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has the right to do so. Note that the definitive versions of all EG papers (Eurographics,...) can be downloaded from http://www.eg.org/EG/DL. ACM papers (Siggraph, ...) can be downloaded from http://www.acm.org/dl/. “NSymmetry Direction Field Design” Nicolas Ray, Bruno Vallet, WanChiu Li and Bruno Lévy ACM Transactions on Graphics  Presented at SIGGRAPH, 2008 Abstract: Many algorithms in computer graphics and geometry processing use two orthogonal smooth direction fields (unit tangent vector fields) defined over a surface. For instance, these direction fields are used in texture synthesis, in geometry processing or in nonphotorealistic rendering to distribute and orient elements on the surface. Such direction fields can be designed in fundamentally different ways, according to the symmetry requested: inverting a direction or swapping two directions may be allowed or not. Despite the advances realized in the last few years in the domain of geometry processing, a unified formalism is still lacking for the mathematical object that characterizes these generalized direction fields. As a consequence, existing direction field design algorithms are limited to use nonoptimum local relaxation procedures. In this paper, we formalize Nsymmetry direction fields, a generalization of classical direction fields. We give a new definition of their singularities to explain how they relate with the topology of the surface. Namely, we provide an accessible demonstration of the PoincareHopf theorem in the case of Nsymmetry direction fields on 2manifolds. Based on this theorem, we explain how to control the topology of Nsymmetry direction fields on meshes. We demonstrate the validity and robustness of this formalism by deriving a highly efficient algorithm to design a smooth field interpolating user defined singularities and directions. BibTex reference @INPROCEEDINGS{ray:NSD:2008,
AUTHOR = "Nicolas Ray and Bruno Vallet and WanChiu Li and Bruno Lévy",
TITLE = "NSymmetry Direction Field Design",
BOOKTITLE = "ACM Transactions on Graphics",
NOTE = "Presented at SIGGRAPH",
YEAR = "2008",
}
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