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...

A new numerical algorithm using quintic splines is developed and analyzed: quintic spline Taylor-series expansion (QSTSE). QSTSE is an Eulerian #ux-based scheme that uses quintic splines to compute space derivatives and Taylor series expansion to march in time. The new scheme is strictly mass conservative and positive de"nite while maintaining high peak retention. The new algorithm is compared ...

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...

This paper presents a new motion planning primitive to be used for the iterative steering of vision-based autonomous vehicles. This primitive is a parameterized quintic spline, denoted as -spline, that allows interpolating an arbitrary sequence of points with overall second-order geometric ( -) continuity. Issues such as completeness, minimality, regularity, symmetry, and flexibility of these -...