We present a Hermite interpolation problem via splines of odd-degree which, to the best knowledge of the authors, has not been considered in the literature on interpolation via odd-degree splines. In this new interpolation problem, we conjecture that the interpolation error is bounded in the supremum norm independently of the locations of the knots. Given an integer k ≥ 3, our spline interpolan...

Let A be an infinite sign regular (sr) matrix which can be viewed as a bounded linear operator from lx to itself. It is proved here that if the range of A contains the sequence (...,1,-1,1,-1,...), then A is onto. If A'' exists, then DA~'D is also sr, where D is the diagonal matrix with diagonal entries alternately 1 and -1. In case A is totally positive (tp), then DA~]D is also tp under additi...

A scheme to specify planar C2 Pythagorean-hodograph (PH) quintic spline curves by control polygons is proposed, in which the “ordinary” C2 cubic B-spline curve serves as a reference for the shape of the PH spline. The method facilitates intuitive and efficient constructions of open and closed PH spline curves, that typically agree closely with the corresponding cubic B-spline curves. The C2 PH ...

The algorithms and programs in this handy book deal almost exclusively with cubic splines. A short introduction stresses the maximum "smoothness" of "natural" splines. The next chapter reviews the numerical solution of tridiagonal linear systems by Gauss elimination and of block tridiagonal linear systems by relaxation. Chapter 3 offers programs for cubic spline interpolation with various (sepa...

This study is concerned with the visualization of monotone data using a piecewise C rational trigonometric interpolating scheme. Four positive shape parameters are incorporated in the structure of rational trigonometric spline. Conditions on two of these parameters are derived to attain the monotonicity of monotone data and other two are left free. Figures are used widely to exhibit that the pr...

Inverse solutions to interpolation techniques in computer graphics may increase the accuracy of the rendered frames. An example is the use of an arbitrary time stamp in time interpolation to evaluate the t-parameter, which in turn can be used for time-variant spatial interpolation. In this paper, an analytic inverse is presented for a shape-preserving piecewise cubic Hermite interpolant, used i...

It is observed that the Powell-Sabin 12-split triangle is reen-able since the same split of the 4 similar subtriangles of a triangle contains the lines of split of the original triangle. This property of the split is the key to the existence of a subdivision scheme, for the evaluation of the C 1 quadratic spline on the split which interpolates function and gradient values at the 3 vertices of t...

PH curves; B-spline curves; Nodal points; CNC interpolators; Variable feedrate control; Contour error. Abstract This paper presents a C2 Pythagorean-Hodograph (PH) spline curve interpolator for high speed contouring applications. With the knot vector and control points given, the C2 PH quintic spline curve is a ‘‘good’’ interpolant to the nodal points of the cubic B-spline curve, with the same ...

We study how to use bivariate splines for scattered data interpolation and fitting with preservation of non-negativity of the data values. We propose a minimal energy method to find a C1 smooth interpolation/fitting of non-negative data values from scattered locations based on bivariate splines. We establish the existence and uniqueness of the minimizer under mild assumptions on the data locati...

We conjecture that splines of degree n can interpolate points on a smooth curve in R m with order of contact k ? 1 = n ? 1 + b(n ? 1)=(m ? 1)c at every n-th knot. Moreover, this Geometric Hermite Interpolant (GHI) has the optimal approximation order k + 1. We give a proof of this conjecture for planar quadratic spline curves and describe a simple construction of curvature continuous quadratic s...