Triangulations and Applications (Mathematics and Visualization) Review

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(More customer reviews)This is an outstanding book. It is clearly written and goes into great detail. There is source code available that is very well designed and clearly commented. (search for Triangulation Template Library) There are ample illustrations to help you visualize the algorithms.
It is a short book but very complete. It has an academic flavor with definitions, theorems, lemmas and extensive references. There are exercises at the end of the chapters so it was designed to be useful as a textbook for a college computer science course.
I bought it to learn the algorithms and techniques on my own, with an eye toward applying them in geometric modeling for computer games. I found it easy to follow and skipped many of the proofs on the first reading. There are several code snippets throughout the text, some are give in pseudo-code and other are C++. They use OpenGL and GLUT to demonstrate the use of the library. The triangulation library is C++ and not directly tied to OpenGL and should be applicable to Direct3D or other graphics APIs.

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This book will serve as a valuable source of information about triangulations for the graduate student and researcher. With emphasis on computational issues, it presents the basic theory necessary to construct and manipulate triangulations. In particular, the book gives a tour through the theory behind the Delaunay triangulation, including algorithms and software issues. It also discusses various data structures used for the representation of triangulations.

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

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(More customer reviews)Numerical geometry of non-rigid shapes is the first attempt to present a focused and broad study of topics in non-rigid shape analysis. The book presents theoretical foundations, methods, algorithms and applications involving non-rigid shapes in different fields including computer vision, pattern recognition, and computer graphics. A special focus is made on practical value of the book - it is accompanied with code examples and references to commercial and public-domain software. Recommended as a textbook for computer vision and pattern recognition courses, reference for students and experts in the field.

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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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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.

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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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Curves and Surfaces for Geometric Design offers both a theoretically unifying understanding of polynomial curves and surfaces and an effective approach to implementation that you can bring to bear on your own work-whether you're a graduate student, scientist, or practitioner.

Inside, the focus is on "blossoming"-the process of converting a polynomial to its polar form-as a natural, purely geometric explanation of the behavior of curves and surfaces.This insight is important for far more than its theoretical elegance, for the author proceeds to demonstrate the value of blossoming as a practical algorithmic tool for generating and manipulating curves and surfaces that meet many different criteria.You'll learn to use this and related techniques drawn from affine geometry for computing and adjusting control points, deriving the continuity conditions for splines, creating subdivision surfaces, and more.

The product of groundbreaking research by a noteworthy computer scientist and mathematician, this book is destined to emerge as a classic work on this complex subject.It will be an essential acquisition for readers in many different areas, including computer graphics and animation, robotics, virtual reality, geometric modeling and design, medical imaging, computer vision, and motion planning.
* Achieves a depth of coverage not found in any other book in this field.* Offers a mathematically rigorous, unifying approach to the algorithmic generation and manipulation of curves and surfaces. * Covers basic concepts of affine geometry, the ideal framework for dealing with curves and surfaces in terms of control points.* Details (in Mathematica) many complete implementations, explaining how they produce highly continuous curves and surfaces.* Presents the primary techniques for creating and analyzing the convergence of subdivision surfaces (Doo-Sabin, Catmull-Clark, Loop).* Contains appendices on linear algebra, basic topology, and differential calculus.

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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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Written from a mathematical standpoint accessible to students, teachers, and professionals studying or practicing in engineering, mathematics, or physics, the new second edition is a comprehensive introduction to the theory and application of transformations. Presenting the more abstract foundation material in the first three chapters, Geometric Transformations in 3D Modeling reduces the clutter of theoretical derivation and development in the remainder of the text and introduces the operational and more application-oriented tools and concepts as the need arises. It assumes the reader has already taken analytic geometry and first-year calculus and has a working knowledge of basic matrix and vector algebra. This self-contained resource is sure to appeal to those working in 3D modeling, geometric modeling, computer graphics, animation, robotics, and kinematics. Distinctive Features- Explores and develops the subject in much greater breadth and depth than other books, offering readers a better understanding of transformation theory, the role of invariants, the uses of various notation systems, and the relations between transformations.- Describes how geometric objects may change position, orientation, or even shape when subjected to mathematical operations, while properties characterizing their geometric identity and integrity remain unchanged.- Presents eigenvalues, eigenvectors, and tensors in a way that makes it easier for readers to understand.- Contains revised and improved figures, with many in color to highlight important features.- Provides exercises throughout nearly all of the chapters whose answers are found at the end of the book.

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