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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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References (10)

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

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 Sciencede Gruyter

Published: Jan 1, 2016

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