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Mathematics for Computer Graphics

John Vince
Publication Date: 
Number of Pages: 
Uncergraduate Topics in Computer Science
[Reviewed by
Charles Ashbacher
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Over twenty years ago I taught an experimental course in elementary computer graphics for computer science majors. It turned out to be one of the most exciting courses that I ever taught. We used Turbo Pascal on microcomputers, so the computations were slow. Yet several of the students commented on how neat it was to see the modified image appear on the screen. One of the things I had them do was transform a stop sign in several ways. The highest level of mathematics we used was matrix transformations and I only had to spend about an hour explaining what they were and how the operations were performed. The students already knew how to program, so all they had to do was apply the operators.

There is no question that this book describes many of the essential operations of computer graphics in a manner that can be understood by the reader possessing the knowledge of standard courses in precalculus. Basic number systems, matrices, trigonometry, coordinate systems and vectors are all briefly summarized, leading up to a series of transformation expressions in two and three dimensions. More advanced topics follow, with interpolation, analytic and algebraic geometry, followed by differential and integral calculus, including partial derivatives. Alas, the calculus topics are introduced too fast and without enough graphics context to be worthwhile.

The real problem with this book is that there are no student exercises and too few figures illustrating the consequences of the operations. As for those students in my computer graphics class, seeing is knowing and appreciating; there is too little of that in here. Mathematics for computer graphics without the graphics is far too weak to generate the “oohs and aahs” that this field is capable of generating. This is fine as a math book but weak in the graphics part.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.