On the interpolating 5-point ternary subdivision scheme: A revised proof of convexity-preservation and an application-oriented extension
| Autor: | Paola Novara, Lucia Romani |
|---|---|
| Přispěvatelé: | Novara, P, Romani, L |
| Rok vydání: | 2018 |
| Předmět: |
Ternary refinement
General Computer Science Piecewise-uniform scheme MathematicsofComputing_NUMERICALANALYSIS 010103 numerical & computational mathematics 02 engineering and technology 01 natural sciences Convexity Theoretical Computer Science 0202 electrical engineering electronic engineering information engineering Limit (mathematics) 0101 mathematics ComputingMethodologies_COMPUTERGRAPHICS Subdivision Mathematics Discrete mathematics Numerical Analysis business.industry Applied Mathematics Regular polygon 020206 networking & telecommunications MAT/08 - ANALISI NUMERICA Convexity preservation Interpolating subdivision Conic section Modeling and Simulation Polygon Conic precision business Ternary operation Convex function |
| Zdroj: | Mathematics and Computers in Simulation. 147:194-209 |
| ISSN: | 0378-4754 |
| DOI: | 10.1016/j.matcom.2016.09.012 |
| Popis: | 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 C 2 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. |
| Databáze: | OpenAIRE |
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