This book originates from the lectures given at the international conference "Theory and Practice of Geometric Modeling", Blaubeuren, FRG, October 3-7, 1988, that brought together leading experts from universities, system developers, and system users, to discuss new concepts and future trends in geometric modeling. The book covers a variety of topics on an advanced level and is organized as follows. Part A contains new algorithms and techniques for modeling objects that are bounded by free form surfaces. Part B focuses on surface/surface intersections, new types of blending surfaces and speed ups for ray tracing. Part C contains some new geometric tools. Part D discusses different representation schemes in solid modeling, conversions between these different schemes, and some applications. Part E covers some issues of product modeling, automatic tolerancing, high level specification of solid models (constraints, features) and the need for better user interfaces.