I'm curious what your thoughts are on my approach for robustness.

I've written similar operations[1] that include elliptical arcs AND Bézier curves, and robustness has been an issue. An assortment of polygon clipping approaches use ONLY line segments and fixed precision numbers to work around this.

If I discretize the line segments to 20bits (fixed), potentially in tiles (to reduce inaccuracies), then I can represent exact rational intersections (and parametric t values) with 64-bit numerators and 64-bit denominators[2].

This significantly concerns me about computation cost (and memory if I need to store them), but using this scheme to ensure absolute correctness (and ordering) of intersections does seem to work in CPU proof-of-concepts. Perhaps it is possible to only use this expensive method to disambiguate if it cannot be done from floating-point numbers.

My initial GPU concept imagined a sorting of intersected segments, however a radix sort over a 128-bit object seems like a non-starter, and if I try that, a merge sort may still be viable?

Thank you for the links and recommendations!

[1]: https://github.com/phetsims/kite

[2]: https://github.com/phetsims/alpenglow/blob/main/js/webgpu/wg...