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Mathematical Illustrations: A Manual of Geometry and Postscript

Bill Casselman
Cambridge University Press
Publication Date: 
Number of Pages: 
[Reviewed by
Tom Shulte
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This book transformed my understanding of PostScript. Before, I was only vaguely aware of PostScript as a language to send data to certain printers. Mathematical Illustrations enlarges that view to showcase PostScript as a rich language capable of presenting graphics, from technical illustrations in perspective to function graphing.

While the purpose of this text is to aid mathematicians, scientists, engineers, and graphic designers in using PostScript for geometric exhibition, along the way the reader learn much about PostScript as a programming language. This includes ideas that can be applied to more general programming tasks, such as array and stack handling.

This is the type of book that readily suggests itself of including a disk of source code examples, but the book comes with no such extra media. However, this is more than made up by the fact that the book’s site includes not only such code samples, but the entire text of the manual: You have the option of obtaining the content online in PDF format or, of course, PostScript.

Whether reading the book in hand or accessing the content online, do not let the need for a PostScript implementation be the only reason to peruse this enlightening volume. The work also serves as a practical introduction to how geometry is applied in the creation of graphical images. Of particular mathematical interest are the sections on curves (including Bézier curves and their mathematical motivation), nonlinear 2D transformation (including stereographic projection). Three sections on 3D representation provide a good background for a mathematical approach to 3D depiction for the artist, mathematician, and technical illustrator. The lucid and detailed section on applying triangulation to breaking down complex shapes into connected triangles for depiction is very interesting and laid out so completely as to present the concepts in a way that could easily be applied to other environments.

Complete to the point of even helping you get your PostScript environment set up, this manual is a rich and educational guide to applying geometry and getting the most out of PostScript.

By night, Thomas Schulte is a graduate student studying mathematics at Oakland University in Auburn Hills, Michigan. By day he is a software engineer at Plexus Systems with a special interest in applying vector markup language (VML) for Web presentations of statistical process control (SPC) charts and business graphs.


1. Getting started in PostScript; 2. Elementary coordinate geometry; 3. Variables and procedures; 4. Coordinates and conditionals; 5. Drawing polygons: loops and arrays; 6. Curves; 7. Drawing curves automatically: procedures as arguments; 8. Non-linear 2D transformations: deconstructing paths; 9. Recursion in PostScript; 10. Perspective and homogeneous coordinates; 11. Introduction to drawing in three dimensions; 12. Transformations in 3D; 13. PostScript in 3D; 14. Drawing surfaces in 3D; Appendix 1. Summary of PostScript commands; Appendix 2. Setting up your PostScript environment; Appendix 3. Structured PostScript documents; Appendix 4. Simple text display; Appendix 5. Zooming; Appendix 6. Evaluating polynomials: getting along without variables; Appendix 7. Importing PostScript files; Epilogue