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O. Diamanti, A. Vaxman, D. Panozzo, O. Sorkine-Hornung:
"Integrable PolyVector fields";
ACM Transactions on Graphics, 34/4 (2015), 38; S. 1 - 12.

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.

http://dx.doi.org/10.1145/2766906