The Geometry Toolbox for Graphics and Modeling [Hardcover]

Gerald Farin (Author), Dianne Hansford (Author)

Book Description

ISBN-10: 1568810741 | ISBN-13: 978-1568810744 | Publication Date: August 1, 1998 | Edition: 1

The Geometry Toolbox takes a novel and particularly visual approach to teaching the basic concepts of two- and three-dimensional geometry. It explains the geometry essential for today's computer modeling, computer graphics, and animation systems. While the basic theory is completely covered, the emphasis of the book is not on abstract proofs but rather on examples and algorithms. The Geometry Toolbox is the ideal text for professionals who want to get acquainted with the latest geometric tools. The chapters on basic curves and surfaces form an ideal stepping stone into the world of graphics and modeling. It is also a unique textbook for a modern introduction to linear algebra and matrix theory.

Product Details

• Hardcover: 288 pages
• Publisher: A K Peters/CRC Press; 1 edition (August 1, 1998)
• Language: English
• ISBN-10: 1568810741
• ISBN-13: 978-1568810744
• Product Dimensions: 9.3 x 7.4 x 0.9 inches
• Shipping Weight: 1.4 pounds
• Average Customer Review: 4.4 out of 5 stars  See all reviews (8 customer reviews)
• Amazon Best Sellers Rank: #1,845,002 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

11 of 12 people found the following review helpful:

4.0 out of 5 stars Unique approach of many topics, but not much 3D, March 30, 2002

By 

E. Fletcher Dunn (Dallas, TX USA) - See all my reviews

This review is from: The Geometry Toolbox for Graphics and Modeling (Hardcover)

For many topics, this book provides more thorough coverage for beginners than other books, and is a good resource for building up your intuition about vectors and matrices. Especially good is his discussion of matrices and operations on matrices such as gaussian elimination.

A few minor things I didn't like:

1. The whole book has a slightly "mathematical" slant, as opposed to a "geometric" slant. In other words, contrary to the title, this book is actually more about linear algebra (pure mathematics) than about geometry. For example, solving systems of equations, gaussian elimination, and the like, really don't have anything to do with geometry. Likewise, the notation is more "mathematical" than "geometric" - using e1, e2, and e3 for the basis vectors rather than x, y, and z like everybody else.

2. The book covers many topics very well in 2D - the problem is that it doesn't cover much in 3D. Some topics, of course, extend naturally from 2D into 3D and so detailed discussion isn't necessary. Other's topics dont. For example, orientation in 3D, left-handed vs. right-handed coordinate spaces, perspective projection and homegenous coordinates, quaternions. Coverage of these topics would have added a lot.

3. Other people seem to like the diagrams, but I didn't think they were that good. I think a better way to describe the diagrams is that the book has *more* diagrams than most other books, but not necessarily better ones. I personally don't like hand-drawn illustrations. And 3D diagrams needs to be rendering using shading and perspective foreshortening - schemtic-style isometric diagrams are difficult to interpret. Another example, all of the elementary geometric transformations were discussed by showing the effect of the transformation on an object. This is wonderful - most books don't do this! The only problem is that the object he choses to use is a confusing-looking circle thingy. Using a very simple object, such as a teapot would have been much better.

All-in-all, this book has some unique coverage and I would recommend it, especially for the discussion of matrices and transformations, and nested coordiante spaces. The books tends to spend time on more "purely mathematical" subject matter, which is not a bad thing, just a warning. The information on 3D topics is conspicuously lean, which is somewhat of a negative. However, I was pleased with my purchase and was able to look at several things from a different perspective.

7 of 8 people found the following review helpful:

5.0 out of 5 stars Good introduction to matrices for graphics, November 7, 2000

By 

Peter S. Shirley (Salt Lake City, UT USA) - See all my reviews
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This review is from: The Geometry Toolbox for Graphics and Modeling (Hardcover)

I teach computer graphics and this is the best treatment of transformation matrices for geometry I have seen. It is a little jewel. It also has a nice treatment of basic linear algebra in terms of geometric operations. My favorite part was the discussion of Cramer's rule and Gaussian Elimination in terms of geometry. A wonderful read, and I found the figures to be very helpful.

5.0 out of 5 stars Great for visualization, September 18, 2008

By 

Carl-Erik Kopseng - See all my reviews
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Amazon Verified Purchase

This review is from: The Geometry Toolbox for Graphics and Modeling (Hardcover)

I had gone through a normal linear algebra course earlier, but when I needed to do a computer graphics class, I found out that my geometric understanding of linear algebra was weak. The professor then introduced me to this little jewel, which thoroughly lets you get a grip on the geometric aspects. Very recommended, but is now replaced by "Practical Linear Algebra: A Geometry Toolbox".