in this paper we introduce an improvement in the path planning algorithm for the humanoid soccer playing robot which uses ferguson splines and pso (particle swarm optimization). the objective of the algorithm is to find a path through other playing robots to the ball, which should be as short as possible and also safe enough. ferguson splines create preliminary paths using random generated para...

by using the trigonometric uniform splines of order 3 with a real tension factor, a numericalmethod is developed for solving a linear second order boundary value problems (2vbp) withdirichlet, neumann and cauchy types boundary conditions. the moment at the knots isapproximated by central finite-difference method. the order of convergence of the methodand the theory is illustrated by solving tes...

Elastic splines (including dynamic \snakes" and elastic contours), minimising an energy norm of the membrane and/or thin-plate types, have been used to model many surfaces in visual reconstruction and related biomedical applications. In this paper, we model the displacement of the material between successive cardiac images using vector splines. We deene a family of elastic splines. These spline...

We study the 3D reconstruction of a binary scene from X-ray tomographic data. In the special case of a compact and uniform object lying in a uniform background, the scene is entirely defined by the object surface. Then, we select parametric surface models, and we directly estimate their parameters from the data. After showing the ability of spherical harmonics and first order splines (polyhedra...

This paper develops the manifold T-splines, which naturally extend the concept and the currently available algorithms/techniques of the popular planar tensor-product NURBS and T-splines to arbitrary manifold domain of any topological type. The key idea is the global conformal parameterization that intuitively induces a tensor-product structure with a finite number of zero points, and hence offe...

The present authors have introduced polynomial splines over T-meshes (PHT-splines) and provided the theories and applications for PHT-splines over hierarchical T-meshes. This paper generalizes PHT-splines to arbitrary topology over general T-meshes with any structures. The general PHT-spline surfaces can be constructed through an unified scheme to interpolate the local geometric information at ...

A refinable spline is a compactly supported refinable function that is piecewise polynomial. Refinable splines, such as the well known B-splines, play a key role in computer aided geometric designs. Refinable splines have been studied in several papers, most noticably in [7] for integer dilations and [3] for real dilations. There are general characterizations in these papers, but these characte...

This paper is concerned with a study of some new formulations of smoothness conditions and conformality conditions for multivariate splines in terms of B-net representation. In the bivariate setting, a group of new parameters of bivariate quartic and quintic polynomials over a planar simplex is introduced, new formulations of smoothness conditions of bivariate quartic C1 splines and quintic C2 ...

Discrete generalized splines are continuous piecewise defined functions which meet some smoothness conditions for the first and second divided differences at the knots. Direct algorithms and recurrence relations are proposed for constructing discrete generalized B-splines (discrete GB-splines for short). Properties of discrete GB-splines and their series are studied. It is shown that discrete G...

In science and engineering there often is a need for the approximation of scattered multi-dimensional data. A class of powerful scattered data approximators are the multivariate simplex B-splines. Multivariate simplex B-splines consist of Bernstein basis polynomials that are defined on a geometrical structure called a triangulation. Multivariate simplex B-splines have a number of advantages ove...