Many thanks to all who have chimed in here! I want to make sure you've seen the latest proposal for how we plan to give form designers the option to detect and reject self-intersections in lines and traces.
We have now released v2025.4.0-beta.2 which includes an implementation for the intersects function. You can try it out with this form and check @seadowg's math! You'll soon be able to use this function to give immediate feedback to data collectors within the trace/shape capture experience but also show warning notes or use it anywhere else you use functions.
One interesting thing to note is that some cases that look like intersections may not actually be. That's because points and lines are displayed with thickness that they don't have in reality. Here's an example where it looks like there are two intersections but none are computed because it's the fake thickness of the points/lines that intersect:
