Sometimes I come to this site when I have a (usually geometric) programming problem that involves math, like testing the orientation of a spherical polygon. That question got an answer, but it was a really vague and brief answer that while probably mathematically sound didn’t actually help much when implementing an actual computable procedure for it.
Project the vertices on a unit cube centered on the sphere to get a polyhedron. This takes Euclidean norms of vectors, but no trigonometry.
Then you compute the signed volume by the shoelace formula generalized to 3D.
I know people don’t have to answer my questions at all, and I’m grateful to have gotten at least some help on my problem, but for someone who isn’t a math expert, and just needs it to solve a programming problem, answers like that kind of remind me of the draw an owl meme.
It seemed like the answerer didn’t really understand that the reason I wanted a method that didn’t involve trig functions isn’t because I wanted to see if there exists some way to do without them, but because
asin() are slow. And suggestions like “find the intersections with the circumscribed cube and integrate by method of vertical prisms” aren’t really useful to me in that context.
How can I ask questions in a way that the answers will be more useful for the problem I’m actually working on? I’m worried saying outright “the answer needs to be numerically stable and more efficient than the naive approach” would be inappropriate for Math.SE, but at the same time the answers I’m getting right now aren’t very helpful.
Again, I’m not complaining about people who took time out of their day to help me with my problem, I just want to know how to ask for solutions that translate into useful code.