SGP 2021 Graduate School – Directional Field Processing – Amir Vaxman

Directional fields are core objects of geometry processing. They represent movement, flow, alignment, or geometric transformations. Their applications range from fluid simulation, through architectural design, to mesh generation. We will discuss the theoretical and empirical challenges in representing and discretizing directional fields on surfaces and in volumes, and some of their desired properties with relation to the applications; namely, smoothness, integrability, constrained size or symmetry, and more. We will further discuss how recent approaches optimized for these properties. Finally, we will demonstrate some of the common design paradigms for directional fields using the software library Directional.