On the interpolating 5-point ternary subdivision scheme: A revised proof of convexity-preservation and an application-oriented extension

Paola Novara and Lucia Romani

Mathematics and Computers in Simulation (MATCOM), 2018, vol. 147, issue C, 194-209

Abstract: In this paper we provide the conditions that the free parameter of the interpolating 5-point ternary subdivision scheme and the vertices of a strictly convex initial polygon have to satisfy to guarantee the convexity preservation of the limit curve. Furthermore, we propose an application-oriented extension of the interpolating 5-point ternary subdivision scheme which allows one to construct C2 limit curves where locally convex segments as well as conic pieces can be incorporated simultaneously. The resulting subdivision scheme generalizes the non-stationary ternary interpolatory 4-point scheme and improves the quality of its limit curves by raising the smoothness order from 1 to 2 and by introducing the additional property of convexity preservation.

Keywords: Interpolating subdivision; Ternary refinement; Convexity preservation; Piecewise-uniform scheme; Conic precision (search for similar items in EconPapers)
Date: 2018
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:147:y:2018:i:c:p:194-209

DOI: 10.1016/j.matcom.2016.09.012

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