 2 ) bit operations.