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Curves and surfaces in computer aided geometric design - Yamaguchi F.

Curves and surfaces in computer aided geometric design

Author: Yamaguchi F.
Publishers: Tokyo
Year of publication: 1988
Number of pages: 390
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Download: curvesandsurfacesincomputer1988.djvu

Fujio Yamaguchi
Curves and Surfaces in Computer Aided Geometric Design
Fujio Yamaguchi
Curves and Surfaces in Computer Aided Geometric Design
With 244 Figures and 9 Tables
Springer-Verlag
Berlin Heidelberg NewYo
London Paris Tokyo
Professor Fujio Yamaguchi
Department of Mechanical Engineering School of Science and Engineering Waseda University
3-4-1, Okubo, Shinjuku-ku, Tokyo 160/Japan
Originally published in Japanese as
Keizyo Syori Kogaku (1) & Keizyo Syori Kogaku (2)
© Nikkan Kogyo Shinbun Co.
ISBN 3-540-17449-4 Springer-Verlag Berlin Heidelberg New York ISBN 0-387-17449-4 Springer-Verlag New York Berlin Heidelberg
Library of Congress Catalogmg-in-Publication Data Yamaguchi, Fujio, 1935-
[Konpyuta disupurei ni yoru ęĺóá shon k5gaku. English]
Curves and surfaces in computer aided geometric design / Fujio Yamaguchi P cm Translation of. Konpyflta disupurei ni yoru keijo shori kogaku.
Bibliography. Includes index ISBN 0-387-17449-4 (U.S)
1 Geometrical drawing—Data processing 2 Engineering design—Data processing 3. Computer graphics I. Title
QA464 Y2813 1988 620' 00425'0285— dcl9 88-26569
This work is subject to copyright All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid Violations fall under the prosecution act of the German Copyright Law.
© Springer-Verlag Berlin Heidelberg 1988 Printed in Germany
The use of registered names, trademarks, etc in this publication does no the absence of a statement, that such names are exempt from the rel laws and regulations and therefore free for general use
Typesetting. H.Hagedorn, Berlin Offsetprinting Kutschbach, Berlin Bookbinding ¦ Ludentz & Bauer, Berlin
2161/3020-543210/Prmted on acid-free paper
Preface
This is an English version of the book in two volumes, entitled “Keijo Shori Kogaku (1), (2)” (Nikkan Kogyo Shinbun Co.) written in Japanese. The purpose of the book is a unified and systematic exposition of the wealth of research results in the field of mathematical representation of curves and surfaces for computer aided geometric design that have appeared in the last thirty years.
The material for the book started life as a set of notes for computer aided geometric design courses which I had at the graduate schools of both computer science, the university of Utah in U.S.A. and Kyushu Institute of Design in Japan. The book has been used extensively as a standard text book of curves and surfaces for students, practical engineers and researchers.
With the aim of systematic exposition, the author has arranged the book in 8 chapters:
Chapter 0: The significance of mathematical representations of curves and surfaces is explained and historical research developments in this field are reviewed.
Chapter 1: Basic mathematical theories of curves and surfaces are reviewed and summarized.
Chapter 2: A classical interpolation method, the Lagrange interpolation, is discussed. Although its use is uncommon in practice, this chapter is helpful in understanding Chaps. 4 and 6.
Chapter 3: This chapter discusses the Coons surface in detail, which is one of the most important contributions in this field.
Chapter 4: The fundamentals of spline functions, spline curves and surfaces are discussed in some detail.
Chapter 5: This chapter discusses the so-called Bezier curve and surface which are frequently used in practical applications.
Chapter 6: This chapter deals with Â-spline curves and surfaces, which are more general than the Bezier ones. Special emphasis is placed on this chapter in this book because B-spline curves and surfaces are expected to play an important role in the future.
Chapter 7: The last chapter discusses the rational polynomial curves which are capable of representing conic sections exactly.
The present author has learnt much from the published work of others, particularly from late Prof. S. A. Coons, Prof. M. Hosaka (Tokyo Denki University), Prof. A. R. Forrest (University of East Anglia), Prof. R. F. Riesen-feld (University of Utah), Prof. I. D. Faux (Cranfleld Institute of Technology),
VI
Preface
Prof. M. J. Pratt (Cranfield Institute of Technology) and he has drawn extensively on them. He has done his best to give credit where it is due.
Finally, the author’s thanks go to Mr. Harold Solomon for the translation from the original Japanese.
Hino, Tokyo, September 1988
Fujio Yamaguchi
Contents
On the Symbols Used in This Book.............................................. XI
0. Mathematical Description of Shape Information.............................. 1
0.1 Description and Transmission of Shape Information......................... 1
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