Mathematical Illustrations: A manual of geometry and postscript

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Mathematical Illustrations: A manual of geometry and postscript

Mathematical Illustrations

[ Bill Casselman’s home page ]

Table of contents

Introductory
Chapters 1 – 15
Appendices
Epilogue
Supplement
Code samples and packages
Other reading on PostScript
Other reading
on mathematical graphics
Errata et corrigenda
Copyright notice

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This manual has been available on this site since about 1996, with improvements taking place frequently. The current version has been published as a book of about 350 pages by Cambridge University Press. By agreement with the Press, however, it will remain posted on this web site. Many improvements in the current version over previous ones are due to the (anonymous) referees of the Press, whom I wish to thank heartily. I also wish to thank Lauren Cowles, of the New York office of the Press, for much help with preparing the original version for publication. The paper edition appears also in Duotone red and black. For information on obtaining the paper edition, take a look at the Cambridge Press catalogue .

From January 1, 2004 on, no changes except simple error corrections will be made to the main body of the text here — at least for a while. Corrections to both paper and web editions will be found below.

I am grateful to all those who have pointed out errors or lacunae in older versions of this manual, and I hope readers will continue to send me mail about what they find – both good and bad – at cass@math.ubc.ca .

Copyright © 2005 by Bill Casselman. Permission is granted for users of this resource to make one copy for their own personal use. Further reproduction is strictly prohibited without the express permission of the copyright holder.

Introductory

This text is offered in PDF format, but also in PostScript. To read the PostScript files, which are often faster to load, you will need a PostScript interpreter. But you will need one in any event in order to read the book fruitfully. You can obtain Ghostscript and viewers at the GhostScripthome pages. You will probably want to set it as the program with which your browser reads .ps files (of type application/postscript ).

Preface

pdf
ps

Table of contents (for the entire text)

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Chapters 1 – 15

Chapter 1Getting started

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Chapter 2Elementary coordinate geometry

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Chapter 3Variables and procedures

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Chapter 4Coordinates and conditionals

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Chapter 5Loops and arrays

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Chapter 6Curves

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Interlude

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Chapter 7Procedures as arguments

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Chapter 8Non-linear transformations in 2D

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Chapter 9Recursion in PostScript

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Chapter 10Perspective and homogeneous coordinates

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Chapter 11Introduction to drawing in 3D

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Chapter 12Rigid motion in 3D

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Chapter 13PostScript in 3D

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Chapter 14Drawing surfaces in 3D

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Chapter 15The regular polyhedra

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Another way of constructing the regular polyhedra

Appendices

Appendix 1Summary of important PostScript commands

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Appendix 2Setting up your PostScript environment

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Appendix 3Structured PostScript documents

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Appendix 4Simple text display

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Appendix 5Zooming

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Appendix 6Evaluating polynomials

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Appendix 7Importing PostScript files

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Epilogue

Graphics style in exposition

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Supplement

Another way to construct the regular polyhedra

pdf

A better version of Hodgman-Sutherland

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Code samples and packages

The plural pictures

means there are several pages.

Simple diagrams from Chapter 1 ( pictures ) ( source )
Arrows
Straight ( pictures ) ( source )
Curved ( pictures ) ( source )
An example of zooming in ( pictures ) ( source )
Cubes
Frame, orthogonal projection ( picture ) ( source )
Frame, perspective projection ( picture ) ( source )
Solid ( picture ) ( source )
Shading ( picture ) ( source )
Shadowed ( picture ) ( source )
Moving ( pictures ) ( source )
A simple sphere in PostScript ( picture ) ( source )
A sphere with Gouraud shading ( picture ) ( source )
A doughnut in PostScript ( picture ) ( source )
A figure where chopping is necessary to make a binary space partition ( picture ) ( source )
An open box ( picture ) ( source )
The package arrows.inc [Chapter 1]
The package lines.inc [Chapter 4]
The package hodgman-sutherland.inc [Chapter 4]
The package mkpath.inc [Chapter 7]
The package transform.inc [Chapter 8]
Map data in PostScript form ( maps.zip ) from original data at
http://archive.msmonline.com/1999/12/vis2.htm (2.5 MB) [Chapter 8]
The package hull.inc [Chapter 9]
The package ps3d.inc [Chapter 13]
The package bsp.inc – for building binary space partitions [Chapter 14]
The package polyhedra.inc – for drawing regular polyhedra [Chapter 15]
The PERL script psinc – for including files explicitly instead of running them [Appendix 2]
The package zoom.inc [Appendix 5]
The package hs.inc [Supplementary note on Hodgman-Sutherland]
The package stack.inc [Supplementary note on Hodgman-Sutherland]

Other references on PostScript

The following official guides from Adobe are available on line:

PostScript language tutorial and cookbook (the `bluebook’) – a classic, with lots of short useful samples.
PostScript language design (the `greenbook’)
Much relevant stuff , including the PostScript language reference language manuals(originally the `redbook’) – sooner or later you will have to look at this. It verges on readable.

Other technical ( very technical) documentation is also on line at http://partners.adobe.com/asn/tech/ps/index.jsp and http://partners.adobe.com/asn/tech/ps/technotes.jsp . You can retrieve here, among other things, an earlier edition of thereferencemanual.

Other Cool Things:

(NOTE: TEMPORARILY DEAD)

Luc Devroye’s PostScript pages with lots of further links (including one back to here)
Mathematical BBS on PostScript with lots of further links (including one back to here)
The phrase PostScript humour may look like an oxymoron to you, but you can find an attempt at PostScript: a computer language . There is more from the same guy at http://www.prepressure.com/postscript .
The incredible PostScript web server (follow link to PS-HTTPD)
Don Lancaster’s pages including lots of libraries of useful stuff (and also of much useless stuff). Some discussion of how to achieve transparency.
On line PostScript operator dictionary (taken directly from the reference manual). The header pages are in German, but the rest in English.
David Maxwell’s short PS manual . David Maxwell was a graduate student here at UBC when he did these pages, but has since gone on to a More Satisfying Life.
Inkguides Much stuff on fonts.

Other reading on the use of illustration in mathematical exposition

Pictures and proofs (an article in the October, 2000 issue of the Notices of the A.M.S. on the use of illustrations in mathematics)
A review of one of Edward Tufte ‘s classics on information graphics (from the January, 1999 issue of the Notices )

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