Abstract : Many algorithms in texture synthesis, non-photorealistic rendering (hatching), or re-meshing re- quire to dene the orientation of some features (texture, hatches or edges) at each point of a surface. In early works, tangent vector (or tensor) elds were used to dene the orientation of these features. Extrapolating and smoothing such elds is usually performed by minimizing an energy composed of a smoothness term and of a data tting term. More recently, dedicated structures (N-RoSy and N-symmetry direction elds ) were introduced in order to unify the ma- nipulation of these elds, and provide control over the eld's topology (singularities). On the one hand, controlling the topology makes it possible to have few singularities, even in the presence of high frequencies (ne 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 opera- tions such as smoothing and directional constraints, but restates the objective function in a way that avoids the singularities yielded by smaller geometric details. The resulting design tool is intuitive, simple, and allows to create elds with simple topology, even in the presence of high geometric frequencies. The generated eld can be used to steer global parameterization methods (e.g. QuadCover).