Nonuniform rational B-splines (NURBS) are used in modeling curvesand surfaces such as animated objects, aircraft wings, or otherengineering parts. The basic idea is to produce a patchwork of pieces ofmathematically simpler curves or surfaces that, when joined in asuitably smooth fashion across boundaries, closely approximate theobject being modeled so that calculations can beperformed.
This field is perhaps 40 years old, and with most of the keypractitioners, including the book’s author, either alive or onlyrecently deceased, the time is ripe for an overview with an addedhistorical perspective, including photographs provided by several ofthese key workers.
The material is aimed at those who need to understand NURBS fortheir work. Typically, these will be practicing engineers or senior orpostgraduate students. The author claims that this book could thus bethe basis for a course for such students. Unfortunately, he tends toassume that readers already understand some of the underlyingterminology and concepts of geometry, so the work will be of more use tocurrent practitioners and those with geometric insight. Nevertheless,the book is well laid out, and almost free of misprints. It containsexcellent diagrams and ample relevant algorithms, and is easy tofollow.
Chapter 1 introduces the basic concepts of parametric curves andsurfaces, and piecewise definition and continuity. Robin Forrestprovides the historical context for the next chapter, on Béziercurves. It introduces control polygons, blending functions, matrixrepresentation, derivatives of curves, and continuity. The firstalgorithm in the text, for the calculation of points on a Béziercurve, appears here. All of the algorithms are presented in aneasy-to-read pseudocode, and a supplementary Web site contains Cimplementations.
Rich Reisenfeld puts the work of Bézier, Coons, and othersin context, after which two chapters present the solid material at theheart of general B-splines and rational B-splines. This completes thefirst half of the book, on curves. The coverage is excellent, andmodelers should find what they need either here or in the cited works.The material flows but can also be used in a cookbook fashion. Ahistorical contribution from Elaine Cohen, Tom Lyche, and RichReisenfeld helps draw the work together, and the section and algorithmon knot removal are especially good.
Following an introduction by Lewis Knapp, the second half of thebook deals with surfaces in a similar fashion. The first chapter heredescribes Bézier surfaces, using the previous work as thestarting point. The next two chapters cover B-spline surfaces andrational B-spline surfaces and follow a similar course to the firsthalf. The algorithms, appropriately, become more frequent. The sectionson weighting factors could be expanded, as could that on sweep surfaces,but overall the work is coherent and is drawn together by theperspectives provided by Ken Versprille and by the author.
Some exercises are provided, but perhaps not enough for a seniorcourse. A file format for interchange of B-spline surface descriptionsis also given, and various useful algorithms are gathered into anappendix. The reference list is good, although partially driven by thehistorical material. The index should be longer, however. The associatedWeb site will be useful to C coders.
As a combination survey and textbook, the book works well. Readingit was a pleasure. Some supplemental material would be needed in orderto use it as the basis of a course. The historical contributions areeffective in providing rationale and interest, and I recommend this workas a starting point for the many potential users of NURBS.
