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A sampler of useful computational tools for applied geometry, computer graphics, and image processing
Cohen-Or D. (ed), Greif C., Ju T., Mitra N., Shamir A., Sorkine-Hornung O., Zhang H., CRC Press, Inc., Boca Raton, FL, 2015. 246 pp.  Type: Book (978-1-498706-28-5)
Date Reviewed: Mar 3 2016

Performing skillful manipulations with digital objects is not only a lot of fun for the enthusiast, but it also provides a great deal of knowledge and experience related to a variety of socially useful applications like identification of x-ray or ultrasonographic (USG) images with some useful suggestions of the diagnosis for the therapist. The areas of application are as wide as the research in computer graphics. However, those with a mathematical background seem to hold the most potential to build software that can challenge such competitive advantages. With the aim of helping researchers, students, graphical developers, practitioners, and enthusiasts to achieve this objective, geometric problems are presented step-by-step with the support of mathematical background, art, and source code. This book is written by educators to be used in a computer graphics course.

Something readers will find particularly attractive is the light approach to treating the mathematical apparatus as a tool to develop graphical applications. Another attribute of this book is the graphical design that appears after the brief introductory part. Each of the 13 chapters is presented in a few sentences, supported with a graphical object. The language of the course material is light, simple, and particularly gripping, making it attractive to the reader with any level of mathematical or computer graphics knowledge. The chapters discuss analytical geometry, linear algebra, least-square solutions, principal component analysis, singular value decomposition, spectral transform, the solution of linear systems, Laplace and Poisson equations, curvatures via differential geometry, dimensionality reduction, scattered data interpolation, topology, graphs and images, and skewing schemes.

I like this title as very expressive; however, my objection is that it may mislead some readers who understand computational tools as add-ons or software supporting graphical problem-solving tools. However, at the very beginning of the book, the “About this Book” section states, “This book presents ... some mathematical tools that are useful in many domains such as computer graphics, image processing, computer vision, digital geometry processing and geometry in general.” Overall, I can heartily recommend this title to anyone interested in learning the mathematical fundamentals required to develop computer graphics.

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Reviewer:  Jolanta Mizera-Pietraszko Review #: CR144203 (1605-0303)
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Computational Geometry And Object Modeling (I.3.5 )
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