Bicubic splines and biquartic polynomials

Lukáš Mino, Imrich Szabó, Csaba Török
2016 Open Computer Science  
AbstractThe paper proposes a new efficient approach to computation of interpolating spline surfaces. The generalization of an unexpected property, noticed while approximating polynomials of degree four by cubic ones, confirmed that a similar interrelation property exists between biquartic and bicubic polynomial surfaces as well. We prove that a 2×2-component C1 -class bicubic Hermite spline will be of class C2 if an equispaced grid is used and the coefficients of the spline components are
more » ... ed from a corresponding biquartic polynomial. It implies that a 2×2 uniform clamped spline surface can be constructed without solving any equation. The applicability of this biquartic polynomials based approach to reducing dimensionalitywhile computing spline surfaces is demonstrated on an example.
doi:10.1515/comp-2016-0001 fatcat:7x6lmppwtfejfibp7qxvvqygyu