Directional Field Synthesis, Design, and Processing

TLDR

Directional fields and vector fields are increasingly important in computer graphics and geometry processing, with applications ranging from mesh generation to texture mapping, and have led to diverse definitions and synthesis objectives such as fairness, feature alignment, symmetry, and topology. The report aims to systematically review directional field synthesis for graphics applications, outlining its challenges and recent solutions. It surveys the various representations, discretizations, and optimization strategies used to synthesize directional fields.

Abstract

Abstract Direction fields and vector fields play an increasingly important role in computer graphics and geometry processing. The synthesis of directional fields on surfaces, or other spatial domains, is a fundamental step in numerous applications, such as mesh generation, deformation, texture mapping, and many more. The wide range of applications resulted in definitions for many types of directional fields: from vector and tensor fields, over line and cross fields, to frame and vector‐set fields. Depending on the application at hand, researchers have used various notions of objectives and constraints to synthesize such fields. These notions are defined in terms of fairness, feature alignment, symmetry, or field topology, to mention just a few. To facilitate these objectives, various representations, discretizations, and optimization strategies have been developed. These choices come with varying strengths and weaknesses. This report provides a systematic overview of directional field synthesis for graphics applications, the challenges it poses, and the methods developed in recent years to address these challenges.