Mathematical Illustrations: A Manual of Geometry and PostScript

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This practical introduction to the techniques needed to produce high-quality mathematical illustrations is suitable for anyone with basic knowledge of coordinate geometry. Bill Casselman combines a completely self-contained step-by-step introduction to the graphics programming language PostScript with an analysis of the requirements of good mathematical illustrations. The many small simple graphics projects can also be used in courses in geometry, graphics, or general mathematics. Code for many of the illustrations is included, and can be downloaded from the book's web site:; scientists, engineers, and even graphic designers seeking help in creating technical illustrations need look no further.

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Editorial Reviews

From the Publisher
"This is a wonderful read...This book is highly recommended for a variety of readers. Authors of 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 it 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, geometry and how to use illustrations to illuminate...This book will take a permanent place on my bookshelf and I will surely recommend it highly to anyone interested in geometry, mathematics, and illustrations as well as those who appreciate a good mathematical read."
Computing Reviews

"The geometry that best illustrates vector-graphic drawing methods is the subject of Casselman's book... I recommend it to all who are professionally or even casually interested in mathematical illustration... To read this text profitably requires, in addition to paper and pencil, a computer running a PostScript interpreter... Still, for lazy or computerphobic readers there remains close to a third of the book that is superb geometry. These passages can be enjoyed without even a glance at PostScript... Today most images end up in PostScript on the way to the printer, regardless of their origins. Sometimes it becomes necessary to open the arcane code in a text editor and modify PostScript by hand. Even if you will never need to go this far, Casselman's book teaches you to appreciate the marvels of PostScript and of the geometry ideas relevant to this curious computer language."
American Scientist

"...this manual is a rich and educational guide to applying geometry and getting the most out of PostScript."
MAA Reviews

"Casselman is a mathematician interested in graphics and the book will appeal as much to mathematicians as it will appeal to programmers. Casselman's book certainly does its best to address the two topics of geometry and PostScript, and in this respect it is excellent."
Notices of the AMS

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Product Details

  • ISBN-13: 9780521547888
  • Publisher: Cambridge University Press
  • Publication date: 11/15/2004
  • Edition description: New Edition
  • Pages: 318
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.94 (d)

Meet the Author

Bill Casselman holds a doctorate from Princeton University for his work on automorphic forms. He is currently Professor of Mathematics at the University of British Columbia. Additionally, he is the technical editor of the online collected works of Robert Langlands and the Graphics Editor of NOTICES of the American Mathematical Society.

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Table of Contents

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.

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