Showing posts with label computer mathematics. Show all posts
Showing posts with label computer mathematics. Show all posts

Computer Graphics and Geometric Modeling Review

Computer Graphics and Geometric Modeling
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This book is a valuable reference for programmers that want a good introduction to geometric modeling. The book provides enough material to allow you to write many programs dealing with the covered topics. The algorithms outlined in the book are general. They can be adapted to a wide variety of problems, but you must fill in the details. Also, depending on your needs, you may need to consult more advanced books.

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This is a book for those interested in understanding how graphics programs work and how present-day computer graphics can generate reallistic-looking curves, surfaces, and solid objects. The book emphasizes the mathematics behind computer graphics and most of the required math is included in an appendix. The main topics covered are: -scan conversion methods; selecting the best pixels for generating lines, circles and other objects -geometric transformations and projections; translations, rotations, moving in 3d, perspective projections -curves and surfaces; construction, wire-frames, rendering, normals -other topics; CRTs, antialiasing, animation, color, perception, polygons, compression. With its numerous illustrative examples and exercises, the book makes a splendid text for a two-semester course in computer graphics for advanced undergraduates or graduate students. It also serves a fine reference for professionals in the computer graphics field.

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Introduction to Solid Modeling Review

Introduction to Solid Modeling
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I read the book " Introduction to solid modelling" & I liked it because it gives a first hand exposure to solid modelling to the engineering professionals who are on the brink of trying to understand solid modelling & its uses in their respective area of applications. It also helps the "C" savvy engineering application developers to understand the intricacies in developing a cad package using solid modelling techniques.

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

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

Geometric Modeling
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This book is a definitive introduction to geometric modeling. However, the sections on solid modeling and surface-surface intersection are lacking in depth. A serious reader may consider consulting books by Farin and Piegl for Geometric modeling and Hoffman/Mantyla for solid modeling.

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Describes and compares all the important mathematical methods for modeling curves, surfaces, and solids.Prepares the reader for more advanced topics, such as 3D modeling, CAD/CAM, animation, and scientific visualization.Incorporates references throughout the text to direct the reader to more specialized treatments of the subjects.Carefully designed illustrations and exercises support each mathematical concept presented.Offers hundreds of exercises to test the readers comprehension.


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Geometric Transformations for 3D Modeling Review

Geometric Transformations for 3D Modeling
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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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