The Geometry Toolbox for Graphics and Modeling

Rating:
Summary: Unique approach of many topics, but not much 3D
Review: 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.

Rating:
Summary: Unique approach of many topics, but not much 3D
Review: 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.

Rating:
Summary: been looking for this
Review: good focused coverage

Rating:
Summary: Good Fundamental Review
Review: I read this book cover to cover. Covers the affine geometry the best I have seen. Ample examples and figures.

Rating:
Summary: Good introduction to matrices for graphics
Review: 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.

Rating:
Summary: Good introduction to matrices for graphics
Review: 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.

Rating:
Summary: Best math book for graphics programmers I've found
Review: I've read quite a few math texts looking for an understanding of the math necessary for 3D graphics software. This was the first one that I was able to read straight through, like a novel. I highly recommend it for an understanding of 3D math. It has clear descriptions that build gradually.

Rating:
Summary: this book is terrible
Review: We used this book for the freshmen Linear Algebra and Geometry course at my school. If it wasn't for the teacher's lectures I would not have understood any of the content in this book at all. Most of the figures are thrown in to waste ink, confuse the reader, or (in very rare occasions) represent an equation graphically. This should not under any circumstances be used as a classroom textbook (or as a reference book, etc.).

Rating:
Summary: this book is terrible
Review: When I learn math I like to understand and be able to visualize the equation instead of memorizing it. This book does not bore you with equations and dry explanations; instead it gives you enough sketches and proofs to know how an equation comes about, and diagrams to explain the geometrical interpretation of the tools (matrix, eigenvalues, etc.) used regularly in computer graphics. For what it is intended to do, I doubt you can find one better than this. It really goes to show how much the authors understand the subject to be able to explain something so intuitively. I highly recommend this to people who are involved in computer graphics field and want to brush up on their math.

Rating:
Summary: Excellent introduction to linear algebra and geometry
Review: When I learn math I like to understand and be able to visualize the equation instead of memorizing it. This book does not bore you with equations and dry explanations; instead it gives you enough sketches and proofs to know how an equation comes about, and diagrams to explain the geometrical interpretation of the tools (matrix, eigenvalues, etc.) used regularly in computer graphics. For what it is intended to do, I doubt you can find one better than this. It really goes to show how much the authors understand the subject to be able to explain something so intuitively. I highly recommend this to people who are involved in computer graphics field and want to brush up on their math.