Applied Geometry for Computer Graphics and CAD (Springer Undergraduate Mathematics Series) [Paperback]

Duncan Marsh (Author)

Book Description

ISBN-10: 1852338016 | ISBN-13: 978-1852338015 | Publication Date: November 5, 2004 | Edition: 2nd

Focusing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD). Over 300 exercises are included, some new to this edition, and many of which encourage the reader to implement the techniques and algorithms discussed through the use of a computer package with graphing and computer algebra capabilities. A dedicated website also offers further resources and useful links.

Editorial Reviews

Review

From the reviews: a nice introduction to the foundations of applications of geometry to computer graphics and computer-aided design….A useful textbook. Zentralblatt MATH Mathematics students often ask where they can find a nice introduction to computer graphics and computer-aided design; professors have also been known to pose the same question. They will all find an answer here: Marsh’s book should guide them effectively and painlessly towards the applications of mathematics and geometry in graphics and CAD. Computer-Aided Design 32 (2000) From the reviews of the second edition: "This is a mathematics textbook on the basics of the geometry involved in computer graphics and computer-aided design, written at an undergraduate level suitable for students of mathematics, computer science, and engineering. … All of the book’s topics are presented in a clean and concise way, with nice illustrations and attention to both geometric ideas and practical issues of computing. … This book would be useful for instructors who want a specific reference … ." (Adam Coffman, Mathematical Reviews, 2005h) "Images generated by a computer are ubiquitous, they are used in science, in engineering, and by the entertainment business. This textbook is an introduction to the mathematics behind these images. … This exposition is intended for a broad audience with basic mathematical knowledge (vectors, matrices, calculus)." (P. Schmitt, Monatshefte für Mathematik, Vol. 151 (4), 2007)

From the Back Cover

Focusing on the manipulation and representation of geometrical objects, this book explores the application of geometry to computer graphics and computer-aided design (CAD). An introduction to transformations of the plane and three-dimensional space describes how objects can be constructed from geometric primitives and manipulated. This leads into a treatment of projections and the method of rendering objects on a computer screen by application of the complete viewing operation. Subsequently, the emphasis is on the two principal curve and surface representations, namely, Bézier and B-spline (including NURBS). As in the first edition, applications of the geometric theory are exemplified throughout the book, but new features in this revised and updated edition include: the application of quaternions to computer graphics animation and orientation; discussions of the main geometric CAD surface operations and constructions: extruded, rotated and swept surfaces; offset surfaces; thickening and shelling; and skin and loft surfaces; an introduction to rendering methods in computer graphics and CAD: colour, illumination models, shading algorithms, silhouettes and shadows. Over 300 exercises are included, some new to this edition, and many of which encourage the reader to implement the techniques and algorithms discussed through the use of a computer package with graphing and computer algebra capabilities. A dedicated website also offers further resources and links to other useful websites. Designed for students of computer science and engineering as well as of mathematics, the book provides a foundation in the extensive applications of geometry in real world situations.

Product Details

• Paperback: 368 pages
• Publisher: Springer; 2nd edition (November 5, 2004)
• Language: English
• ISBN-10: 1852338016
• ISBN-13: 978-1852338015
• Product Dimensions: 9.2 x 6.9 x 0.8 inches
• Shipping Weight: 1.4 pounds (View shipping rates and policies)
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,474,229 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

5 of 5 people found the following review helpful:

4.0 out of 5 stars Good computer graphics text, November 3, 2006

By 

A. T. Jones (Placitas, NM) - See all my reviews
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This review is from: Applied Geometry for Computer Graphics and CAD (Springer Undergraduate Mathematics Series) (Paperback)

This text has a novel approach to entry level computer graphics using homogeneous coordinates entirely. I struggled a bit with the use of these representations in perspective transformations. However once I got it I found the derivations and formulas to be easy to get and easy to use. The book has an extensive set of exercises with complete answers. I deducted one star because the theoretical aspects of homogeneous transformations could use expansion and simplification.

1 of 1 people found the following review helpful:

5.0 out of 5 stars An Excellent Workbook for Computer Graphics, February 9, 2011

By 

J. Wrenholt (Lincoln, NE United States) - See all my reviews
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This review is from: Applied Geometry for Computer Graphics and CAD (Springer Undergraduate Mathematics Series) (Paperback)

This book is unusual in a way I wish more math and computer science books would follow.

What you get is a brief description of the mathematics, the formulas that are useful, and a completely worked out example with illustrations. Although Computer is in the title there is no source code in the book. But the examples are worked out in such detail that is easy to translate them into code. And then you can use the numerical results of the examples to test each step in your own code. Beautiful.

So, looking for parametric formulas for quadrics, or quaternions, or frenet frames for Bezier curves? You will find just what you need to make it work for you. This book is packed only with the most useful real-world math for computer graphics.

What it leaves out is a lot of explanation as to why any of those topics may matter to you. It also avoids a lot of the theoretical math and extraneous factors that aren't essential to subject. This is also probably not the best tutorial for beginners but would be a great supplement to any of the core computer graphics textbooks.

My recommendations are Practical Linear Algebra: A Geometry Toolbox to get you up to speed with the math and Computer Graphics Using Open GL (2nd Edition) to get your head oriented.

Then you will understand why this book deserves 5 stars.