Consider a family of functions of a single variable x: Φ(x; a0, a1, . . . , an), where a0, . . . , an are the parameters. The problem of interpolation for Φ can be stated as follows: Given n + 1 real or complex pairs of numbers (xi, fi), i = 0, . . . , n, with xi 6= xk for i 6= k, determine a0, . . . , an such that Φ(xi; a0, . . . , an) = fi, i = 0, . . . , n. The above is a linear interpolatio...

In [4] the first named author discussed the explicit solutions of the cubic spline interpolation problems. We are now concerned with quintic spline functions. Let 5B[0, n] denote the class of quintic spline functions S(x) defined in the interval [0, n] and having the points 0, 1, • • • , n — 1 as knots. This means that the restriction of S(x) to the interval (*>, J > + 1 ) (P = 0, • • • , n — \...

In this paper we study multivariate polynomial interpolation on Aitken–Neville sets by relating them to generalized principal lattices. We express their associated divided differences in terms of spline integrals.

We derive upper and lower bounds on the dimensions of trivariate spline spaces defined on tetrahedral partitions. The results hold for general partitions, and for all degrees of smoothness r and polynomial degrees d.

In this paper we present a new method for the model of interpolation sweep surfaces by the C-continuous generalized quasicubic interpolation spline. Once given some key position, orientation and some points which are passed through by the spine and initial cross-section curves, the corresponding sweep surface can be constructed by the introduced spline function without calculating control point...

This paper presents a new segmentation algorithm by fitting active contour models (or snakes) to objects using adaptive splines. The adaptive spline model describes the contour of an object by a set of piecewisely interpolating C polynomial spline patches which are locally controlled. Thus the resulting description of the object contour is continuous and smooth. Polynomial splines provide a fas...

This paper presents a new segmentation algorithm by tting active contour models (or snakes) to objects using adaptive splines. The adaptive spline model describes the contour of an object by a set of piecewisely interpolating C polynomial spline patches which are locally controlled. Thus the resulting description of the object contour is continuous and smooth. Polynomial splines provide a fast ...

We establish properties of and propose a conjecture concerning P m(S(x + m)) 2 where S is a piecewise polynomial cardinal spline in L(R). 2000 Mathematics subject classification: 65A15, 62G07

GIS databases often need to include maps from diverse sources. These can differ one another by many characteristics: different projections or reference systems, (slightly) different scales, etc. Theoretical and/or empirical transformations are available in literature to obtain maps in a unique system with a fixed tolerance. These transformations are nevertheless insufficient to completely remov...