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Geometry Aware Direction Field Processing
ACM Transactions on Graphics, 2009
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 and N-symmetry direction fields ) 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, which can be a tedious task. It would be better to let them emerge naturally from the direction extrapolation and smoothing. This paper introduces an intermediate representation that still allows the intuitive design op- erations such as smoothing and directional constraints, but restates the objective function in a way that avoids the singularities yielded by the smaller geometric details. The resulting design tool is intuitive, simple, and allows to create fields with simple topology, even in the presence of high geometric frequencies. The so-generated field can be used to steer global parameterization methods (e.g. QuadCover).
AUTHOR = "Nicolas Ray and Bruno Vallet and Laurent Alonso and Bruno Lévy
TITLE = "Geometry Aware Direction Field Processing",
JOURNAL = "ACM Transactions on Graphics",
YEAR = "2009",
Supplemental material, links, hindsight ...
N-Symmetry Direction Field Design provides provably correct
full control of the topology of the designed vector field (index of
singularities and index of generators).