A non-stationary subdivision scheme for curve interpolation

(R) function, then the limit function of the scheme approximates the original function quadratically

A new class of trigonometric B-Spline Curves

We construct one-frequency trigonometric spline curves with a de Boor-like algorithm for evaluation and analyze their shape-preserving properties. The convergence to quadratic B-spline curves is also analyzed. A fundamental tool is the concept of the normalized B-basis, which has optimal shape-preserving properties and good symmetric properties

Ternary Three Point Non-Stationary Subdivision Scheme

Abstract: A ternary three-point approximating non-stationary subdivision scheme is presented that generates the family of C 2 limiting curve. The proposed scheme can be considered as the non-stationary counterpart of the ternary three-point approximating stationary scheme. The comparison of the proposed scheme has been demonstrated using different examples with the existing ternary three-point stationary scheme, which shows that the limit curves of the proposed scheme behave more pleasantly and are very close to generate the conic section

Control Curves and Knot Insertion for Trigonometric Splines

. We introduce control curves for trigonometric splines and show that they have properties similar to those for classical polynomial splines. In particular, we discuss knot insertion algorithms, and show that as more and more knots are inserted into a trigonometric spline, the associated control curves converge to the spline. In addition, we establish a convex-hull property and a variation-diminishing result. 1. Introduction Since their introduction in [Schoenberg64], trigonometric splines have been studied in a number of papers. They turn out to have many properties in common with the classical polynomial splines. For example, they are linear combinations of locally supported functions (called trigonometric B-splines) which satisfy a three-term recurrence relation [LycheWinther79]. Approximation properties of trigonometric 1) This paper continues Per Erik's long-term interest in trigonometric splines, and was written posthumously based on seminars and discussions at Vanderbilt Univ..