How many times do technical authors need to write programs to build illustrations for their work? And in PostScript? Not, one would guess, that often. It is a safe bet that most technical authors who need illustrations have Visio, Gimp, Photoshop, VTK, or some other high-powered package.

Why, then, would anyone write programs to make such illustrations in PostScript? Perhaps because the author has found that programming, and especially programming that draws pictures, can be terrific fun. Though it can be frustrating, annoying, and aggravating often enough, it is still compelling fun. And, though the point is not often made these days, programming can help someone to better understand a problem (or a solution).

To top it all off, the author believes that good illustrations are an essential part of mathematical writing. Indeed, he says: “Pictures should be drawn with as much care as paragraphs are written.” And he proves the worth of that statement, by doing exactly that in this book. This is a wonderful book. It is concise enough to be a good read, but just wordy enough to make the essentials clear. The illustrations are clear and easy to understand, which is perfect, since the author’s goal is to spur the reader to produce good illustrations.

The illustrations are built in PostScript, primarily because PostScript has been commonly used as a page description language, and as a printer language, but also because PostScript can be used to produce stunningly good graphics, with very fine control over the output. However, PostScript is, as anyone who has ever programmed in it knows, less than a congenial programming environment. The PostScript code included is very readable (at least as readable as PostScript code gets), well organized, and nicely laid out. The code does show a distinct preference for defining variables in dictionaries instead of keeping them on the stack, but this choice does make the code quite a bit easier to read.

The book takes the reader through the basics of PostScript, basic geometry, drawing various kinds of figures (including a variety of curves), three-dimensional graphics, and surface shading. The final chapter, on triangulation of polygons, is a fitting ending point. It is both an excellent example of exactly the kind of illustration that supports mathematical reasoning, and an excellent example of mathematical reasoning in text.

The author’s Web page has the code for all of the examples (and more), which should make it easy to experiment. The Web page also has the text of the entire book, in chapter-by-chapter portable document format (PDF), with a supplement on the regular polyhedra, and links to PostScript references.

This book is highly recommended for a variety of readers. Authors in mathematics (and various related fields) might learn about how to build better illustrations. Students of mathematics might use the text to explore a variety of mathematical problems, including the convex hull, triangulation, three-dimensional projections, and more (indeed, the author notes that the book has been used as a text in an undergraduate geometry class). Programming students might use the book as a springboard, to learn an underused (and perhaps underappreciated) programming language, as well as some basics of geometry. Even casual readers might learn more than a bit of programming and geometry, as well as how to use illustrations to illuminate (rather than obfuscate, as seems to be too often the case).

Appendices are included that define the basic PostScript command set, demonstrate some basics of how to build PostScript documents, and offer a few more useful tricks. The index is good. There are a few minor misprints, but nothing that should interfere with most readers’ understanding of the book.

This book will probably take a permanent place on my bookshelf, and I will surely recommend it highly to anyone interested in geometry, mathematics, or illustration, as well as to those who appreciate a good mathematical read.