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...

In this paper, we suppose that a density of probability f is expressed as a finite linear combination of second order B-spline functions. Then, we obtain a finite mixture of B-spline. We extend the Expectation Maximization (EM) algorithm in order to estimate the new mixture density. The experiments show that the proposed estimator using B-spline functions can produce a satisfactory estimation o...

We consider two-stage scattered data fitting with truncated hierarchical B-splines (THB-splines) for the adaptive reconstruction of industrial models. The first stage scheme is devoted to computation local least squares variational spline approximations, exploiting a simple fairness functional handle distributions locally varying density points. Hierarchical quasi-interpolation based on THB-spl...

We construct a polynomial spline similar to the box spline, except that we relax the condition that its knots are spaced uniformly in each direction. The recurrence relation for this spline is a generalization of the recurrence relations for the box spline and univariate B-spline. The construction generalizes to exponential-polynomial splines [5]. §

The paper reviews the history of B-spline methods for atomic structure calculations bound states. It highlights various aspects variational method, particularly with regard to orthogonality requirements, iterative self-consistent eigenvalue problem, and related sphf, dbsr-hf, spmchf programs. B-splines facilitate mapping solutions from one grid another. following describes a two-stage approach ...

In this paper, we show that B-spline quarks and the associated quarklets fit into theory of biorthogonal multiwavelets. Quark vectors are used to define sequences subspaces [Formula: see text] which fulfill almost all conditions a multiresolution analysis. Under some special on parameters, they even satisfy those properties. Moreover, prove possess modulation matrices perfect reconstruction con...

The comprehensive numerical study has been made here for the solution of One dimensional heat equation the Finite Element method is adopted for the solution with B-spline basis function the important finding of the present study is to understand the basics behind the FEM method while the B-spline basis function come into the picture here the solution is made using Quadratic B-spline and Cubic B...