Nonuniform rational B-splines (NURBS) are used in modeling curves and surfaces such as animated objects, aircraft wings, or other engineering parts. The basic idea is to produce a patchwork of pieces of mathematically simpler curves or surfaces that, when joined in a suitably smooth fashion across boundaries, closely approximate the object being modeled so that calculations can be performed.

This field is perhaps 40 years old, and with most of the key practitioners, including the book’s author, either alive or only recently deceased, the time is ripe for an overview with an added historical perspective, including photographs provided by several of these key workers.

The material is aimed at those who need to understand NURBS for their work. Typically, these will be practicing engineers or senior or postgraduate students. The author claims that this book could thus be the basis for a course for such students. Unfortunately, he tends to assume that readers already understand some of the underlying terminology and concepts of geometry, so the work will be of more use to current practitioners and those with geometric insight. Nevertheless, the book is well laid out, and almost free of misprints. It contains excellent diagrams and ample relevant algorithms, and is easy to follow.

Chapter 1 introduces the basic concepts of parametric curves and surfaces, and piecewise definition and continuity. Robin Forrest provides the historical context for the next chapter, on Bézier curves. It introduces control polygons, blending functions, matrix representation, derivatives of curves, and continuity. The first algorithm in the text, for the calculation of points on a Bézier curve, appears here. All of the algorithms are presented in an easy-to-read pseudocode, and a supplementary Web site contains C implementations.

Rich Reisenfeld puts the work of Bézier, Coons, and others in context, after which two chapters present the solid material at the heart of general B-splines and rational B-splines. This completes the first half of the book, on curves. The coverage is excellent, and modelers should find what they need either here or in the cited works. The material flows but can also be used in a cookbook fashion. A historical contribution from Elaine Cohen, Tom Lyche, and Rich Reisenfeld helps draw the work together, and the section and algorithm on knot removal are especially good.

Following an introduction by Lewis Knapp, the second half of the book deals with surfaces in a similar fashion. The first chapter here describes Bézier surfaces, using the previous work as the starting point. The next two chapters cover B-spline surfaces and rational B-spline surfaces and follow a similar course to the first half. The algorithms, appropriately, become more frequent. The sections on weighting factors could be expanded, as could that on sweep surfaces, but overall the work is coherent and is drawn together by the perspectives provided by Ken Versprille and by the author.

Some exercises are provided, but perhaps not enough for a senior course. A file format for interchange of B-spline surface descriptions is also given, and various useful algorithms are gathered into an appendix. The reference list is good, although partially driven by the historical material. The index should be longer, however. The associated Web site will be useful to C coders.

As a combination survey and textbook, the book works well. Reading it was a pleasure. Some supplemental material would be needed in order to use it as the basis of a course. The historical contributions are effective in providing rationale and interest, and I recommend this work as a starting point for the many potential users of NURBS.