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Mathematics for computer graphics (3rd ed.)
Vince J., Springer, New York, NY, 2010. 312 pp. Type: Book (978-1-849960-22-9)
Date Reviewed: Sep 29 2010

Many computer graphics students have difficulty understanding and applying the applicable mathematics. The mathematics required for computer graphics does not normally involve calculus, but it can be intense nonetheless. Extensive applications of algebra, trigonometry, analytical geometry, matrices, quaternions, and geometric algebra permeate the study and teaching of computer graphics. It is often hard to find sources in the mathematics curriculum where these topics can be learned at a suitable level. This slim volume could be a computer graphics student’s (and professor’s) next best friend.

The sequence of topics starts at the very beginning with a personal reflection on the author’s study of mathematics and an introduction to the book. The next chapter starts with a review of number systems, and basic algebra--for example, at the level of high school algebra--follows. Next, in order, are chapters on trigonometry, Cartesian coordinates, and vectors, followed by a lengthy chapter on transforms of vectors in two-dimensional and three-dimensional space. A pair of chapters on interpolation and curves and patches (for example, Bezier curves and splines) introduces handling approximations and fitting. Another long chapter on analytical geometry builds on the topics developed in the previous chapters on vectors and transforms. Barycentric coordinates are not often studied, but Vince makes them his next topic in the development of analytical geometry. A chapter on geometric algebra (for example, Clifford algebras) concludes the formal presentation of content. The last chapter has more than a dozen practical problems that are worked out at length.

The topics are developed linearly and coherently, the style of writing is crisp, and the approach is practical. Although the theory is light, rigorous detailed derivations on each topic--sometimes from more than one approach--are plentiful and characterize the author’s approach throughout the entire book. It is surprising to find really practical mathematics packaged in about 300 pages. For those studying or teaching computer graphics, this book will be a valuable companion to have on hand.

Reviewer:  Anthony J. Duben Review #: CR138420 (1107-0718)
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