Univariate subdivision schemes are efficient iterative methods to generate smooth limit curves starting from a sequence of arbitrary points. Aim of this paper is to present and investigate a new family of 6-point interpolatory non-stationary subdivision schemes capable of reproducing important curves of great interest in geometric modeling and engineering applications, if starting from uniformly spaced initial samples. This new family can reproduce conic sections since it is obtained by a parameter depending affine combination of the cubic exponential B-spline symbol generating functions in the space V_{4,\gamma}={1,x,e^{tx},e^{−tx}} with t in {0,s,is|s>0}. Moreover, the free parameter can be chosen to reproduce also other interesting analytic curves by imposing the algebraic conditions for the reproduction of an additional pair of exponential polynomials giving rise to different extensions of the space V_{4,\gamma}.

Conti, C., Romani, L. (2010). A New Family of Interpolatory Non-Stationary Subdivision Schemes for Curve Design in Geometric Modeling. In ICNAAM 2010, International Conference of Numerical Analysis and Applied Mathematics 2010, AIP Conference Proceedings 1281 (pp.523-526). Springer [10.1063/1.3498528].

A New Family of Interpolatory Non-Stationary Subdivision Schemes for Curve Design in Geometric Modeling

Romani, L
2010

Abstract

Univariate subdivision schemes are efficient iterative methods to generate smooth limit curves starting from a sequence of arbitrary points. Aim of this paper is to present and investigate a new family of 6-point interpolatory non-stationary subdivision schemes capable of reproducing important curves of great interest in geometric modeling and engineering applications, if starting from uniformly spaced initial samples. This new family can reproduce conic sections since it is obtained by a parameter depending affine combination of the cubic exponential B-spline symbol generating functions in the space V_{4,\gamma}={1,x,e^{tx},e^{−tx}} with t in {0,s,is|s>0}. Moreover, the free parameter can be chosen to reproduce also other interesting analytic curves by imposing the algebraic conditions for the reproduction of an additional pair of exponential polynomials giving rise to different extensions of the space V_{4,\gamma}.
paper
Subdivision, Interpolation, Non-stationary symbols, Exponential Polynomials, Exponential-reproduction
English
ICNAAM 2010, International Conference of Numerical Analysis and Applied Mathematics 2010
2010
ICNAAM 2010, International Conference of Numerical Analysis and Applied Mathematics 2010, AIP Conference Proceedings 1281
978-0-7354-0834-0
2010
1281
523
526
none
Conti, C., Romani, L. (2010). A New Family of Interpolatory Non-Stationary Subdivision Schemes for Curve Design in Geometric Modeling. In ICNAAM 2010, International Conference of Numerical Analysis and Applied Mathematics 2010, AIP Conference Proceedings 1281 (pp.523-526). Springer [10.1063/1.3498528].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/18924
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