Artists who wanted to represent 3D scenes on 2D canvases developed projective geometry. While it isn’t studied much these days, it has enjoyed some renewed interest with the development of computer graphics and games. This book is not a textbook. The author wanted to convey some of the fascination he feels for the subject. It is not at all oriented toward computer graphics issues, although the link between mathematics and visual perception may be helpful.

The first two chapters contrast the synthetic and analytic approaches. In the synthetic approach, as in Euclidean geometry, simple axioms of projective geometry lead to standard results such as Desargues’ theorem and the theorem of Pappus. Nice figures, some in color, illustrate perspective. Chapter 1 also includes sections on the complete quadrilateral and affine geometry. The second chapter, on the analytic approach, explains homogeneous coordinates, which appear in computer graphics. The theorems of the first chapter are derived in the second using coordinate representations.

Chapters 3 through 6 treat figures of increasing complexity, covering linear figures, quadratic figures, cubic figures, and quartic figures. Each chapter includes many diagrams, often in color, of the curves and surfaces discussed. The chapter on quartic surfaces introduces algebraic geometry and contains a nice discussion of Kummer’s surface, including diagrams and models. The last chapter (7) is on finite geometries.

Overall, this is a nice introduction for those with an interest in geometry.