Integrable PolyVector Fields

摘要

We present a framework for designing curl-free tangent vector fieldsrnon discrete surfaces. Such vector fields are gradients of locallydefinedrnscalar functions, and this property is beneficial for creatingrnsurface parameterizations, since the gradients of the parameterizationrncoordinate functions are then exactly aligned with the designedrnfields. We introduce a novel definition for discrete curl between unorderedrnsets of vectors (PolyVectors), and devise a curl-eliminatingrncontinuous optimization that is independent of the matchings betweenrnthem. Our algorithm naturally places the singularities requiredrnto satisfy the user-provided alignment constraints, and our fields arernthe gradients of an inversion-free parameterization by design.