'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...

The basic idea of the Meir/Sharma/Hall/Meyer error analysis for cubic spline interpolation (see [SM66], [H68], [HM76]) has been extended to cover also certain deficient quartic and quintic spline interpolation schemes, the latter already by them, the former by Howell/Varma [HV89] and, perhaps, others. It is the purpose of this note to describe the most general situation to which this idea appli...

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...

A piecewise quintic G spline surface interpolating the vertices of a triangular surface mesh of arbitrary topological type is presented. The surface has an explicit triangular B ezier representation, is a ne invariant and has local support. The twist compatibility problem which arises when joining an even number of polynomial patches G continuously around a common vertex is solved by constructi...

We use C 1 quintic superspline functions to interpolate any given scattered data. The space of C 1 quintic superspline functions is introduced in Lai and LeMehaute'99] and is an improvement of the Alfeld scheme of 3D scattered data interpolation. We have implemented the spline space in MATLAB and tested for the accuracy of reproduction of all quintic polynomials. We present some numerical evide...

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...

Deboor, C. , A Practical Guide to splines, Applied Mathematical Science, Vol. 27 Springer Verlag, New York, 1979. Hall, C. A. and Meyer, W. W. , J. Approximation Theory, 16(1976), pp. 105-122. Howel, G. and Verma, A. K. , Best Error Bond of Quartic Spline Interpolation, J. Appron Theory 58 (1989), 58-67. Davis, P. J. , Interpolation and approximation. New Yrok, 1961. Agrawal, R. P. and Wong, P....