Generalization of the incenter subdivision scheme

We introduce a new interpolatory subdivision scheme generalizing the incenter subdivision [8]. The proposed scheme is equipped with a shape controlling tension parameter, is Hermitian, and reproduces circles from non-uniform samples. We prove that for any value of the free parameter the limit curve is G1 continuous. The scheme is shape preserving and avoids undesirable oscillations by producing curves with a finite number of inflection points at the regions where the control polygon suggests a change of convexity. Several examples are presented demonstrating the properties of the scheme.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► A new Hermitian curve subdivision scheme generalizing incenter subdivision. ► A user-defined tension parameter controls the shape of the limit curve. ► The scheme produces G1 continuous curves. ► Convexity preservation and reproduction of circles from irregular samples. ► For a certain value of the tension, a common measure of discrete curvature converges.