Geometric conditions for tangent continuity of interpolatory planar subdivision curves (Q448989)

The most common subdivision schemes are based on linear refinement rules, which are applied separately to each coordinate of the control points, and the analysis of these schemes is well understood. Since the resulting limit curves are not sufficiently sensitive to the geometry of the control polygons, there is a need for geometric subdivision schemes. Such schemes take the geometry of control polygons into account by using nonlinear refinement rules and are known to generate limit curves with less artefacts.NEWLINENEWLINESufficient conditions for a convergent interpolatory planar subdivision scheme to produce tangent continuous limit curves are derived in this paper. These conditions as well as the proofs are purely geometric and do not rely on any parameterization.