Given a triangulated surface, a unit length tangent vector field can be used to orient entities located on the surface, such as glyphs or strokes. When these entities are invariant under a π/2 rotation (squares, or curvature hatching), the orientation can be represented by a frame field i.e. four orthogonal tangent unit vectors at each point of the surface. The generation of such fields is a key component of recent quad meshing algorithms based on global parameterization, as it defines the orientation of the final facets. State-of-the-art methods are able to generate smooth frame fields subject to some hard constraints (direction and topology) or smooth constraints (matching the curvature direction). When we have a surface triangular mesh, and a vector defined on each facet, we can't directly know if all the vectors are colinear. We first have to define the (so called) parallel transport of every edge to compare the vectors on a common plan. When dealing with CAD models, the field must be aligned with feature edges. A problem occurs when there is a low angle corner formed by two colliding feature edges. Our solution not only defines the parallel transport to obtain smoothed frame fields on a surface triangular mesh, it also redefines the parallel transport wherever there is a low angle corner, to smooth a frame field as if these corners' angles were π/2.