Numerical Geometry of Non-Rigid Shapes (Monographs in Computer Science) Review

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(More customer reviews)The book is accompanied by a website [...] that hosts additional materials such as lecture slides, exercises, code tutorials and examples, data, links to relevant software, and will host much more stuff as it grows. Materials from the site are intended for students, as an enhancement to the text, as well as for teachers preparing courses on relevant subjects.

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Deformable objects are ubiquitous in the world surrounding us, on all levels from micro to macro. The need to study such shapes and model their behavior arises in a wide spectrum of applications, ranging from medicine to security. In recent years, non-rigid shapes have attracted growing interest, which has led to rapid development of the field, where state-of-the-art results from very different sciences - theoretical and numerical geometry, optimization, linear algebra, graph theory, machine learning and computer graphics, to mention several - are applied to find solutions.This book gives an overview of the current state of science in analysis and synthesis of non-rigid shapes. Everyday examples are used to explain concepts and to illustrate different techniques. The presentation unfolds systematically and numerous figures enrich the engaging exposition. Practice problems follow at the end of each chapter, with detailed solutions to selected problems in the appendix. A gallery of colored images enhances the text.This book will be of interest to graduate students, researchers and professionals in different fields of mathematics, computer science and engineering. It may be used for courses in computer vision, numerical geometry and geometric modeling and computer graphics or for self-study.

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The Geometry Toolbox for Graphics and Modeling Review

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(More customer reviews)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.

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Curves and Surfaces in Geometric Modeling: Theory & Algorithms (The Morgan Kaufmann Series in Computer Graphics) Review

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(More customer reviews)This is a great book, definitely the best among the various books on geometric design and CAGD (other good ones include Farin, Mortsenson, Piegl and Tiller, Hoscheck and Lasser). It is not as encyclopedic as the sources listed above, but it a lot more coherent and a lot clearer, because it follows the unifying concept of blossoming. As a result, one gets multiple complementary views of polynomial curves and surfaces: algebraic, geometric, combinatorial, and algorithmic. For example, we can see where the Bernstein polynomials come from, instead of mysteriously being dropped from the sky. The systematic use of blossoms (polar forms) is particularly elegant in the presentation of surfaces, where it clarifies greatly the differences between rectangular and triangular patches. The discussion of subdivision versions of the de Casteljau algorithm is very thorough and unique. Gallier's book is also the only book to discuss subdivision surfaces in some detail (Doo-Sabin, Catmull-Clark, and Loop). In particular, an analysis of the convergence of Loop's scheme is given. For this, the author gives a remarkable crash course on the discrete Fourier transform. However, this chapter is too dense and should have been split. Also, much more pictures are needed. It seems that the author was in a rush. The appendix on vector spaces is gorgeous, and the one on differentials is also excellent. This book is highly recommended to mathematically inclined readers interested in geometric modeling and computer graphics. Too bad that applications to medicine such as organ modeling, or to computer animation, are not presented. Nevertheless, Mathematica code is provided for most of the algorithms. A web site would be helpful.

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Geometric Transformations for 3D Modeling Review

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(More customer reviews)Pedagogically, Mortenson's presentation is easy for a reader to follow. Accompanied by generous numbers of diagrams. He gives understandable interpretations of how matrices are used to represent different types of transformations. The underlying geometrical rationale is clear.
En route, the reader is gently introduced to group theory. For finite groups. A way to bind geometry and symmetry. Interestingly, the notation he uses for the symmetries and groups is Schonflies. In 1982, this was already being phased out by crystallographers, in favour of International notation. But maybe mathematicians prefer the older style.
There is also a quick discussion of tensors. Giving rise to contra and covariant vectors. And the metric tensor is introduced as a key idea. All this is a jumping off point for physicists studying General Relativity, though it is not actually mentioned by name.

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