4 ms·

Mathematical Illustrations: A Manual of Geometry and PostScript

64 points by Bogdanp 1y ago

wosined 1y ago
What are the advantages of PostScript vs Asymptote?
- JadeNB 1y ago
  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.
  - WillAdams 1y ago
    A quick search shows a paper on it just a couple of years back: https://tug.org/TUGboat/tb44-2/tb137hefferon-asymptote.pdf 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.
  - wosined 1y ago
    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/ https://asymptote.sourceforge.io/gallery/2Dgraphs/index.html https://asymptote.sourceforge.io/gallery/2Dgraphs/index.html https://asymptote.sourceforge.io/gallery/3Dgraphs/index.html https://asymptote.sourceforge.io/gallery/3Dgraphs/index.html
  - aoki 1y ago
    > 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 1y ago
  Low-level, cool stack manipulation, and it predated Asymptote (2003) by being released in 1984.
JadeNB 1y ago
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-india-zero https://www.ams.org/publicoutreach/feature-column/fcarc-indi...). I'm sure he has tons of other interests about which I don't know.
WillAdams 1y ago
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 https://www.goodreads.com/book/show/58059196-make Trigonometry: https://www.goodreads.com/book/show/123127774-make https://www.goodreads.com/book/show/123127774-make Calculus: https://www.goodreads.com/book/show/61739368-make https://www.goodreads.com/book/show/61739368-make of greater interest (and for the Pythonistas there is: https://pythonscad.org/ 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-scripting https://inkscape.org/~pakin/%E2%98%85simple-inkscape-scripti... Maybe Graphite will spur interest?
- detourdog 1y ago
  >- OpenSCAD --- see the book >series: Geometry: >https://www.goodreads.com/book/show/58059196-make https://www.goodreads.com/book/show/58059196-make Trigonometry: >https://www.goodreads.com/book/show/123127774-make https://www.goodreads.com/book/show/123127774-make Calculus: >https://www.goodreads.com/book/show/61739368-make 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 1y ago
    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-with-openscad https://www.goodreads.com/book/show/41392892-programming-wit...
- zzo38computer 1y ago
  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.
groos 1y ago
What a delight! Thanks for the link.
max_ 1y ago
Is there a single giant PDF for this?
- WillAdams 1y ago
  Not that I know of, back when I read it I had to stitch the files together.
- lioeters 1y ago
  https://isidore.co/CalibreLibrary/Casselman,%20Bill/Mathematical%20Illustrations_%20A%20Manual%20of%20Geometry%20and%20PostScript%20(5811)/Mathematical%20Illustrations_%20A%20Manual%20of%20Ge%20-%20Casselman,%20Bill.pdf https://isidore.co/CalibreLibrary/Casselman,%20Bill/Mathemat... (PDF 3.9MB)
smurpy 1y ago
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 1y ago
  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 1y ago
    METAPOST seems to be similarly stable, and has an interesting programming/math model (DEK keeps it open in window and uses it (or METAFONT which it is based on?) for interactive math).
- lioeters 1y ago
  > touch of the 'tsim Brush of the dyxlesia as well evidently.
  - 1y ago
smurpy 1y ago
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 https://archive.org/details/postscriptlangua0000unse The Red Book (Language Reference) https://archive.org/details/postscriptlangua0000unse_l1h3 https://archive.org/details/postscriptlangua0000unse_l1h3 The Green Book (Language Design) https://archive.org/details/PSGreenBook https://archive.org/details/PSGreenBook
glkindlmann 1y ago
Like others[1] I was saddened that Mac's Preview program stopped opening .ps/.eps files with the release of Ventura in late 2022. I never understood exactly why; I guess security issues around the PostScript interpreter. But that made it lot less convenient to hack around in .ps files. Ghostscript's interactive display program(s?) never seemed as convenient as Preview. Still, this book is awesome and I've been inspired by it for awhile. I used to love whipping up diagrams and simple vector art in .ps/.eps files. In a fit of procrastination in ~2006 I created a minimalist horizontal rule for an IEEE conference submission, and that diamondrule.eps[2] has now become the standard. I would say that EPS is still more convenient than SVG as a format to contain, in one self-contained file, raster graphics with overlaid vector graphics. [1] https://tidbits.com/2022/10/27/preview-in-ventura-drops-support-for-postscript-and-encapsulated-postscript-files/ https://tidbits.com/2022/10/27/preview-in-ventura-drops-supp... [2] https://github.com/ieeevgtc/tvcg-journal-latex/blob/main/diamondrule.eps https://github.com/ieeevgtc/tvcg-journal-latex/blob/main/dia...
- WillAdams 1y ago
  See: https://news.ycombinator.com/item?id=13701897 https://news.ycombinator.com/item?id=13701897

64 points by Bogdanp 1y ago

wosined 1y ago

What are the advantages of PostScript vs Asymptote?

