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 having a modest acquaintance with coordinate geometry. The author combines a completely self-contained, step-by-step introduction to the graphics programming language PostScript with advice on what goes into good mathematical illustrations, chapters showing how good graphics can be used to explain mathematics, and a treatment of all the mathematics needed to make such illustrations. The many small, simple graphics projects can also be used in courses in geometry, graphics, or general mathematics.
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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: 9780521839211
  • Publisher: Cambridge University Press
  • Publication date: 11/15/2004
  • Pages: 320
  • Product dimensions: 6.14 (w) x 9.21 (h) x 0.87 (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 1
2 Elementary coordinate geometry 26
3 Variables and procedures 44
4 Coordinates and conditionals 57
5 Drawing polygons : loops and arrays 81
6 Curves 92
7 Drawing curves automatically : procedures as arguments 120
8 Nonlinear 2D transformations : deconstructing paths 133
9 Recursion in PostScript 147
10 Perspective and homogeneous coordinates 160
11 Introduction to drawing in three dimensions 179
12 Transformations in 3D 181
13 PostScript in 3D 205
14 Drawing surfaces in 3D 217
15 Triangulation : basic graphics algorithms 243
App. 1 Summary of PostScript commands 259
App. 2 Setting up your PostScript environment 271
App. 3 Structured PostScript documents 276
App. 4 Simple text display 279
App. 5 Zooming 283
App. 6 Evaluating polynomials : getting along without variables 287
App. 7 Importing PostScript files 294
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