Mathematical Illustrations: A Manual of Geometry and PostScript
18 comments
·June 16, 2025smurpy
Haha! I used to do LOTS of work in PostScript. The biggest project was a system which was part Python for the management, but PS for the content of a database publishing engine, motivated by the the need to generate crazily complicated real estate books, back in the day. There was a whole huge template system for different kinds of commercial and residential property and all sorts of different sections, ranges and indices. It was responsible for generating hundreds of multi-hundred page documents per day for dozens of real estate boards across Western Canada. Each publication was about as complicated as a Yellow Pages and generated daily and automatically from ever-changing data. In fact, the underlying database schema could evolve automatically through the update mechanisms in RETS (the Real Estate Transaction System API), though that was on the Python side. The rendering happened using GhostScript out to PDF for printing and electronic distribution to realtors. A stupid amount of detail, but what else is a touch of the 'tsim for anyway?!?
My other PostScript stuff was mostly fun and experimental: some fractal hacks which made printers and typesetters groan and some collaborative knowledge visualization stuff. I got started with PostScript on my NextStation in 1991 and it served me well, being the basis of a whole career of programmatic visualization.
smurpy
As a language it is lovely, if you're a fan of minimalism -- being stack-happy, like FORTH. It is well worth learning even just to flex the mind, but especially if you need to make complex diagrams and value stable APIs.
WillAdams
As cool as this is, I think most folks would find the newer tools:
- Asymptote
- Eukleides
- TikZ
- METAPOST
- Nodebox
- OpenSCAD --- see the book series: Geometry: https://www.goodreads.com/book/show/58059196-make Trigonometry: https://www.goodreads.com/book/show/123127774-make Calculus: https://www.goodreads.com/book/show/61739368-make
of greater interest (and for the Pythonistas there is: https://pythonscad.org/ ) --- I'd be interested to know of other tools in this space.
That said, most folks just use Inkscape (though at least it has scripting): https://inkscape.org/~pakin/%E2%98%85simple-inkscape-scripti...
Maybe Graphite will spur interest?
zzo38computer
I still think PostScript is good (although I had some ideas about how it could be improved, some of which are: allowing automatic allocation for some things by passing null instead of the object to store into, allowing setting the encoding separately from the font, a resource for environment variables, two-way communication with external programs, alpha transparency, FFI, magic dictionaries, etc).
PostScript can be used with or without graphics; I have used it in both ways, because I think PostScript is not a bad programming language, and has many advantages.
WillAdams
I miss Display PostScript from my NeXT Cube, and really wish that some programming system would bring a bit of that back.
I'd be very interested in a recommendation for a GUI programming toolkit and UI set which focused on/made available vector graphics.
detourdog
>- OpenSCAD --- see the book >series: Geometry: >https://www.goodreads.com/book/show/58059196-make Trigonometry: >https://www.goodreads.com/book/show/123127774-make Calculus: >https://www.goodreads.com/book/show/61739368-make
Do these books actually reference OpenScad or is OpenScad a tool for experimenting with the ideas in the series?
WillAdams
The idea is to use OpenSCAD to make 3D objects which explore the concepts being taught.
If you want to learn OpenSCAD itself then you want:
https://www.goodreads.com/book/show/41392892-programming-wit...
groos
What a delight! Thanks for the link.
max_
Is there a single giant PDF for this?
WillAdams
Not that I know of, back when I read it I had to stitch the files together.
wosined
What are the advantages of PostScript vs Asymptote?
WillAdams
Low-level, cool stack manipulation, and it predated Asymptote (2003) by being released in 1984.
JadeNB
Probably mostly the fact that this was started (according to the website) in 1996 and essentially frozen in 2004, which I believe predates the public announcement of Asymptote.
Does Asymptote get much use these days? I thought it was pretty cool, though a bit hard to wrap my mind around, when I first tried it, but nowadays it seems that attention has moved on to TikZ.
wosined
Does Asymptote get much use these days?
Not sure. I use it and it is reguarly updated.
https://asymptote.sourceforge.io/ https://asymptote.sourceforge.io/gallery/2Dgraphs/index.html https://asymptote.sourceforge.io/gallery/3Dgraphs/index.html
aoki
> Does Asymptote get much use these days?
Kids who get most of the way through AoPS (typically) end up learning some Asymptote as that is the supported way to draw figures on the AoPS website
WillAdams
A quick search shows a paper on it just a couple of years back:
https://tug.org/TUGboat/tb44-2/tb137hefferon-asymptote.pdf
I found Asymptote interesting, but I'm trying to wrap my mind around METAPOST (and by extension METAFONT) as an easier thing to implement/use.
JadeNB
Bill Casselman is an amazing mathematician with a diversity of interests. As this makes clear, he's been embracing computation and computational mathematics "since before it was cool." He also has an interest in mathematical history, and travelled to India to see the oldest-known occurrence of 0 (https://www.ams.org/publicoutreach/feature-column/fcarc-indi...). I'm sure he has tons of other interests about which I don't know.
Here is the three original Postscript Books. They are the classic way to learn PS.
The Blue Book (Tutorial and Cookbook) https://archive.org/details/postscriptlangua0000unse
The Red Book (Language Reference) https://archive.org/details/postscriptlangua0000unse_l1h3
The Green Book (Language Design) https://archive.org/details/PSGreenBook