We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve with the ability to perfectly reproduce ellipses. We prove that the proposed Hermite functions form a Riesz basis and that they reproduce prescribed exponential polynomials. We present a method based on Green's functions to unravel their multi-resolution and approximation-theoretic properties. Finally, we derive the corresponding vector and scalar subdivision schemes, which lend themselves to a fast implementation. The proposed vector scheme is interpolatory and level-dependent, but its asymptotic behavior is the same as the classical cubic Hermite spline algorithm. The same convergence properties-i.e., fourth order of approximation-are hence ensured.

Conti, C., Romani, L., Unser, M. (2015). Ellipse-preserving Hermite interpolation and subdivision. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 426(1), 211-227 [10.1016/j.jmaa.2015.01.017].

Ellipse-preserving Hermite interpolation and subdivision

ROMANI, LUCIA
;
2015

Abstract

We introduce a family of piecewise-exponential functions that have the Hermite interpolation property. Our design is motivated by the search for an effective scheme for the joint interpolation of points and associated tangents on a curve with the ability to perfectly reproduce ellipses. We prove that the proposed Hermite functions form a Riesz basis and that they reproduce prescribed exponential polynomials. We present a method based on Green's functions to unravel their multi-resolution and approximation-theoretic properties. Finally, we derive the corresponding vector and scalar subdivision schemes, which lend themselves to a fast implementation. The proposed vector scheme is interpolatory and level-dependent, but its asymptotic behavior is the same as the classical cubic Hermite spline algorithm. The same convergence properties-i.e., fourth order of approximation-are hence ensured.
Articolo in rivista - Articolo scientifico
Cardinal Hermite cycloidal splines; Ellipse-reproduction; Exponential Hermite splines; Hermite interpolation; Subdivision; Analysis; Applied Mathematics
English
1-giu-2015
2015
426
1
211
227
none
Conti, C., Romani, L., Unser, M. (2015). Ellipse-preserving Hermite interpolation and subdivision. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 426(1), 211-227 [10.1016/j.jmaa.2015.01.017].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/98490
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