Theory and practice of geometric modeling [result of the lectures and discussions during the conference

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. Front Matter....Pages I-X Front Matter....Pages 1-1 A Useful Polynomial Representation of Multiply Continuous Functions in the Unit Domain....Pages 3-16 Computing B-spline Control Points....Pages 17-32 Approximate Parametrization of Algebraic Curves....Pages 33-54 Geometric Modeling of Smooth Surfaces using Triangular Patches....Pages 55-64 The Generation of Ship Hulls with Given Design Parameters Using Tensor Product Surfaces....Pages 65-79 Filling Polygonal Holes with Rectangular Patches....Pages 81-91 Mesh Fairing GC 1 Surface Generation Method....Pages 93-108 Bernstein-Bézier Representation of Solid Models....Pages 109-125 Constructive Solid Geometry with Sculptured Primitives Using Inner and Outer Sets....Pages 127-142 A Uniform Representation Scheme for Freeform Geometric Modelling....Pages 143-163 Front Matter....Pages 165-165 The generalized inverse matrix and the surface-surface intersection problem....Pages 167-185 Using Plane Vector Fields to Obtain All the Intersection Curves of Two General Surfaces....Pages 187-204 Topological considerations in blending boundary representation solid models....Pages 205-220 Blend Design as a Boundary-Value Problem....Pages 221-234 Cyclide Blending in Solid Modelling....Pages 235-245 Some Remarks on Cyclides in Solid Modeling....Pages 247-252 Ray Tracing of Boundary Models with Implicit Blend Surfaces....Pages 253-271 Ray Tracing Parametric Surfaces by Subdivision in Viewing Plane....Pages 273-287 Front Matter....Pages 289-289 A Coordinate-Free Approach to Geometric Programming....Pages 291-305 Containment Algorithms for Objects in Rectangular Boxes....Pages 307-325 Front Matter....Pages 327-327 Integrated Polytrees: A Generalized Model for the Integration of Spatial Decomposition and Boundary Representation....Pages 329-348 On Boundary to CSG and Extended Octrees to CSG Conversions....Pages 349-367 Relationship Between S-bounds and Active Zones in Constructive Solid Geometry....Pages 369-382 Solid Modeling Schemes and Solid Reconstruction....Pages 383-401 The use of geometric models in robotic applications....Pages 403-417 Experiences Using Adjacency Analysis for Building Topology Structures....Pages 419-432 Information Structures and Database Support for Solid Modeling....Pages 433-447 Front Matter....Pages 449-449 Intelligent CAD-Systems based on Technical Associative Modelling....Pages 451-467 Graphical Interaction on Procedural Object Descriptions....Pages 469-482 Feature Oriented System Design for Geometric Modeling....Pages 483-498 Matching Measured Components to Solid Models....Pages 499-507 Dimension-driven Geometry in CAD : A Survey....Pages 509-523 Representation and Communication in Geometric Modelling....Pages 525-544 Back Matter....Pages 545-547 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.