After a brief review of efficient computational tools for polynomial partitioning in geometry, I will present a concrete application of these and other algebraic tools. I will focus on circle-shooting among triangles in 3D, as a representative example of our recent work on intersection queries.
The main result is joint work with Pankaj Agarwal, Esther Ezra, Matya
Katz, and Micha Sharir.
A preliminary version appeared in SoCG'22
https://doi.org/10.4230/LIPIcs.SoCG.2022.4
and on arXiv
https://doi.org/10.48550/arXiv.2203.10241.