In this paper, geometric Hermite interpolation by planar cubic G1 splines is studied. Three data points and three tangent directions are interpolated per each polynomial segment. Sufficient conditions for the existence of such G1 spline are determined that cover most of the cases encountered in practical applications. The existence requirements are based only upon geometric properties of data a...

Given spatially located observed random variables (x; z) = f(x i ; z i)g i , we propose a new method for nonparametric estimation of the potential functions of a Markov Random Field p(xjz), based on a roughness penalty approach. The new estimator maximises the penalized log-pseudolikelihood function and is a natural cubic spline. The calculations involved do not rely on Monte Carlo simulation. ...

This paper presents representation techniques as the image can be represented in Cubic B-splines that are used to represent the curvilinear features of an image. The algorithm is devised to convert a raster image into vector image. The algorithm first detects the curvilinear features of the image, then based on the curvilinear edges and feature attributes it constructs a triangulation, and fina...

This research focuses on trajectory generation algorithms that take into account the stealthiness of autonomous UAVs; generating stealthy paths through a region laden with enemy radars. The algorithm is employed to estimate the risk cost of the navigational space and generate an optimized path based on the user-specified threshold altitude value. Thus the generated path is represented with a se...

In the context of radial basis function interpolation, the construction of native spaces and the techniques for proving error bounds deserve some further clari cation and improvement. This can be described by applying the general theory to the special case of cubic splines. It shows the prevailing gaps in the general theory and yields a simple approach to local error bounds for cubic spline int...

Article history: Available online 30 June 2010

In this paper, geometric interpolation by G cubic spline is studied. A wide class of sufficient conditions that admit a G cubic spline interpolant is determined. In particular, convex data as well as data with inflection points are included. The existence requirements are based upon geometric properties of data entirely, and can be easily verified in advance. The algorithm that carries out the ...

This report looks at employing optimization techniques to generate cubic splines restricted to lie on the surfaces. We implement a recent algorithm designed for exactly this problem, and attempt to understand its motivation and examine its effectiveness. We also pose the problem in AMPL and apply a standard nonlinear solver to verify our results, and to compare the relative benefits of using th...

T-splines is a recently developed surface modelling technique which is a generalization of B-splines and allows true local refinement. Another well established method supporting local refinement is hierarchical B-splines. This paper presents algorithms for transformation between T-splines and hierarchical (rational) B-splines. With the transformation, a surface expressed in terms of T-splines c...