JadeNB 1y ago
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.
- WillAdams 1y ago
  A quick search shows a paper on it just a couple of years back: https://tug.org/TUGboat/tb44-2/tb137hefferon-asymptote.pdf 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.
- wosined 1y ago
  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/ https://asymptote.sourceforge.io/gallery/2Dgraphs/index.html https://asymptote.sourceforge.io/gallery/2Dgraphs/index.html https://asymptote.sourceforge.io/gallery/3Dgraphs/index.html https://asymptote.sourceforge.io/gallery/3Dgraphs/index.html
- aoki 1y ago
  > 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 1y ago
Low-level, cool stack manipulation, and it predated Asymptote (2003) by being released in 1984.

JadeNB 1y ago

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-india-zero https://www.ams.org/publicoutreach/feature-column/fcarc-indi...). I'm sure he has tons of other interests about which I don't know.

WillAdams 1y ago

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 https://www.goodreads.com/book/show/58059196-make Trigonometry: https://www.goodreads.com/book/show/123127774-make https://www.goodreads.com/book/show/123127774-make Calculus: https://www.goodreads.com/book/show/61739368-make https://www.goodreads.com/book/show/61739368-make of greater interest (and for the Pythonistas there is: https://pythonscad.org/ 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-scripting https://inkscape.org/~pakin/%E2%98%85simple-inkscape-scripti... Maybe Graphite will spur interest?

detourdog 1y ago
>- OpenSCAD --- see the book >series: Geometry: >https://www.goodreads.com/book/show/58059196-make https://www.goodreads.com/book/show/58059196-make Trigonometry: >https://www.goodreads.com/book/show/123127774-make https://www.goodreads.com/book/show/123127774-make Calculus: >https://www.goodreads.com/book/show/61739368-make 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 1y ago
  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-with-openscad https://www.goodreads.com/book/show/41392892-programming-wit...
zzo38computer 1y ago
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.

groos 1y ago

What a delight! Thanks for the link.

max_ 1y ago

Is there a single giant PDF for this?

WillAdams 1y ago
Not that I know of, back when I read it I had to stitch the files together.
lioeters 1y ago
https://isidore.co/CalibreLibrary/Casselman,%20Bill/Mathematical%20Illustrations_%20A%20Manual%20of%20Geometry%20and%20PostScript%20(5811)/Mathematical%20Illustrations_%20A%20Manual%20of%20Ge%20-%20Casselman,%20Bill.pdf https://isidore.co/CalibreLibrary/Casselman,%20Bill/Mathemat... (PDF 3.9MB)

smurpy 1y ago

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 1y ago
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 1y ago
  METAPOST seems to be similarly stable, and has an interesting programming/math model (DEK keeps it open in window and uses it (or METAFONT which it is based on?) for interactive math).
lioeters 1y ago
> touch of the 'tsim Brush of the dyxlesia as well evidently.
- 1y ago

smurpy 1y ago

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 https://archive.org/details/postscriptlangua0000unse The Red Book (Language Reference) https://archive.org/details/postscriptlangua0000unse_l1h3 https://archive.org/details/postscriptlangua0000unse_l1h3 The Green Book (Language Design) https://archive.org/details/PSGreenBook https://archive.org/details/PSGreenBook

glkindlmann 1y ago

Like others[1] I was saddened that Mac's Preview program stopped opening .ps/.eps files with the release of Ventura in late 2022. I never understood exactly why; I guess security issues around the PostScript interpreter. But that made it lot less convenient to hack around in .ps files. Ghostscript's interactive display program(s?) never seemed as convenient as Preview. Still, this book is awesome and I've been inspired by it for awhile. I used to love whipping up diagrams and simple vector art in .ps/.eps files. In a fit of procrastination in ~2006 I created a minimalist horizontal rule for an IEEE conference submission, and that diamondrule.eps[2] has now become the standard. I would say that EPS is still more convenient than SVG as a format to contain, in one self-contained file, raster graphics with overlaid vector graphics. [1] https://tidbits.com/2022/10/27/preview-in-ventura-drops-support-for-postscript-and-encapsulated-postscript-files/ https://tidbits.com/2022/10/27/preview-in-ventura-drops-supp... [2] https://github.com/ieeevgtc/tvcg-journal-latex/blob/main/diamondrule.eps https://github.com/ieeevgtc/tvcg-journal-latex/blob/main/dia...

WillAdams 1y ago
See: https://news.ycombinator.com/item?id=13701897 https://news.ycombinator.com/item?id=13701897