Implementing point cloud to grid conversion for digital elevation maps (DEM) presents one with many options for interpolation and we intend to explore algorithms for interpolation during the conversion process with a specific focus on Voronoi natural neighbor interpolation. By partitioning the environment into Voronoi cells and using the information from neighboring cells and their respective g...

Interpolation by rational spline motions is an important issue in robotics and related fields. In this paper a new approach to rational spline motion design is described by using techniques of geometric interpolation. This enables us to reduce the discrepancy in the number of degrees of freedom of the trajectory of the origin and of the rotational part of the motion. A general approach to geome...

An algorithm is presented that constructs a C 2-continuous B-spline quaternion curve which interpolates a given sequence of unit quaternions on the rotation group SO(3). The de Casteljau type construction method of B-spline curves can be extended to generate B-spline quaternion curves Sch92]; however, the B-spline quaternion curves do not have C 2-continuity in SO(3). The authors KKS94a] recent...

This paper is concerned with the spline interpolation of functions with a boundary layer component. It is shown that polynomial formulas of spline interpolation for such functions lead to significant errors. We proposed nonpolynomial spline interpolation formulas, fitted to a boundary layer component. Nonsmooth and smooth on whole interval interpolants are constructed. The accuracy of construct...

Method for image prediction with nonlinear control lines which are derived from extracted feature points from the previously acquired imagery data based on Kriging method and morphing method is proposed. Through comparisons between the proposed method and the conventional linear interpolation and widely used Cubic Spline interpolation methods, it is found that the proposed method is superior to...

In this paper, to overcome the innate drawbacks of some old methods, we present a new quintic spline method for integro interpolation. The method is free of any exact end conditions, and it can reconstruct a function and its first order to fifth order derivatives with high accuracy by only using the given integral values of the original function. The approximation properties of the obtained int...

B-splines provide an accurate and efficient method for interpolating regularly spaced data. In this paper, I study the applicability of B-spline interpolation in the context of the inverse interpolation method for regularizing irregular data. Numerical tests show that, in comparison with lower-order linear interpolation, B-splines lead to a faster iterative conversion in under-determined proble...

By the use of locally supported basis functions for spherical spline interpolation the applicability of this approximation method is spread out since the resulting interpolation matrix is sparse and thus eecient solvers can be used. In this paper we study locally supported kernels in detail. Investigations on the Legendre coeecients allow a characterization of the underlying Hilbert space struc...

in this paper, a numerical method is developed for solving a linear sixth order boundaryvalue problem (6vbp ) by using the hyperbolic uniform spline of order 3 (lower order). thereis proved to be first-order convergent. numerical results confirm the order of convergencepredicted by the analysis.