Geometric Modeling: Methods and Applications (Computer Graphics: Systems and Applications)

This book is based on lectures presented at an international workshop on geometric modeling held at Hewlett Packard GmbH in Boblingen, FRG, in June 1990. International experts from academia and industry were selected to speak on the most interesting topics in geometric modeling. The resulting papers, published in this volume, give a state-of-the-art survey of the relevant problems and issues. The following topics are discussed: - Methods for constructing surfaces on surfaces: four different solutions to the multidimen­ sional problem of constructing an interpolant from surface data are provided. - Surfaces in solid modeling: current results on the implementation of free-fonn solids in three well established solid models are reviewed. - Box splines and applications: an introduction to box spline methods for the representation of surfaces is given. Basic properties of box splines are derived, and refinement and evaluation methods for box splines are presented in detail. Shape preserving properties, the construction of non-rectangular box spline surfaces, applications to surface modeling, and imbedding problems, are discussed. - Advanced computer graphics techniques for volume visualization: the steps to be executed in the visualization process of volume data are described and tools are discussed that assist in handling this data. - Rational B-splines: an introduction to the representation of curves and surfaces using rational B-splines is given, together with a critical evaluation of their potential for industrial application. Front Matter....Pages i-vii Methods for Constructing Surfaces on Surfaces....Pages 1-15 Surfaces in Solid Modeling....Pages 17-34 Box Splines and Applications....Pages 35-93 Advanced Computer Graphics Techniques for Volume Visualization....Pages 95-114 Rational B-splines....Pages 115-130 Scattered Data Interpolation and Applications: A Tutorial and Survey....Pages 131-160 Variational Principles in Curve and Surface Design....Pages 161-184 G n−1 — Functional Splines for Modeling....Pages 185-211 Numerically-Controlled Milling of CAD Surface Data....Pages 213-225 Aspects of Form Feature Modelling....Pages 227-250 Advanced Methods for Parametric Design....Pages 251-266 A Tutorial Introduction to Blossoming....Pages 267-286 Back Matter....Pages 287-288 This book is based on lectures presented at a workshop held at Hewlett Packard, Böblingen, FRG, in May 1990. The primary purpose of the workshop was to provide a forum for the exchange of technology between universities and industrial CAD/CAM centers. The workshop brought together international experts in the area of geometric modeling, industrial designers, and developers of industrial applications. Contributions cover a wide range of topics, including: - Surfaces on surfaces - Surfaces in solid modeling - Rational curves and surfaces - Scattered data methods - Smooth curve and surface design - Algebraic surfaces - NC-milling - Box splines - Feature modeling - Parametric design - Blossoming (or polarization).