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The NURBS Book (Monographs in Visual Communication) 2nd Edition

by Les A. Piegl (Author), Wayne Tiller (Author)
4.7 4.7 out of 5 stars 26 ratings
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Until recently B-spline curves and surfaces (NURBS) were principally of interest to the computer aided design community, where they have become the standard for curve and surface description. Today we are seeing expanded use of NURBS in modeling objects for the visual arts, including the film and entertainment industries, art, and sculpture. NURBS are now also being used for modeling scenes for virtual reality applications. These applications are expected to increase. Consequently, it is quite appropriate for The.N'URBS Book to be part of the Monographs in Visual Communication Series. B-spline curves and surfaces have been an enduring element throughout my pro­ fessional life. The first edition of Mathematical Elements for Computer Graphics, published in 1972, was the first computer aided design/interactive computer graph­ ics textbook to contain material on B-splines. That material was obtained through the good graces of Bill Gordon and Louie Knapp while they were at Syracuse University. A paper of mine, presented during the Summer of 1977 at a Society of Naval Architects and Marine Engineers meeting on computer aided ship surface design, was arguably the first to examine the use of B-spline curves for ship design. For many, B-splines, rational B-splines, and NURBS have been a bit mysterious.
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  1. ISBN-10
    3540615458
  2. ISBN-13
    978-3540615453
  3. Edition
    2nd
  4. Publisher
    Springer
  5. Publication date
    November 14, 1996
  6. Language
    English
  7. Dimensions
    6.1 x 1.5 x 9.25 inches
  8. Print length
    660 pages
  9. See all details
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Editorial Reviews

Review

"Piegl and Tiller offer an excellent source of information on NURBS (nonuniform rational B-spines), which fills a very large gap in the technical literature related to CAD/CAM/CAE. It is written for the average engineer with elementary knowledge of college mathematics and computing. It would be very useful to students, teachers, and designers of geometric modeling systems. A well-presented work, with abundant computer-generated figures." -- Choice

From the Back Cover

The NURBS book covers all aspects of non-uniform rational B-splines necessary to design geometry in a computer aided environment. Basic B-spline features, curve and surface algorithms, and state-of-the-art geometry tools are all discussed. Detailed code for design algorithms and computational tricks are covered too, in a lucid, easy-to-understand style, with a minimum of mathematics and using numerous worked examples. The book is a must for students, researchers, and implementors whose work involves the use of splines.
"Some years ago a few researchers joked about NURBS, saying that the acronym really stands for Nobody Understands Rational B-Splines write the authors in their foreword; they formulate the aim of changing NURBS to EURBS, that is, Everybody ... . There is no doubt that they have achieved this goal. ...
... I highly recommend the book to anyone who is interested in a detailed description of NURBS. It is extremely helpful for students, teachers and designers of geometric modelling systems. ..."
- H. Pottmann, Computer Aided Design, 1996

Product details

  • Publisher ‏ : ‎ Springer; 2nd edition (November 14, 1996)
  • Language ‏ : ‎ English
  • Paperback ‏ : ‎ 660 pages
  • ISBN-10 ‏ : ‎ 3540615458
  • ISBN-13 ‏ : ‎ 978-3540615453
  • Item Weight ‏ : ‎ 2.15 pounds
  • Dimensions ‏ : ‎ 6.1 x 1.5 x 9.25 inches
  • Customer Reviews:
    4.7 4.7 out of 5 stars 26 ratings

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4.7 out of 5 stars
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Top reviews from the United States

