N-Symmetry Direction Field Design - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles ACM Transactions on Graphics Year : 2008

N-Symmetry Direction Field Design

Nicolas Ray
Bruno Vallet
Bruno Lévy

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 non-photorealistic 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 non-optimum local relaxation procedures. In this paper, we formalize N-symmetry 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 Poincare-Hopf theorem in the case of N-symmetry direction fields on 2-manifolds. Based on this theorem, we explain how to control the topology of N-symmetry 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.
Fichier principal
Vignette du fichier
NSDFD-TOG.pdf (15.84 Mo) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

inria-00331900 , version 1 (20-10-2008)

Identifiers

Cite

Nicolas Ray, Bruno Vallet, Wan-Chiu Li, Bruno Lévy. N-Symmetry Direction Field Design. ACM Transactions on Graphics, 2008, 27 (2), pp.Article 10. ⟨10.1145/1356682.1356683⟩. ⟨inria-00331900⟩
515 View
752 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More