Computational Geometry – 99102

Geometric computing is creeping into virtually every corner of science and engineering, from design and manufacturing to astrophysics and cartography. This report describes presentations made at a workshop focused on recent advances in this computational geometry field. Previous Dagstuhl workshops on computational geometry dealt mostly with theoretical issues: the development of provably efficient algorithms for various geometric problems on point sets, arrangements of curves and surfaces, triangulations and other sets of objects; proving various combinatorial results on sets of geomtric objects, which usually have implications on the performance of performance guarantees of geometric algorithms; describing the intrinsic computational complexity of various geometric problems. This workshop continued some of this tradition, but as one more point there was a strong emphasis on the exchange of ideas regarding carrying the many theoretical findings of the last years into computational practice. There were presentations about the recent development of software libraries such as CGAL, LEDA, JDSL, VEGA, and TPIE, and also some experimentation with them. These libraries should help to simplify the realization of abstractly conceived geometric algorithms as actually executable software. The participants and organizers of this workshop would like to thank the Dagstuhl office and the local personnel for the engaged and competent support in all matters. The cordial atmosphere provided for an unusually successful and enjoyable workshop.