O. Diamanti, A.Vaxman, D. Panozzo, O. Sorkine-Hornung, Designing N-PolyVector Fields with Complex Polynomials, Eurographics Symposium on Geometry Processing (SGP), 2014.

Abstract:

We introduce N-PolyVector fields, a generalization of N-RoSy fields for which the vectors are neither necessarily orthogonal nor rotationally symmetric. We formally define a novel representation for N-PolyVectors as the root sets of complex polynomials and analyze their topological and geometric properties. A smooth N-PolyVector field can be efficiently generated by solving a sparse linear system without integer variables. We exploit the flexibility of N-PolyVector fields to design conjugate vector fields, offering an intuitive tool to generate planar quadrilateral meshes.

Bibtex: 

@article{dvpsh-dnpvfcp-14,
author = {Olga Diamanti and Amir Vaxman and Daniele Panozzo and Olga Sorkine-Hornung},
title = {Designing $N$-{PolyVector} Fields with Complex Polynomials},
journal = {Computer Graphics Forum (proceedings of EUROGRAPHICS Symposium on Geometry Processing)},
volume = {33},
number = {5},
pages = {1--11},
year = {2014},
}