Theory and Practice of Geometric Modeling

This book is a result of the lectures and discussions during the conference "Theory and Practice of Geometric Modeling". The event has been organized by the Wilhelm-Schickard-Institut fiir Informatik, Universitat Tiibingen and took place at the Heinrich-Fabri-Institut in Blaubeuren from October 3 to 7, 1988. The conference brought together leading experts from academic and industrial research institutions, CAD system developers and experien­ ced users to exchange their ideas and to discuss new concepts and future directions in geometric modeling. The main intention has been to bridge the gap between theoretical results, performance of existing CAD systems and the real problems of users. The contents is structured in five parts: A Algorithmic Aspects B Surface Intersection, Blending, Ray Tracing C Geometric Tools D Different Representation Schemes in Solid Modeling E Product Modeling in High Level Specifications The material presented in this book reflects the current state of the art in geometric modeling and should therefore be of interest not only to university and industry researchers, but also to system developers and practitioners who wish to keep up to date on recent advances and new concepts in this rapidly expanding field. The editors express their sincere appreciation to the contributing authors, and to the members of the program committee, W. Boehm, J. Hoschek, A. Massabo, H. Nowacki, M. Pratt, J. Rossignac, T. Sederberg and W. Tiller, for their close cooperation and their time and effort that made the conference and this book a success.

A Algorithmic Aspects.- A Useful Polynomial Representation of Multiply Continuous Functions in the Unit Domain.- Computing B-Spline Control Points.- Approximate Parametrization of Algebraic Curves.- Geometric Modeling of Smooth Surfaces Using Triangular Patches.- The Generation of Ship Hulls with Given Design Parameters Using Tensor Product Surfaces.- Filling Polygonal Holes with Rectangular Patches.- Mesh Fairing GC1 Surface Generation Method.- Bernstein-Bézier Representation of Solid Modeling.- Constructive Solid Geometry with Sculptured Primitives Using Inner and Outer Sets.- A Uniform Representation Scheme for Freeform Geometric Modelling.- B Surface Intersections, Blending, Ray Tracing.- The Generalized Inverse Matrix and the Surface-Surface Intersection Problem.- Using Plane Vector Fields to Obtain all the Intersection Curves of Two General Surfaces.- Topological Considerations in Blending Boundary Representation Solid Models.- Blend Design as a Boundary-Value Problem.- Cyclide Blending in Solid Modelling.- Some Remarks on Cyclides in Solid Modeling.- Ray Tracing of Boundary Models with Implicit Blend Surfaces.- Ray Tracing Parametric Surfaces by Subdivision in Viewing Plane.- C Geometric Tools.- A Coordinate-Free Approach to Geometric Programming.- Containment Algorithms for Objects in Rectangular Boxes.- D Different Representation Schemes in Solid Modeling.- Integrated Polytrees: A Generalized Model for the Integration of Spatial Decomposition and Boundary Representation.- On Boundary to CSG and Extended Octrees to CSG Conversions.- Relationship Between S-Bounds and Active Zones in Constructive Solid Geometry.- Solid Modeling Schemes and Solid Reconstruction.- The Use of Geometric Models in Robotic Applications.- Experiences Using Adjacency Analysis forBuilding Topology Structures.- Information Structures and Database Support for Solid Modeling.- E Product Modeling and High Level Specifications.- Intelligent CAD-Systems Based on Technical Associative Modelling.- Graphical Interaction on Procedural Object Descriptions.- Feature Oriented System Design for Geometric Modeling.- Matching Measured Components to Solid Models.- Dimension-Driven Geometry in CAD: A Survey.- Representation and Communication in Geometric Modelling.- List of Authors.