Displaying similar documents to “Basis of quartic splines over triangulation.”

A note on tension spline

Segeth, Karel

Similarity:

Spline theory is mainly grounded on two approaches: the algebraic one (where splines are understood as piecewise smooth functions) and the variational one (where splines are obtained via minimization of quadratic functionals with constraints). We show that the general variational approach called smooth interpolation introduced by Talmi and Gilat covers not only the cubic spline but also the well known tension spline (called also spline in tension or spline with tension). We present the...

B-spline bases and osculating flats: One result of H.-P. Seidel revisited

Marie-Laurence Mazure (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

Along with the classical requirements on B-splines bases (minimal support, positivity, normalization) we show that it is natural to introduce an additional “end point property". When dealing with multiple knots, this additional property is exactly the appropriate requirement to obtain the poles of nondegenerate splines as intersections of osculating flats at consecutive knots.

Interpolating and smoothing biquadratic spline

Radek Kučera (1995)

Applications of Mathematics

Similarity:

The paper deals with the biquadratic splines and their use for the interpolation in two variables on the rectangular mesh. The possibilities are shown how to interpolate function values, values of the partial derivative or values of the mixed derivative. Further, the so-called smoothing biquadratic splines are defined and the algorithms for their computation are described. All of these biquadratic splines are derived by means of the tensor product of the linear spaces of the quadratic...