Shape Interrogation for Computer Aided Design and Manufacturing

Description

Shape interrogation is the process of extraction of information from a geometric model. It is a fundamental component of Computer Aided Design and Manufacturing (CAD/CAM) systems. The authors focus on shape interrogation of geometric models bounded by free-form surfaces. Free-form surfaces, also called sculptured surfaces, are widely used in the bodies of ships, automobiles and aircraft, which have both functionality and attractive shape requirements. Many electronic devices as well as consumer products are designed with aesthetic shapes, which involve free-form surfaces. This book provides the mathematical fundamentals as well as algorithms for various shape interrogation methods. From the reviews: "This book provides the mathematical fundamentals as well as algorithms for various shape interrogation methods including nonlinear polynomial solvers, intersection problems, differential geometry of intersection curves, distance functions, curve and surface interrogation, umbilics and lines of curvature, geodesics, and offset curves and surfaces. [… ] It may well be one of the most important books of the 2002s that has been written on shape interrogation for graduate students in mathematics, engineering, computer science, focusing on geometrical modeling and solid modeling. The book will inform and enlighten professionals in industry and therefore remains essential reading for them too. Currently there are several excellent books in the area of geometric modeling and in the area of solid modeling. The major contribution of this book lies in its skilful manner of providing a bridge between these two areas that is guaranteed to make the target audience cry out aloud with delight." Current Engineering Practice 2002-2003, Vol. 45, Issue 3-4 "This book gives a detailed description of algorithms and computational methods for shape interrogation [… ] The book can be used in a course for advanced graduate students and also as a reference text for researchers and practitioners in CAD/CAM. [… ] is a very detailed and complete book on topics that are important in both the theory and the practice of geometric modeling." L. Henrique de Figueiredo, Mathematical Reviews 2003 a "... This book by Patrikalakis and Maekawa is the first thorough, long overdue, look at this crucial area. [… ] It will serve well any researcher, either in academia or industry, working in the area of freeform design or manufacturing. This work continues from the point where the traditional geometric design and solid modeling books stop. ... Shape interrogation and computational geometry of freeform shapes have been a part of the geometric design and manufacturing community for a long time. This book makes efforts and is likely to become the 'Bible' for this area. As a high-quality produced book, it is a must reference for any advanced researcher or developer who works with splines and freeform representations. If you consider yourself one, this book should probably be on your bookshelf." G. Elber, Computer-Aided Design 35 (2003) 1053 Front Matter....Pages i-xvi Representation of Curves and Surfaces....Pages 1-33 Differential Geometry of Curves....Pages 35-48 Differential Geometry of Surfaces....Pages 49-72 Nonlinear Polynomial Solvers and Robustness Issues....Pages 73-108 Intersection Problems....Pages 109-160 Differential Geometry of Intersection Curves....Pages 161-180 Distance Functions....Pages 181-194 Curve and Surface Interrogation....Pages 195-230 Umbilics and Lines of Curvature....Pages 231-264 Geodesics....Pages 265-291 Offset Curves and Surfaces....Pages 293-365 Back Matter....Pages 367-408