“Integrable PolyVector fields”

  • ©Olga Diamanti, Amir Vaxman, Daniele Panozzo, and Olga Sorkine-Hornung




    Integrable PolyVector fields

Session/Category Title: Geometry Field Trip




    We present a framework for designing curl-free tangent vector fields on discrete surfaces. Such vector fields are gradients of locally-defined scalar functions, and this property is beneficial for creating surface parameterizations, since the gradients of the parameterization coordinate functions are then exactly aligned with the designed fields. We introduce a novel definition for discrete curl between unordered sets of vectors (PolyVectors), and devise a curl-eliminating continuous optimization that is independent of the matchings between them. Our algorithm naturally places the singularities required to satisfy the user-provided alignment constraints, and our fields are the gradients of an inversion-free parameterization by design.


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