Geometry Expressions

I’ve written before about the geometry construction language, Eukleides. In that post, I said that ‘I [was] drawn to Eukleides because it is a language […], and not a mouse-flinging WYSIWYG virtual compass.’ Those WYSIWYG mouse-flingers are known as interactive geometry software (IGS), and I’ve never been a huge fan of them. Most of them are built in Java, and it shows. Even beyond Java issues, they largely feel made by interns employed by mathematicians rather than folks who have read The Design of Everyday Things. At the same time, complicated constructions like Gauss’s 17-gon1 can quickly become unwieldy in written code. I have experimented with many, though never really settled on an IGS.

Geometry Expressions (GX) is currently on sale for $10 (instead of $99) due to the pandemic. Saltire, the maker, hasn’t stated when this sale will end, which… is fair. I had previously played with the trial of GX, and found it to be… pretty usable, but also I need to really be in a mood to drop a hundred bucks on hobbyist (I mean, for me) maths software. At $10, I decided to take the plunge. Here are my thoughts so far.

The good

The UI/UX isn’t that bad!
I don’t think this is written in Java? But it might be. It’s cross-platform (macOS/Windows) so it’s entirely possible that it’s written in… something weird. The UX fits in fine with Windows, I can only imagine it’s kind of awful on macOS, but… I haven’t tested that yet. Just a gut feeling. There are UI/UX quirks that I’ll get into later, but it’s… manageable!
Export options
One thing that I really don’t love about Eukleides is that you can basically just export to EPS. I then have to separately convert this to SVG, and from there, post-process the SVG. Eukleides also only lets you draw from like… eleven basic colors? GX is clearly built with exporting in mind, and integral to this is the fact that you can… well… use color good! But the actual export options are also great. Native SVG, our old friend EPS, your normal raster formats, and… interesting things. Lua, which I haven’t tried yet, and both animated GIFs and interactive HTML/JS, neither of which I’ve done anything interesting with yet.
I mean, it is called an interactive geometry system, but it is really rather magical how that all comes together. Assuming everything is glued together correctly (another topic for later), you can just drag points around and watch your construction work with different parameters. So, in the simple angle bisector shown below, dragging points A or C around will change the angle of ∠ABC, and the construction will adjust, changing ∠ABM and ∠MBC accordingly.
Robust toolset
I guess you wouldn’t really expect less, but Eukleides, for instance, really kind of gives you the bare minimum for objects and the like. GX has fifteen drawing tools which behave as expected. It has fourteen methods of constraint – for instance, in the illustration below, radius r is a constraint. I constructed the first circle and applied the constraint. I could have constructed the other two circles at any size – as soon as I applied the constraint, r, they were bound to it. These can be units as well; a square with side lengths constrained to 2 has double the side length as one constrained to 1. It has fourteen built in construction tools, which don’t interest me much as my use-case is largely doing constructions from scratch. Finally, it has eleven calculations, such as the angle calculations in the construction below.

Basic angle bisector created in Geometry Expressions A B C r H r K r M z 0 ~ 0.4294711 z 1 ~ 0.4294711

All in all, it’s a pretty nice tool for the things I want to use it for. But, unsurprisingly, there are some pretty frustrating snags.

The bad

Incident snapping does not work well
I said pretty frustrating, but I’m starting off with an incredibly frustrating UX gaffe. In the above construction, I followed the method of doing an angle bisector by hand with a compass and straightedge. Since I was doing this on an IGS that could precisely measure things for me, however, the construction itself had to be quite precise. I tried several times, and kept coming up with angles that were slightly off. The problem was that center points H and K were not quite aligned with the intersection of circle B along ∠ABC. Why did this happen? When creating the two intersecting circles (H and K), the cursor changed to a design that clearly indicated it was snapping incident to the relevant intersection. Additionally, the two intersecting objects were highlighted. But it didn’t actually snap. The only way to get this to work was to use the construction tools to make intersection points; the circle tool was willing to snap incident to existing point just fine. This is absurd. Certainly the solution is to make snapping function across the board, but if that can’t be done, don’t make the UI change such that it appears as though that’s happening. I don’t know how such a decision can be shipped.
It’s easy to feel like you have to undo a lot
The tools are pretty good for constructing and the like, but… less-so for touching things up or fixing goofs. There were plenty of time where I created things and just felt kind of… lost in either how I accidentally made a thing, or how to get a thing to do what I wanted vs. just… getting it right from the outset. For instance, I haven’t figured out how to rotate a polygon around its midpoint, only vertices (and these rotations don’t seem to have any shift-constraints, nor do translations). Mild example but little things like that make the toolset feel less fleshed-out than I’d like.
Nonstandard UX behaviors
To an extent, this still feels like some mathematician’s hired hand whipped up some controls without studying, say, Illustrator. There aren’t keyboard shortcuts that I can find for the tools (the menu doesn’t even have alt-keys defined, which is infuriating). Scroll-wheel zooms (actually, I believe it scales the document, which is even sillier) instead of… scrolling (this is one of my biggest pet peeves in image editing software). Scroll/pan is achieved by holding right-click instead of Space. Et cetera. It’s not as bad as many that I’ve played with, but it can be cumbersome to use.
Unclean SVG export
I’m glad I can export right to SVG! But the export is… a lot. There’s a lot of extra stuff in there, and weird behaviors like every digit in 0.4294711 up there being a separate textbox. I actually imported it into Illustrator and cleaned a couple of things up (there were some points and extra bits that I couldn’t quite figure out how to get rid of, &c.) but… the text is really small! It’s not font-size, and my knowledge of SVG isn’t quite at the point where I’m going to solve it for this post. And while I apologize for the text being difficult to read, it does help demonstrate that the SVG output is just a bit much. I also had to touch up the rightward double arrow; GX’s export opted to find this in a Symbol font instead of using U+21D2. Little things, but room for improvement.

In conclusion

For $102? I’m happy with this purchase. It doesn’t do too much; it’s not a full-featured CAS with an IGS built in. Because of this, all of your tools are right there in front of you and are fairly self-explanatory. The UX could use some polish, but it isn’t terrible. There are a lot of export options, and hopefully I can figure out how to do something fun with the interactive ones. I don’t know that I would be bothering to write this if I was just checking out the trial at a $99 price point, however. It’s specialized software, and I get that; we’re also increasingly numb to the work that goes into software and the value of said work. But, boy, if I was going to pay full-price? I sure as hell would want keyboard shortcuts, functioning snapping, and just a little bit of general UX touch-up.

If you’re reading this, and you’re a recreational maths nerd, and you’re stuck at home, and Saltire is still offering GX for $10… I think it’s hard to pass up.

  1. This is entirely a tangential rant, but… I feel like I’m hearing more and more people use the phrase ‘ruler and compass’ instead of ‘straightedge and compass’ for these constructions, and I… hate it? The word ‘ruler’ absolutely implies measurement, and part of the constraint is that you can’t measure anything, you can only copy existing distances via the compass. ↩︎
  2. Well, $20; I snagged a macOS license as well. Maybe I’ll report on that in the future, if it’s notable. ↩︎