In this paper we propose a method to approximate a parametric 3 D-function by bicubic B-spline functions

Abstract Two numerical regimes for the one- and two-dimensional hyperbolic telegraph equations are contrasted in this article. The first implemented regime is uniform algebraic trigonometric tension B-spline DQM, while second DQM. resulting system of ODEs solved by SSP RK43 method after aforementioned spatially discretized. To assess success chosen tactics, a comparison errors shown. graphs can...

The problems of determining the B–spline form of a C Pythagorean– hodograph (PH) quintic spline curve interpolating given points, and of using this form to make local modifications, are addressed. To achieve the correct order of continuity, a quintic B–spline basis constructed on a knot sequence in which each (interior) knot is of multiplicity 3 is required. C quintic bases on uniform triple kn...

A collocation procedure is developed for the linear and nonlinear Fredholm and Volterraintegro-differential equations, using the globally defined B-spline and auxiliary basis functions.The solutionis collocated by cubic B-spline and the integrand is approximated by the Newton-Cotes formula.The error analysis of proposed numerical method is studied theoretically. Numerical results are given toil...

In this paper we prove that the degree elevation of B-spline curves can be interpreted as corner cutting process in theory. We also discover the geometric meaning of the auxiliary control points during the corner cutting. Our main idea is to gradually elevate the degree of B-spline curves one knot interval by one knot interval. To this end, a new class of basis functions, to be called bi-degree...

In this paper, we discuss the B-spline wavelets introduced by Chui and Wang in [1]. The definition for B-spline wavelet packets is proposed along with the corresponding dual wavelet packets. The properties of B-spline wavelet packets are also investigated.

This paper introduces a kind of new wavelet radiosity method called multiresolution B-spline radiosity, which uses B-splines of different scales to represent radiosity distribution functions. A set of techniques and algorithms, such as function extrapolation, adaptive quadrature, scale adjustment and octree, are proposed to implement it. This method sets up hierarchical structures on surfaces, ...

This paper describes an unbounded resolution paint system. The image is represented using a bi-orthogonal wavelet basis. The wavelet framework makes it possible to implement the necessary multiscale image operations in an efficient manner and without artifacts. This approach has also many other advantages, including conciseness of the representation. The architecture of the unbounded resolution...

A scheme to specify planar C2 Pythagorean-hodograph (PH) quintic spline curves by control polygons is proposed, in which the “ordinary” C2 cubic B-spline curve serves as a reference for the shape of the PH spline. The method facilitates intuitive and efficient constructions of open and closed PH spline curves, that typically agree closely with the corresponding cubic B-spline curves. The C2 PH ...