Geometry Aware Direction Field Processing

@inproceedings{RayRM2008,
 abstract = { Many algorithms in texture synthesis, non-photorealistic rendering (hatching), or re-meshing require to define the orientation of some features (texture, hatches or edges) at each point of a surface. In early works, tangent vector (or tensor) fields were used to define the orientation of these features. Extrapolating and smoothing such fields is usually performed by minimizing an energy composed of a smoothness term and of a data fitting term. More recently, dedicated structures (N-RoSy Palacios and Zhang [2007] and N-symmetry direction fields Ray et al. [2006b]) were introduced in order to unify the manipulation of these fields, and provide control over the field’s topology (singularities). On the one hand, controlling the topology makes it possible to have few singularities, even in the presence of high frequencies (fine details) in the surface geometry. On the other hand the user has to explicitly specify all singularities instead of letting them emerge naturally from the direction extrapolation and smoothing, which can be a tedious task. This paper introduces an intermediate representation that keeps the intuitive design operations such as smoothing and giving directional constraints, but restates the objective function in a way that avoids the singularities yielded by the smaller geometric details. The resulting designing tool is intuitive, simple, and allows to create fields with simple topology, even in the presence of high geometric frequencies. },
 author = { Ray, Nicolas AND Vallet, Bruno AND Alonso, Laurent AND Levy, Bruno },
 booktitle = { 28th gOcad Meeting },
 month = { "june" },
 publisher = { ASGA },
 title = { Geometry Aware Direction Field Processing },
 year = { 2008 }
}