Search

In this paper, we present an efficient method for constructing symmetric subdivision schemes reproducing high-degree polynomials, without solving a system of linear equations. Original symmetric subdivision and its deduced subdivisions have similar increasing characteristics to the family of pseudo-splines from the polynomial reproduction point of view. Several examples are given to illustrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

In this paper, a G 2 continuous quintic-polynomial-based unit quaternion interpolation spline curve with tension parameters is presented to interpolate a given sequence of solid orientations. The curve in unit quaternion space S 3 is an extension of the quintic polynomial interpolation spline curve in Euclidean space. It preserves the interpolatory property and G 2 continuity. Meanwhile, the unit quaternion interpolation spline curve possesses the local shape adjustability due to the presence of tension parameters. The change of one tension parameter will only affect the adjacent two pieces of curves. Compared with the traditional B-spline unit quaternion interpolation curve and v -spline unit quaternion interpolation curve, the proposed curve can automatically interpolate the given data points, without solving the nonlinear system of equations over quaternions to obtain the control points, which greatly improves the computational efficiency. Simulation results demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper presents 6-point subdivision schemes with cubic precision. We first derive a relation between the 4-point interpolatory subdivision and the quintic B-spline refinement. By using the relation, we further propose the counterparts of cubic and quintic B-spline refinements based on 6-point interpolatory subdivision schemes. It is proved that the new family of 6-point combined subdivision schemes has higher smoothness and better polynomial reproduction property than the B-spline counterparts. It is also showed that, both having cubic precision, the well-known Hormann-Sabin’s family increase the degree of polynomial generation and smoothness in exchange of the increase of the support width, while the new family can keep the support width unchanged and maintain higher degree of polynomial generation and smoothness. [ABSTRACT FROM AUTHOR]

A five-point binary subdivision scheme with a parameter u is presented. The generating polynomial method and the Hölder exponent are used to investigate the uniform convergence and C k continuity of this subdivision scheme, where k depends on the choice of the parameter u . Moreover, the conditions on the initial points are discussed for the given limit curve to be convexity preserving and an example is given to illustrate our conclusion. [ABSTRACT FROM AUTHOR]

As we know, the classical Neville''s algorithm is an effective method used to solve the interpolation problem by polynomials. In this paper, we adopt the idea of the Neville''s algorithm to construct a kind of blending rational interpolants via continued fractions. For a given set of support points, there are many ways to build up the interpolation schemes, by which we mean that there are many choices to make to determine the initial interpolants on subsets of support points and then update them step by step to form a solution to the full interpolation problem. Numerical examples are given to show the advantage of our method and a multivariate analogy is also discussed. [Copyright &y& Elsevier]

Abstract In this paper, a new combined approximating and interpolating ternary 4-point subdivision scheme with multiple parameters is proposed. A set of nice properties, such as support, continuity and polynomial generation, are briefly discussed. The new combined scheme not only contains a lot of classical ternary schemes as special cases, but also generates brand-new ternary schemes. Compared to other approximating subdivision schemes, limit curves generated by the new scheme are more consistent with the corresponding control polygons and keep detail features better. Examples are given to show the effectiveness of the scheme. Furthermore, fractal property is analyzed and fractal curves are also given. [ABSTRACT FROM AUTHOR]