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Reviewer: Joseph J. O'Rourke

This is an excellent textbook on the basics of geometric modeling. Its coverage of curves and surfaces is especially thorough and includes parametric equations, special classes (Bezier and B-spline), intrinsic properties, the minimum distance between two curves, and the intersection of two surfaces. This comprises about half the book. The remaining half covers solid modeling and touches on computer graphics and CAD/CAM. The book is supplemented with four reprinted papers on specific modeling systems. Almost no assumptions are made about the reader's knowledge beyond calculus. Even the basics of linear algebra (vectors and matrices) are explained. No programming experience or other computer science knowledge is assumed. The book is, therefore, quite self-contained. The style of the presentation is rather pragmatic, conveying the hands-on experience of someone who has worked with geometric modeling in an industrial setting. The intent is to teach the nuts-and-bolts (the author's description) of the subject via many numerical examples, detailed figures, and many exercises. The prose is informal yet clear. The book is more tilted towards engineering than science. It is not research oriented; theorems are generally quoted when needed rather than proved. There is little discussion of computer science; there are no data structures and no algorithm design. Although many exercises call for programming, no code appears in the book. There is only rare mention of numerical analysis issues. Higher mathematics is avoided; homogeneous coordinates are described but they are not explained from the viewpoint of projective geometry. Algebraic and differential geometry results are applied but not derived. I am not criticizing the book for these absences, but rather describing its content negatively. One can hardly suggest inclusion of more material in a 763-page book. The only criticism I will offer is that the sections on CAD/CAM at the end of the book are not nearly as effective as the material on curves, surfaces, and solid modeling. I get the sense that the author ran out of energy and hoped to mask this by the inclusion of reprints of published papers in the appendices.