A few issues in intersections beyond triangle meshes

Abstract: Choosing a geometric representation is often about trade-offs—representations beyond the ubiquitous triangle mesh can make certain tasks fundamentally easier, but come with new challenges. In this talk, I will give two examples of these trade-offs I have encountered in my research through a discussion of some issues that arise when computing geometric intersections on higher-order patches and neural SDFs. I’ll then discuss some of my work that builds towards solving these issues: detecting intersections between higher-order patches using an optimization technique called sum-of-squares relaxation ("Sum-of-Squares Geometry Processing", SIGGRAPH Asia 2021) and computing constructive solid geometry operations on neural SDFs ("Constructive Solid Geometry on Neural Signed Distance Fields", SIGGRAPH Asia 2023).

Bio: Zoë is a first year PhD student at Carnegie Mellon University working on Geometry Processing with Keenan Crane. Before that, she received her bachelor's from Massachusetts Institute of Technology where she did research with Justin Solomon.