HIERARCHICAL COMPUTATION OF HERMITE SPHERICAL INTERPOLANT

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LAMNII A.; MRAOUI H.

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION Year:2012 | Volume:2 | Issue:4 Page(s): 247-259

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Information Journal Paper

Title

HIERARCHICAL COMPUTATION OF HERMITE SPHERICAL INTERPOLANT

Author(s)

LAMNII A. | MRAOUI H. | Issue Writer Certificate

Keywords

SPHERICAL SPLINES

HERMITE INTERPOLATION

RECURSIVE COMPUTATION

Abstract

In this paper, we propose to extend the hierarchical bivariate Hermite Interpolant to the spherical case. Let T be an arbitrary spherical triangle of the unit sphere S and let u be a function defined over the triangle T. For kϵN, we consider a Hermite spherical Interpolant problem Hk defined by some data scheme Dk (u) and which admits a unique solution pk in the space Bnk (T) of homogeneous Bernstein-Bezier polynomials of degree nk=2 k (resp. nk=2k+1) defined on T. We discuss the case when the data scheme Dr(u) are nested, i.e., Dr-1 (u) ÌDr(u) for all 1£r£k. This, give a recursive formulae to compute the polynomialpk. Moreover, this decomposition give a new basis for the space Bnk (T), which are the hierarchical structure. The method is illustrated by a simple numerical example.

Cites

TENSION QUARTIC TRIGONOMETRIC BEZIER CURVES PRESERVING INTERPOLATION CURVES SHAPE

References

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APA: Copy

LAMNII, A., & MRAOUI, H.. (2012). HIERARCHICAL COMPUTATION OF HERMITE SPHERICAL INTERPOLANT. INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION, 2(4), 247-259. SID. https://sid.ir/paper/328252/en

Vancouver: Copy

LAMNII A., MRAOUI H.. HIERARCHICAL COMPUTATION OF HERMITE SPHERICAL INTERPOLANT. INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION[Internet]. 2012;2(4):247-259. Available from: https://sid.ir/paper/328252/en

IEEE: Copy

A. LAMNII, and H. MRAOUI, “HIERARCHICAL COMPUTATION OF HERMITE SPHERICAL INTERPOLANT,” INTERNATIONAL JOURNAL OF MATHEMATICAL MODELLING & COMPUTATION, vol. 2, no. 4, pp. 247–259, 2012, [Online]. Available: https://sid.ir/paper/328252/en

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