Generalization of the incenter subdivision scheme
Ioannis Ivrissimtzis | Hernandez-Mederos, Victoria | Estrada-Sarlabous, Jorge
In this paper we present an interpolatory Hermite subdivision scheme depending on a free parameter, which generalizes in certain way the incenter subdivision scheme [DW10]. We prove that for any value of the free parameter the limit curve is G1 continuous. Moreover, if vertices of the initial polygon and the tangent vectors are sampled from a circle with any arbitrary spacing, then the subdivision curve is the circle. The proposed scheme is shape preserving limiting the oscillations of the subdivision curve and introducing inflection points only in those regions of the curve where the control polygon suggests a change of convexity. Several examples are presented to demonstrate the performance of the scheme and we formulate some conjectures supported by numerical experiments.