Subdivision Directional Field Processing

Abstract

We present a novel subdivision scheme for face-based tangent directional fields on triangle meshes. Our subdivision scheme is based on a novel coordinate-free representation of directional fields as halfedge-based scalar quantities, bridging the finite-element representation of fields with that of discrete exterior calculus. By commuting with differential operators, our subdivision is structure-preserving: it reproduces curl-free fields exactly, and divergence-free fields in the weak sense. Moreover, our scheme directly extends to fields with several vectors per face. Finally, we show how our scheme is useful for applications that need robust and efficient face-based directional field processing, such as advection, robust earth mover's distance computation, and directional-field design.