# 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

, Volume 6 (1): 7 – Jan 1, 2016
7 pages

/lp/de-gruyter/bicubic-splines-and-biquartic-polynomials-hOrNJ4i85f
Publisher
de Gruyter
© 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