We prove that the Toeplitz binary value matrix inversion associated with mth order E-spline interpolation can be implemented using only 2 (m + 1) additions. We develop pipelined architectures for real time B-spline interpolation based on simple running average filters. We also show that an ideal interpolating function, which is approximated by a truncated sinc function with M half cycles, can b...

This essay reviews those basic facts about (univariate) B-splines that are of interest in CAGD. The intent is to give a self-contained and complete development of the material in as simple and direct a way as possible. For this reason, the B-splines are defined via the recurrence relations, thus avoiding the discussion of divided differences which the traditional definition of a B-spline as a d...

In this paper, we propose a new multilevel univariate approximation method with high order accuracy using radial basis function interpolation and cubic B-spline quasi-interpolation. The proposed approach includes two schemes, which are based on radial basis function interpolation with less center points, and cubic B-spline quasi-interpolation operator. Error analysis shows that our method produ...

in this paper, boundary value problems of fractional order are converted into an optimal control problems. then an approximate solution is constructed from translations and dilations of a b-spline function such that the exact boundary conditions are satisfied. the fractional differential operators are taken in the riemann-liouville and caputo sense. several example are given and the optimal err...

We develop a numerical method for solving the boundary value problem of The Linear Seventh Ordinary Boundary Value Problem by using seventh degree B-Spline function. Formulation is based on particular terms order problem. obtain Septic formulation and Collocation B-spline Method formulated as an approximation solution. apply presented to solve example seventh-order which results show that there...

In this paper we study the sensitivity of a spline function, represented in terms of Bsplines, to perturbations of the knots. We do this by bounding the difference between a primary spline, and a secondary spline with the same B-spline coefficients, but different knots. We give a number of bounds for this difference, both local bounds and global bounds in general L-spaces. All the bounds are ba...

Measured bidirectional reflectance distribution function (BRDF) data have been used to represent complex interaction between lights and surface materials for photorealistic rendering. However, their massive size makes it hard to adopt them in practical rendering applications. In this paper, we propose an adaptive method for B-spline volume representation of measured BRDF data. It basically perf...

A Recursive form cubic B-spline basis function is used as basis in B-spline collocation method to solve second linear singularly perturbed two point boundary value problem. The performance of the method is tested by considering the numerical examples with different boundary conditions. Results of numerical examples show the robustness of the method when compared with the analytical solution.

In this paper, we introduce the notion of a normalized radial basis function. In the univariate case, taking these basis functions in combinations determined by certain discrete differences leads to the B-spline basis. In the bivariate case, these combinations lead to a generalization of the B-spline basis to the surface case. Subdivision rules for the resulting basis functions can easily be de...