Generalization of the incenter subdivision scheme

Authors:
Victoria HernáNdez-Mederos;Jorge Estrada-Sarlabous;Ioannis Ivrissimtzis
Affiliations:
Instituto de Cibernética, Matemática y Física, ICIMAF, La Habana, Cuba;Instituto de Cibernética, Matemática y Física, ICIMAF, La Habana, Cuba;Department of Computer Science, Durham University, UK
Venue:
Graphical Models
Year:
2013

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Abstract

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 G^1 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.