Curves and Surfaces for CAGD, Fourth Edition: A Practical Guide (Computer Science and Scientific Computing) [Hardcover]

Gerald Farin (Author)

Book Description

ISBN-10: 0122490541 | ISBN-13: 978-0122490545 | Publication Date: October 8, 1996 | Edition: 4

This unified treatment of curve and surface design concepts is the Fourth Edition of the popular text, Curves and Surfaces for Computer-Aided Geometric Design, Third Edition (Academic Press, 1992). Assuming only a background in calculus and basic linear algebra, this revised and updated classic is highly accessible and should be of interest to a wide audience; from computer graphics hobbyists to software developers for CAD/CAM systems. The authors informal style makes this book very reader-friendly, and the IBM disk included in the back of the book will allow the user to gain first-hand experience with the concepts as they are explained.
This book focuses on Bezier and B-spline methods for curves, rational Bezier and B-spline curves, geometric continuity, spline interpolation, and Coons methods. In this Fourth Edition, the content has been thoroughly revised and updated to include a newchapter on recursive subdivision, new material on nonrectangular topology, surface faceting, stereo lithography, and new sections on triangulations and scattered data interpolants. The disk provided in the back of the book has also been updated to include all of the data sets and the C code used in the book.

Covers tensor product Bezier surfaces
Includes a chapter on recursive subdivisions
Incorporates new material on surface faceting, stereo lithography, and nonrectangular topology
Provides many C programs and data sets on the IBM disk included with the book

Editorial Reviews

Review

From the Reviews of the Second Edition
"The book is beautifully geometric, profusely illustrated, and is supported by an extensive bibliography consisting of more than 350 citations. Farin's informal, readable style and the exercises of varying degrees of difficulty make this an ideal text for an introductory course at the advanced undergraduate or graduate levels."
TONY DEROSE
UNIVERSITY OF WASHINGTON, SIAM NEWS
--This text refers to an out of print or unavailable edition of this title.

About the Author

Professor Gerald Farin currently teaches in the computer science and engineering department at Arizona State University. He received his doctoral degree in mathematics from the University of Braunschweig, Germany, in 1979. His extensive CAGD experience includes working as a research mathematician in a computer-aided development for Daimler-Benz, serving on the executive committee of the ASU PRISM project, and speaking at a multitude of symposia and conferences. Farin has authored and edited several books and papers, and he is editor-in-chief of Computer Aided Geometric Design.

Product Details

• Hardcover: 429 pages
• Publisher: Academic Press; 4 edition (October 8, 1996)
• Language: English
• ISBN-10: 0122490541
• ISBN-13: 978-0122490545
• Product Dimensions: 9.2 x 6.2 x 1.1 inches
• Shipping Weight: 1.9 pounds
• Average Customer Review: 5.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,569,927 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

13 of 15 people found the following review helpful:

5.0 out of 5 stars My primary reference for curves and surfaces on computers, April 20, 2000

By 

Christopher Lee-Messer - See all my reviews

This review is from: Curves and Surfaces for CAGD, Fourth Edition: A Practical Guide (Computer Science and Scientific Computing) (Hardcover)

An excellent, in-depth treatment of the subject of representing curves and surfaces on a computer. Written in a clear expository style, it covers the mathematics and algorithms behind Bezier and related classes of curves. Contributed sections on the differential geometry of curves and surfaces provide an excellent introduction to the mathematical framework behind the algorithms. Though not for the casual reader, Farin's book is a perfect reference for the programmer or architect of computer aided design software. I recommend it highly.

5.0 out of 5 stars An Exquisite demonstration of how Applied and Theoretical Mathematics can work together, October 1, 2010

By 

Herbert L Calhoun "paulocal" (Falls Church, VA USA) - See all my reviews
(REAL NAME)   

This review is from: Curves and Surfaces for CAGD, Fourth Edition: A Practical Guide (Computer Science and Scientific Computing) (Hardcover)

This is a beautifully illustrated use of the principles of differential geometry as it applies to practical manufacturing design problems.

The book demonstrates how any engineering drawings -- once only visualizable as "blocked out cubic shapes" (and formerly capable of being rendered into stamps and dies only via "French Curves") -- now can be easily transformed into the projections of three-dimensional parametric surfaces, where the points in the drawings are addressed individually as a triple of Euclidean coordinates on lines and surfaces in a mathematical vector space.

The author shows how an independent coordinate system, in an arbitrary vector space, is the correct language that lends itself best to mathematical explanation as well as to computer implementation of manufacturing design renderings.

Using the methodology of vector spaces, affine maps, and the technique of "piecewise linear interpolation," he takes us step-by-step through the history of computer Aided Graphic Design (CAGD). A crescendo is reached in chapter three, where he introduces the surprisingly simple algorithm of de Casteljau (the acknowledged father of CAGD), and as the saying goes, "the rest is history." From there onwards, nothing is left to the imagination: all formulations are worked out in exquisite detail with "end-of-chapter" exercises for the reader to ponder.

Actual diagrams and renderings from the Mercedes Benz design floor and a computer disk with all examples worked out, completes a tour de force at the intersection of applied and theoretical mathematics, the likes of which are unlikely to be seen again. Five stars!