[boulos]

Great write up!

I’m amused by your subdivision of space note, given Figure 1 :). There are clearly some problems and transforms that are better on N-spheres (N-balls?) and others on rectangles / N-cubes. Do you have a deeper intuition for which? (The x^2 example was simple and cute).

Years ago [1], we applied interval arithmetic to tracing groups of rays (and compared to geometric bounding via planes/frustums). I’d be curious to think through an equivalent with your midpoint ball arithmetic, but I feel like it would “need” to be parameterized as a ball of origins (easy) and then something else for the cone of directions —- maybe theta/phi clusters or “cluster of points on the unit sphere” (but converting back and forth is more expensive than the gains).

[1] http://graphics.stanford.edu/~boulos/papers/ia.pdf