Generalized cardinal Hermite spline interpolation is considered. A special case of this problem is the classical cardinal Hermite spline interpolation with shifted nodes. By means of a corresponding symbol new representations of the cardinal Hermite fundamental splines can be given. Furthermore, a new efficient algorithm for the computation of the cardinal Hermite spline interpolant is obtained...

Abstract— A smooth curve interpolation is very significant in computer graphics or in data visualization. In the present paper -piecewise rational cubic spline function with tension parameter is considered which produces a monotonic interplant to a given monotonic data set. The parameters in the description of the spline curve can be used to modify the shape of the curve, locally and globally. ...

In this paper a rational cubic algebraic spline with two shape parameters is developed to create a high-order smoothness interpolation using function values and derivative values which are being interpolated. This is a kind of rational cubic interpolation with quadratic denominator. This rational spline interpolant is monotonic interpolant to given monotonic data. The more important achievement...

In the present paper, the existence and uniqueness of deficient discrete cubic spline interpolant by matching the given function and first order difference at the intermediate points between successive mesh points for a uniform mesh has been discussed and also a error estimate concerning this deficient discrete cubic spline interpolant is obtained

Abstract: This study proposes new C rational cubic spline interpolant of the form cubic/quadratic with three shape parameters to preserves the geometric properties of the given data sets. Sufficient conditions for the positivity and data constrained modeling of the rational interpolant are derived on one parameter while the remaining two parameters can further be utilized to change and modify t...

We derive a natural extension of Boehm's free-form y-spline, the G* interpolating y-spline. Primarily, the conditions under which singularities in the spline formulation occur are investigated. Also, the effect that these singularities have on the interpolant are studied. Comparisons are made to the behavior of the interpolating v-spline.

Algorithms are presented for computing a quadratic spline interpolant with variable knots which preserves the monotonicity and convexity of the data. It is also shown that such a spline may not exist for fixed knots.

An explicit representation of a C1 piecewise rational cubic spline has been developed, which can produce a monotonic interpolant to given monotonic data. The explicit representation is easily constructed, and numerical experiments indicate that the method produces visually pleasing curves. Furthermore, an error analysis of the interpolant is given.

Given a segment of a conic section in the form of a rational quadratic Bézier curve and any positive odd integer n, a geometric Hermite interpolant, with 2n contacts, counting multiplicity, is presented. This leads to a G spline approximation having an approximation order of O(h). A bound on the Hausdorff error of the Hermite interpolant is provided. Both the interpolation and error bound are e...