Refinable compactly supported bivariate C quartic and quintic spline function vectors on the four-directional mesh are introduced in this paper to generate matrix-valued templates for approximation and Hermite interpolatory surface subdivision schemes, respectively, for both the √ 2 and 1-to-4 split quadrilateral topological rules. These splines have their full local polynomial preservation ord...

'Endpoint error' describes the erratic behavior at the beginning and end of the computed acceleration data which is commonly observed after smoothing and differentiating raw displacement data. To evaluate endpoint error produced by four popular smoothing and differentiating techniques, Lanshammar's (1982, J. Biomechanics 15, 99-105) modification of the Pezzack et al. (1977, J. Biomechanics, 10,...

Asymptote is widely used in astronomy, mechanics, architecture and relevant subjects. In this paper, by analyzing the Frenet frame and the Darboux frame of a curve on the surface, the necessary and sufficient conditions for a quadrilateral boundary being asymptotic of a surface are derived. This quadrilateral is called asymptotic quadrilateral. Given corner data including positions, tangents an...

In order to reconstruct spatial curves from discrete electronic sensor data, two alternative C Pythagorean–hodograph (PH) quintic spline formulations are proposed, interpolating given spatial data subject to prescribed contraints on the arc length of each spline segment. The first approach is concerned with the interpolation of a sequence of points, while the second addresses the interpolation ...

In this paper, Quintic spline in o -step points is used for the solution of fourth-order boundary value problems. Spline relations and boundary formulas are developed and the convergence analysis of the given method is investigated. Numerical illustrations are given to show the applicability and e ciency of our method.

We discuss the implementation of a C quintic superspline method for interpolating scattered data in IR based on a modification of Alfeld’s generalization of the Clough-Tocher scheme described by Lai and LeMéhauté [4]. The method has been implemented in MATLAB, and we test for the accuracy of reproduction on a basis of quintic polynomials. We present numerical evidences that when the partition i...

We present a new semi-topological quantity, called the absolute hodograph winding number, that measures how close the quintic PH spline interpolating a given sequence of points is to the cubic spline interpolating the same sequence. This quantity then naturally leads into a new criterion of determining the best quintic PH spline interpolant. This seems to work favorably compared with the elasti...

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