Beach intended this book as an introduction to the subject for students of mathematics, computer science, and engineering. A basic knowledge of linear algebra, calculus, and a little geometry, including conic sections, will enable the reader to follow the material. The author has steered a middle road between the overtly mathematical, notationally complex approach and the intuitive cookbook approach, making the book accessible to a wide audience. His credentials include stints at General Motors Research Laboratories and the Master Dimensions Group at North American Aviation. The latter experience leads to more material on conic sections than is found in other texts (the master dimensions approach seems to have gone out of fashion).

Chapter 1 is concerned with introductory topics: coordinate systems, transformations, projection, polynomial interpolation, and simple differential geometry. Chapter 2 then treats conics from the classical geometric standpoint and relates them to the master dimensions approach to curve and surface development. Chapter 3 introduces the parametric representation for curves and surfaces. In chapter 4 the author discusses Bessel’s method for interpolating piecewise curves. Overhauser curves are a special case, but other local interpolation schemes including Akima’s algorithm [1] and the Catmull-Rom spline [2] are not mentioned. Chapter5 reviews Coons surfaces. In chapter 6 we are introduced to splines with a useful discussion of nonparametric splines leading to the parametric cubic spline and the bicubic spline surface. In view of the author’s spell at General Motors one might have expected some discussion here of the spline-blended surfaces developed by Gordon, which generalize Coons surfaces in an important and useful way [3]. Chapter 7 is concerned with Bézier curves and surfaces. The de Casteljau construction [4,5] for Bézier curves is described, but de Casteljau is not cited. Uniform B-splines appear in chapter 8, leading to nonuniform B-splines in chapter 9. Here the notation becomes more complex, but it is difficult to see how this complexity can be avoided. Finally, in chapter 10 the book turns to rational parametric curves. An appendix includes FORTRAN code for most of the curve generating methods discussed.

Each chapter concludes with a list of references. According to the author, “no attempt has been made to cite every available document… Instead we have tried to emphasize original documents.…” While brevity is to be admired, several of the pioneers in computer-aided geometric design will be disappointed to find their original contributions ignored, and anyone seeking a balanced historical background will be misled.

Any practical system for computer-aided geometric design needs to be capable not only of computing points on curves and surfaces but of evaluating other properties such as surface area, volume, and center of mass, and of computing intersections between curves and surfaces in a reliable and efficient way. The book gives little information on these topics. Intersections merit a short paragraph on the last page of the final chapter, but Beach does not discuss numerical accuracy, a most important topic in computer-aided geometric design. Overall the book is patchy: what it contains is generally well presented, but some material is omitted and the impression comes through that the author has been out of contact with mainstream developments in the subject for several years. The book could be a useful adjunct to an introductory course on computer-aided geometric design, but it contains no exercises for the student.