For a class of nonstationary approximating subdivision schemes generalizing the cubic B-spline scheme, we derive closed-form expressions to describe the evolution of each initial control vertex during the whole subdivision process, and we find explicit formulas for exact evaluation of the limit curve and its first derivative at any dyadic-rational parameter value. These results provide, for the first time in the subdivision literature, an exact evaluation of limits obtained by nonstationary approximating subdivision algorithms. As will be shown at the end of this paper, the achievement of closed-form expressions for the limit stencils of a nonstationary approximating scheme has immediate benefits in the context of geometric modelling. Moreover, it marks a first step forward towards the development of further new theoretical results aimed at extending the use of nonstationary subdivision algorithms to new fields of applications.

Romani, L., Hernández Mederos, V., Estrada Sarlabous, J. (2016). Exact evaluation of a class of nonstationary approximating subdivision algorithms and related applications. IMA JOURNAL OF NUMERICAL ANALYSIS, 36(1), 380-399 [10.1093/imanum/drv008].

Exact evaluation of a class of nonstationary approximating subdivision algorithms and related applications

ROMANI, LUCIA
;
2016

Abstract

For a class of nonstationary approximating subdivision schemes generalizing the cubic B-spline scheme, we derive closed-form expressions to describe the evolution of each initial control vertex during the whole subdivision process, and we find explicit formulas for exact evaluation of the limit curve and its first derivative at any dyadic-rational parameter value. These results provide, for the first time in the subdivision literature, an exact evaluation of limits obtained by nonstationary approximating subdivision algorithms. As will be shown at the end of this paper, the achievement of closed-form expressions for the limit stencils of a nonstationary approximating scheme has immediate benefits in the context of geometric modelling. Moreover, it marks a first step forward towards the development of further new theoretical results aimed at extending the use of nonstationary subdivision algorithms to new fields of applications.
Articolo in rivista - Articolo scientifico
Approximating schemes; Exact evaluation; Limit point; Limit tangent; Nonstationary subdivision;
nonstationary subdivision; approximating schemes; exact evaluation; limit point; limit tangent.
English
11-mar-2015
2016
36
1
380
399
none
Romani, L., Hernández Mederos, V., Estrada Sarlabous, J. (2016). Exact evaluation of a class of nonstationary approximating subdivision algorithms and related applications. IMA JOURNAL OF NUMERICAL ANALYSIS, 36(1), 380-399 [10.1093/imanum/drv008].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/98499
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