O. Diamanti, A. Vaxman, D. Panozzo, O. Sorkine-Hornung, Integrable PolyVector Fields, Proceedings of ACM SIGGRAPH 2015.


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.


author = {Olga Diamanti and Amir Vaxman and Daniele Panozzo and Olga Sorkine-Hornung},
title = {Integrable {PolyVector} Fields},
journal = {ACM Transactions on Graphics (proceedings of ACM SIGGRAPH)},
volume = {34},
number = {4},
pages = {38:1-38:12},
year = {2015},