Mathematics and Visualization

Bézier and B-Spline Techniques

Authors: Prautzsch, Hartmut, Boehm, Wolfgang, Paluszny, Marco

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  • ISBN 978-3-662-04919-8
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  • ISBN 978-3-540-43761-1
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Softcover $139.00
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  • ISBN 978-3-642-07842-2
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About this Textbook

Computer-aided modeling techniques have been developed since the advent of NC milling machines in the late 40's. Since the early 60's Bezier and B­ spline representations evolved as the major tool to handle curves and surfaces. These representations are geometrically intuitive and meaningful and they lead to constructive numerically robust algorithms. It is the purpose of this book to provide a solid and unified derivation of the various properties of Bezier and B-spline representations and to show the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer-aided Geometric Design (CAGD) with the intent to provide 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 arbitrarily smooth free-form surfaces. In order to keep the book focused, many further CAGD methods are ex­ cluded. In particular, rational Bezier and B-spline techniques are not ad­ dressed since a rigorous treatment within the appropriate context of projec­ tive geometry would have been beyond the scope of this book.

Reviews

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)


Table of contents (19 chapters)

  • Geometric fundamentals

    Prautzsch, Hartmut (et al.)

    Pages 3-8

  • Bézier representation

    Prautzsch, Hartmut (et al.)

    Pages 9-23

  • Bézier techniques

    Prautzsch, Hartmut (et al.)

    Pages 25-41

  • Interpolation and approximation

    Prautzsch, Hartmut (et al.)

    Pages 43-57

  • B-spline representation

    Prautzsch, Hartmut (et al.)

    Pages 59-75

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-662-04919-8
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-540-43761-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $139.00
price for USA
  • ISBN 978-3-642-07842-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Bézier and B-Spline Techniques
Authors
Series Title
Mathematics and Visualization
Copyright
2002
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-04919-8
DOI
10.1007/978-3-662-04919-8
Hardcover ISBN
978-3-540-43761-1
Softcover ISBN
978-3-642-07842-2
Series ISSN
1612-3786
Edition Number
1
Number of Pages
XIV, 304
Topics