IPAB Workshop - 22/09/2022

Title: Alternative Representations for Directional Fields

Abstract: Directional and vector fields are central objects in geometry processing. They are commonly represented with low-order simple elements in FEM and in computer graphics, for simplicity and sparsity. Unfortunately, these representations suffer from artifacts and poor encoding of multi-level details. The challenge at hand is finding representations that faithfully preserve desired properties from the continuum like cohomological structure, integrability, and conjugacy. I will discuss some recent works of extending these classical representations with alternative bases, where then important tasks in downstream applications like meshing, computations of flows, designing stents or properly marketing mangoes can be done robustly and more efficiently.