Optimal Approximation of Biquartic Polynomials by Bicubic Splines
doc. RNDr. Csaba Török, CSc.
Ústav informatiky, PF UPJŠ
Although it was known that a 2x2 component uniform bicubic Hermite spline is a clamped spline of class C^2 if the derivatives at the shared knots are given by the first derivatives of a biquartic polynomial, however the optimality of such approximation remained an open question.
Our aim is to resolve this problem. Unlike the spline curves, in the case of spline surfaces it is insufficient to suppose that the grid should be uniform and the spline's derivatives computed from a biquartic polynomial. We show that the biquartic polynomial coefficients have to satisfy some additional constraints to achieve optimal approximation by bicubic splines.