Shape controlled interpolatory ternary subdivision

• Published in: Applied mathematics and computation Vol. 215; no. 3; pp. 916 - 927
• Main Authors: Beccari, C., Casciola, G., Romani, L.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01-10-2009; Elsevier
• Subjects: Approximations and expansions; Combined subdivision scheme; Conic section; Exact sciences and technology; Interpolation; Mathematical analysis; Mathematics; Non-stationarity; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Sciences and techniques of general use; Tension control; Univariate ternary refinement; Conic section; Univariate ternary refinement; Interpolation; Combined subdivision scheme; Tension control; Non-stationarity; Numerical approximation; Numerical analysis; Applied mathematics
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2009.06.014

Ternary subdivision schemes compare favorably with their binary analogues because they are able to generate limit functions with the same (or higher) smoothness but smaller support.
In this work we consider the two issues of local tension control and conics reproduction in univariate interpolating ternary refinements. We show that both these features can be included in a unique interpolating 4-point subdivision method by means of non-stationary insertion rules that do not affect the improved smoothness and locality of ternary schemes. This is realized by exploiting local shape parameters associated with the initial polyline edges.