Written in a deceptively easy-to-read style, perhaps at the high school level, this textbook provides a solid foundation in the mathematics needed for graphics and modeling. The early chapters introduce all the material needed for understanding the concepts presented in the later chapters. Answers to some of the exercises in each chapter are given. In addition, the appendix is a tutorial on the Postscript language, used to create the figures in the book.

The authors make extensive use of Web site references. Unfortunately, they do not collect all of these in a bibliography, so in order to recall a reference, readers must search for URLs dispersed throughout the book. A case in point is the URL for the home page of the book itself, which is given in the preface and as a footnote on page 11.

This book is a valuable supplement to the typical textbook that spouts abstract math, because it describes each topic geometrically, with the aid of a sketch. For example, in chapter 4 the determinant of a matrix is defined as the area of the parallelogram spanned by two vectors. In chapter 5 this concept is used, along with a sketch illustrating the areas in two dimensions, to present Cramer’s rule for the solution to a linear system as ratios of areas. This is in stark contrast to the typical textbook, which gives the solution solely as ratios of abstractly defined determinants. My favorite presentations of this kind are the demonstration of Gaussian elimination as a sequence of shear transformations, the geometric representation of eigenvectors, and the introduction to barycentric coordinates.

The clarity of the style and the geometric nature of each explanation by themselves make this text an important reference. Its value as a reference is also due to the choice of topics that it brings together. The topics progress from basic coordinates, points, and vectors in chapters 1 and 2 to 2D lines, linear maps in 2D, 2-by-2 linear systems, and affine maps in chapters 3 through 6. These are followed by eigenvalues in chapter 7, triangles in chapter 8, and conics in chapter 9. Chapters 10 through 13 apply these concepts to 3D and define properties that are uniquely three-dimensional, such as the cross product and skewed lines. Finally, chapters 14, 15, and 16 deal with more advanced topics, such as general linear systems, polylines, polygons, and curves.

The treatment of curves in the last chapter is introductory. At this point, the insightful explanations provided earlier in the text are abandoned for mere definitions. For example, the definition of curvature is given as a formula and is not accompanied by a derivation or sketch.

Finishing this book will leave readers eager for the sequel. There are many topics that are conspicuous by their absence, such as homogeneous coordinates, curve basis functions, and surfaces, all of which the authors could present in this format if they want to produce a follow-on work.