  In a previous paper [11] we introduced a weighted binary average of two 2D
point-normal pairs, termed circle average, and investigated subdivision schemes
based on it. These schemes refine point-normal pairs in 2D, and converge to
limit curves and limit normals. Such a scheme has the disadvantage that the
limit normals are not the normals of the limit curve. In this paper we solve
this problem by proposing a new averaging method, and obtaining a new family of
algorithms based on it. We demonstrate their new editing capabilities and apply
this subdivision technique to smooth a precomputed feasible polygonal point
robot path.