  • Wick Renner
    5.0 out of 5 stars Everything you need to know to make your own NURBS implementation
    Reviewed in the United States on September 22, 2021
    Verified Purchase
    I found this book to be very helpful. Using this book I was able to make my own NURBS implementation. The book explains NURBS in great detail to give the reader a good understanding of how they work. The math is all there as well as algorithms to do the NURBS calculations. Methods to calculate NURBS derivatives are given, but unfortunately integration is absent (something I need). The fitting section is a little vague where it references algorithms (specifically Forward Backward and LU Decomposition) but does not give an implementation. You have to use other sources for implementation of these algorithms, I found them in Numerical Recipes. The book seems to be meant for Computer Graphics describing the use of NURBS for 2D surfaces in 3D. Using NURBS in higher dimensions is not included. But for what is not in the book, enough information is given so that an inquisitive reader can figure it out on their own. Best NURBS book out there.
    2 people found this helpful
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  • Persnickety
    5.0 out of 5 stars A must have book for CG, starts with the basics and builds
    Reviewed in the United States on August 1, 2021
    Verified Purchase
    This book explains the basic ideas well, it does expect a certain level of math in the reader, but it really isn't something that a motivated reader can't get in a good online class or tutorial. The first few chapters really cleared up several issues I was confused around. I have not read the entire book, yet, but I don't need to finish to know that this is a must have book. Also, while pricey, it is worth it, the book is very thick, with lots of pseudocode many graphs and examples, and it includes chapter questions. (the book appears to be a popular college course book so a good time to get a (often) very lightly used book, is at the end of quarters/semesters when students are turning them in.
    One person found this helpful
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  • complex zeros
    4.0 out of 5 stars Index lacking
    Reviewed in the United States on May 22, 2014
    I have one pertinent thing to add to the other reviews: the index is quite lacking. I haven't yet been able to find anything I wanted to look up in the index.
    One person found this helpful
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  • Lee Jae Young
    5.0 out of 5 stars informative and convincing contents
    Reviewed in the United States on April 12, 2023
    Verified Purchase
    many examples, illustration. There are many helpful points for understanding
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  • loren snyder
    5.0 out of 5 stars THE book
    Reviewed in the United States on May 5, 2014
    Verified Purchase
    The only competition out there to Piegl and Tiller's seminal work is Gerald Farin's stuff. If you need to know about or use Bezier curves, B splines or NURBS, you need this book. The font being small and the wireframe diagrams being a bit hard to interpret are my only criticisms of this book...really, overall it is excellent and comprehensive.
    2 people found this helpful
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  • kmarinelli
    5.0 out of 5 stars Five Stars
    Reviewed in the United States on August 25, 2014
    Verified Purchase
    It arrived on time and was an excellent product.
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  • Larry Lukis
    5.0 out of 5 stars Perfect for the programmer working with NURBS.
    Reviewed in the United States on October 3, 1998
    I have a reasonable if dated math background, but I'm not a mathematician, I'm a programmer. I was able to work through enough of the math to extract very practical and useful knowledge for my graphics programming work.
    I've gone through 3 other graphics book trying to get enough clear information on NURBs, but they were all either inadequate or obscure.
    "The NURBS Book" is the one you want.
    17 people found this helpful
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  • "mervyn@ynnmail.com"
    4.0 out of 5 stars Excellent introduction to splines for the non-mathematician
    Reviewed in the United States on February 11, 2000
    One of the greates assets of this book is that it is fairly comprehensive while still using a minimum amount of mathematics. The style is lucid, easy to follow; the numerous C-like algorithms can be adapted to one's own use, and deal with the most important aspect of NURBS. This is easily the best introductory NURBS text. The only problem I see is the lack of discussion for ray-surface intersection tests, which are necessary if NURBS are to be rendered by raytracing. I recommend "The Nurbs Book" to any engineers and graphics professionals interested in curved surfaces.
    10 people found this helpful
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Top reviews from other countries

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  • Marco
    5.0 out of 5 stars Ottimo testo
    Reviewed in Italy on August 22, 2019
    Verified Purchase
    Ottimo testo. Consigliato a chiunque si voglia avvicinare in modo pratico all'implementazione di Bspline e NURBS.
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  • Marc Bedard
    5.0 out of 5 stars Five Stars
    Reviewed in Canada on February 25, 2017
    Verified Purchase
    This is still THE reference on the subject.
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  • 微笑みデブ
    5.0 out of 5 stars 実用的な技術書
    Reviewed in Japan on October 17, 2012
    Verified Purchase
    CAD プログラムで B-Spline を処理するのに必要な基礎的な知識がすぐに使える形で記述されています。数式も計算のためだけに記載してあるので、大学以上の数学が苦手でも途中で分からなくなることはありません。ただし、de Boor algorithm のみで B-Spline を計算しており、Blossom についての記述がないので、Knot insertion / removal が分かりにくいです。Hans Peter Seidel の "An Introduction to Polar Forms" という記事も一緒に読むと B-Spline がより扱いやすくなります。
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