Power-Linear Polar Directional Fields

TL;DR

This paper presents a new power-linear method for designing directional fields on meshes, allowing precise control over singularities and improving smoothness and artifact mitigation on various mesh qualities.

Contribution

It introduces a power-linear representation for directional fields that enables flexible singularity placement and reduces artifacts on meshes with diverse topologies.

Findings

Effective control of singularities at arbitrary locations

Smooth directional fields on meshes with poor quality

Reduced artifacts on coarse or uneven meshes

Abstract

We introduce a novel method for directional-field design on meshes, enabling users to specify singularities at any location on a mesh. Our method uses a piecewise power-linear representation for phase and scale, offering precise control over field topology. The resulting fields are smooth and accommodate any singularity index and field symmetry. With this representation, we mitigate the artifacts caused by coarse or uneven meshes. We showcase our approach on meshes with diverse topologies and triangle qualities.