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Bicubic splines and biquartic polynomials

Bicubic splines and biquartic polynomials AbstractThe paper proposes a new efficient approachto computation of interpolating spline surfaces. The generalizationof an unexpected property, noticed while approximatingpolynomials of degree four by cubic ones,confirmed that a similar interrelation property exists betweenbiquartic and bicubic polynomial surfaces as well.We prove that a 2×2-component C1 -class bicubic Hermitespline will be of class C2 if an equispaced grid is used andthe coefficients of the spline components are computedfrom a corresponding biquartic polynomial. It implies thata 2×2 uniform clamped spline surface can be constructedwithout solving any equation. The applicability of this biquarticpolynomials based approach to reducing dimensionalitywhilecomputing spline surfaces is demonstratedon an example. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Computer Science de Gruyter

Bicubic splines and biquartic polynomials

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Publisher
de Gruyter
Copyright
© 2016 L. Mino et al.
eISSN
2299-1093
DOI
10.1515/comp-2016-0001
Publisher site
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Abstract

AbstractThe paper proposes a new efficient approachto computation of interpolating spline surfaces. The generalizationof an unexpected property, noticed while approximatingpolynomials of degree four by cubic ones,confirmed that a similar interrelation property exists betweenbiquartic and bicubic polynomial surfaces as well.We prove that a 2×2-component C1 -class bicubic Hermitespline will be of class C2 if an equispaced grid is used andthe coefficients of the spline components are computedfrom a corresponding biquartic polynomial. It implies thata 2×2 uniform clamped spline surface can be constructedwithout solving any equation. The applicability of this biquarticpolynomials based approach to reducing dimensionalitywhilecomputing spline surfaces is demonstratedon an example.

Journal

Open Computer Science – de Gruyter

Published: Jan 1, 2016

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