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.

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We study scalable parallel computational geometry algorithms for the coarse grained multicomputer model: p processors solving a problem on n data items, were each processor has O(n/p)≫O(1) local memory and all processors are connected via some arbitrary interconnection network (e.g. mesh, hypercube, fat tree). We present O(Tsequential/p+Ts(n, p)) time scalable parallel algorithms for several computational geometry problems. Ts(n, p) refers to the time of a global sort operation. Our results are independent of the multicomputer’s interconnection network. Their time complexities become optimal when Tsequential/p dominates Ts(n, p) or when Ts(n, p) is optimal. This is the case for several standard architectures, including meshes and hypercubes, and a wide range of ratios n/p that include many of the currently available machine configurations. Our methods also have some important practical advantages: For interprocessor communication, they use only a small fixed number of one global routing operation, global sort, and all other programming is in the sequential domain. Furthermore, our algorithms use only a small number of very large messages, which greatly reduces the overhead for the communication protocol between processors. (Note however, that our time complexities account for the lengths of messages.) Experiments show that our methods are easy to implement and give good timing results.

We present a randomized parallel algorithm for constructing

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