A computational geometry workbench

Abstract

We are constructing a workbench for computational geometry. This is intended to provide a framework for the implementation, testing, demonstration and application of algorithms in computational geometry. The workbench is being written in Smalltalk/V using an Apple Macintosh II. The object-oriented model used in Smalltalk is well-suited to algorithms manipulating geometric objects. In addition, the programming environment can be easily extended, and provides excellent graphics facilities, data abstraction, encapsulation, and incremental modification. We have completed the design and implementation of the workbench platform, insofar as such a system can ever be considered complete. Among the features of the system are:an interactive graphical environment, including operations for creation and editing of geometric figures, and for the operation of algorithm on these figures the system supports:high-level representation-independent geometric objects (points, lines, polygons,…) geometric data structures (segment trees, range trees,…) non-geometric data structures (finger trees, splay trees, heaps, …) “standard” algorithmic tools in as general a form as possible. Algorithms currently available in the system include Tarjan and van Wyk's triangulation of a simple polygon, Fortune's Voronoi diagram, Preparata's chain decomposition, and Melkman's convex hull algorithm. tools for the animation of geometric algorithms high-level graphical and symbolic debugging facilities portability, due to the separation of the machine-independent code and the machine-dependent user-interface. automatic handling of basic operations (device-independent graphics, storage management) allowing the implementor to focus on algorithmic issues Our group is currently working on extensions in two directions:implementing additional algorithms from two-dimensional computational geometry providing the framework for implementations of three-dimensional algorithms We are also conducting comparison studies of different algorithms and data structures, including a comparison of different triangulation and convex hull algorithms for large input sizes and an empirical test of the dynamic optimality conjecture of Sleator and Tarjan using both Splay and Finger trees in the Tarjan and van Wyk triangulation. The workbench is being demonstrated during this symposium.