7,019 research outputs found
Error Analysis of a Rational Interpolation Spline
Abstract. This paper deals with the approximation properties of a rational cubic interpolation with linear denominator. The rational cubic spline based on function values only and the two families of parameters, in the description of the rational interpolant, modify the shape of the curve freely. Error expression of the values and the derivatives of interpolating functions are derived, which shows the interpaltion is stable
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An arbitrary mesh network scheme using rational splines
A C1 surface scheme is described which interpolates points defined on an arbitrary mesh network. The scheme involves the blending of strip ‘functions’ developed from a rational spline method. The rational spline provides interval and point tension weights which can be used to control the shape of the surface scheme
Polynomial cubic splines with tension properties
In this paper we present a new class of spline functions with tension properties. These splines are composed by polynomial cubic pieces and therefore are conformal to the standard, NURBS based CAD/CAM systems
Rational-spline approximation with automatic tension adjustment
An algorithm for weighted least-squares approximation with rational splines is presented. A rational spline is a cubic function containing a distinct tension parameter for each interval defined by two consecutive knots. For zero tension, the rational spline is identical to a cubic spline; for very large tension, the rational spline is a linear function. The approximation algorithm incorporates an algorithm which automatically adjusts the tension on each interval to fulfill a user-specified criterion. Finally, an example is presented comparing results of the rational spline with those of the cubic spline
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