Directional fields and vector fields play an increasingly important role in computer graphics and geometry processing. 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. Depending on the specific application, researchers have used various definitions of objectives and constraints to synthesize such fields. For example, these notions are defined in terms of fairness, feature alignment, symmetry, or field topology, among other concepts.

This course provides a systematic overview of directional-field synthesis for graphics applications, the challenges it poses, and the methods developed in recent years to address those challenges. It includes demos and real-time coding to succinctly highlight analysis of directional fields and the challenges in their design.