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Designing N ‐PolyVector Fields with Complex Polynomials
Author(s) -
Diamanti Olga,
Vaxman Amir,
Panozzo Daniele,
SorkineHornung Olga
Publication year - 2014
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/cgf.12426
Subject(s) - quadrilateral , generalization , mathematics , representation (politics) , polygon mesh , integer (computer science) , field (mathematics) , planar , computer science , discrete mathematics , topology (electrical circuits) , algorithm , algebra over a field , pure mathematics , combinatorics , computer graphics (images) , geometry , mathematical analysis , physics , finite element method , politics , political science , law , thermodynamics , programming language
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.