Bezier and B-Spline Techniques [Hardcover]

Hartmut Prautzsch (Author), Wolfgang Boehm (Author), Marco Paluszny (Author)

Book Description

ISBN-10: 3540437614 | ISBN-13: 978-3540437611 | Publication Date: October 3, 2002 | Edition: 1

This book provides a solid and uniform derivation of the various properties Bezier and B-spline representations have, and shows the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer Aided Geometric Design and provides a clear and illustrative presentation of the basic principles, as well as a treatment of advanced material including multivariate splines, some subdivision techniques and constructions of free form surfaces with arbitrary smoothness. The text is beautifully illustrated with many excellent figures to emphasize the geometric constructive approach of this book.

Editorial Reviews

Review

From the reviews: This excellent book gives a well-focused introduction to the essential concepts of computer aided geometric design. The authors provide a solid and unified derivation of the various properties of Bézier and B-spline representations. These piecewise polynomial representations have become the major tool to handle curves and surfaces in various applications, such as computer-aided design and computer graphics. In addition, the authors discuss a number of advanced concepts, including multivariate splines, certain subdivision techniques, and free-form surface splines. [...] The material presented in this book is visualized by many carefully prepared figures, which will be of great help for understanding the theoretical concepts. In addition, the authors have provided a number of useful exercises (without solutions). The book can be used as a textbook for courses at the graduate and intermediate undergraduate levels, for students of mathematics, computer science and engineering, and for self study. It will also be a useful reference book for researchers and practitioners in the field of computer aided geometric design and its various applications. Bert Jüttler, AMS 2004 "The book provides a clear and illustrative presentation of the basic principles in computer-aided geometric design. It is addressed mainly to the students and teachers in mathematics, computer science and engineering sciences. At the end of each chapter several problems are proposed." (Dana Petcu, Zentralblatt MATH, Vol. 1033 (8), 2004) "The book provides a basic presentation of the most important techniques in Computer-aided Geometric Design. The illustrative style gives a clear understanding of the subject and makes it well suited for students or lecturers in mathematics and computer sciences. … Each chapter comes with a small supplement of exercises." (H. G. Feichtinger, Monatshefte für Mathematik, Vol. 142 (3), 2004) "This excellent book gives a well-focused introduction to the essential concepts of computer aided geometric design. … The material presented in this book is visualized by many carefully prepared figures, which will be of great help for understanding the theoretical concepts. In addition, the authors have provided a number of useful exercises. The book can be used as a textbook … . It will also be a useful reference book for researchers and practitioners in the field of computer aided geometric design … ." (Bert Jüttler, Mathematical Reviews, 2004 e) "Computer Aided Geometric Design (CAGD) deals with the algorithmic aspects of curves and surfaces. … the book definitely serves as a solid introduction to recent literature on CAGD. It is based on courses taught by the authors, and the book shows that the material has been thoroughly tested and revised in classrooms. … The book is highly recommended, both as a textbook for courses on geometric computing and as a self-contained introduction to the field of Computer Aided Geometric Design." (G. Vegter, Nieuw Archief voor Wiskunde, Vol. 7 (2), 2006)

Product Details

• Hardcover: 304 pages
• Publisher: Springer; 1 edition (October 3, 2002)
• Language: English
• ISBN-10: 3540437614
• ISBN-13: 978-3540437611
• Product Dimensions: 9.4 x 6.5 x 0.9 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 3.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #2,425,713 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

14 of 15 people found the following review helpful:

3.0 out of 5 stars Good reference maybe, August 8, 2006

By 

Fletcher Dunn (Chicago, Illinois) - See all my reviews
(REAL NAME)   

This review is from: Bezier and B-Spline Techniques (Hardcover)

I'm not sure what sort of person would find this book useful. If you want to LEARN about Bezier or B-Spline curves, then I don't think this book is for you. The authors' stated goal was to "provide a solid and uniform derivation" of Bezier and B-Spline properties. I believe that they have succeeded, almost every factoid I've seen in other books is included and proved rigorously. What is NOT included is any sort of meaningful explanation of the concepts. The material is presented at a breakneck pace, with everything presented exactly once, and most often in mathematical notation rather than in English. This is a good way to pack a lot of material into a few pages, but it makes for pretty difficult reading. I really don't see how a person could possibly follow the exposition in this book unless they basically already knew the material.

If you already are familiar with Bezier and B-Spline techniques, or perhaps you are an expert in a related field like approximation theory, then you might find this useful.

So if the Authors acheived their stated goal, then why only the 3-star rating? I've recently bought quite a few of these books on splines, in preperation to write a chapter in my own (introductory) 3d math book. Most of the material in this book can be found in other books. Of course, all of the books have significant overlap, since they are covering the same subject. But if you could have a book that covers most of the same material AND also has more exposition, I'd go for the one with the more exposition. I don't think there's enough unique material in this book to trade off the loss of the much more graceful exposition in the other books.

In particular, if you're interested in *learning* about Bezier curves or B-Splines, I found these two books much more accessible:

An Introduction to Splines for use Computer Graphics and Geometric Modeling by Bartels et al. has a much slower pace - paradoxially this means that if you're learning the material, you will be able to read it FASTER since you can maintain a constant pace. It focuses on B-Splines and only stops breifly to mention Bezier curves as a general case.

The other book is Curves and Surfaces for COmputer Aided Geometric Design by Farin. He introduces Bezier curves and fully develops them, at a reasonable pace, before discussing B-splines. I personally found this approach to be better from a teaching perspective, since B-Splines are more abstract and Bezier curves are easier to understand. (Be warned that I have a rather old editition, the 2nd, I believe he's on the 5th now. I don't know what all has changed since then.)