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 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 ...

This paper describes a new approach to adaptive estimation of parametric deformable contours based on B-spline representations. The problem is formulated in a statistical framework with the likelihood function being derived from a region-based image model. The parameters of the image model, the contour parameters, and the B-spline parameterization order (i.e., the number of control points) are ...

Flexible discriminant analysis (FDA) is a general methodology which aims at providing tools for multigroup non linear classification. It consists in a nonparametric version of discriminant analysis by replacing linear regression by any nonparametric regression method. A new option for FDA, consisting in a nonparametric regression method based on B-spline functions, will be introduced. The relev...

A prescription for constructing dictionaries for cardinal spline spaces on a compact interval is provided. It is proved that such spaces can be spanned by dictionaries which are built by translating a prototype B-spline function of fixed support into the knots of the required cardinal spline space. This implies that cardinal spline spaces on a compact interval can be spanned by dictionaries of ...

A rational cubic trigonometric spline with two shape parameters which play an important role in manipulating the shape of the curve is described in this paper. Its algebraic analogue with shape parameters has been discussed. Spline is presented both in interpolatory and rational B-spline form and the properties of resulting Bsplines are also studied. Keywords— Computer aided geometric design, r...