Constructing parametric quadratic curves

Abstract Constructing a parametric spline curve to pass through a set of data points requires assigning a knot to each data point. In this paper we discuss the construction of parametric quadratic splines and present a method to assign knots to a set of planar data points. The assigned knots are invariant under a ne transformations of the data points, and can be used to construct a parametric quadratic spline which reproduces parametric quadratic polynomials. Results of comparisons of the new method with several known methods are included

Constructing G1 quadratic Bezier curves with arbitrary endpoint tangent vectors

International audienceQuadratic Bézier curves are important geometric entities in many applications. However, it was often ignored by the literature the fact that a single segment of a quadratic Bézier curve may fail to fit arbitrary endpoint unit tangent vectors. The purpose of this paper is to provide a solution to this problem, i.e., constructing G1 quadratic Bézier curves satisfying given endpoint (positions and arbitrary unit tangent vectors) conditions. Examples are given to illustrate the new solution and to perform comparison between the G1 quadratic Bézier cures and other curve schemes such as the composite geometric Hermite curves and the biarcs

First order absolute moment of Meyer-Konig and Zeller operators and their approximation for some absolutely continuous functions

Natural Science Foundation of Fujian Province of China [2010J01012]; National Defense Basic Scientific Research program of China [B1420110155]; Science and Technology Foundation of Xiamen City of China [20083012]A sharp estimate is given for the first order absolute moment of Meyer-Konig and Zeller operators M (n) . This estimate is then used to prove convergence of approximation of a class of absolutely continuous functions by the operators M (n) . The condition considered here is weaker than the condition considered in a previous paper and the rate of convergence we obtain is asymptotically the best possible. (C) 2011 Mathematical Institute Slovak Academy of Science