This article discusses the mathematical concepts of multivariate parametric solids and their description by B-spline basis functions. Parametric solids can model both the shape and unisotropic interior. Three types of parametric solids, Coons body of types 0, 1, and 2, are used to demonstrate the interior modelling often used as initial or boundary conditions in numerical simulation. Multiple p...

In this paper the approximation of the optimal compressor function using the first-degree spline functions and quadratic spline functions is done. Coefficients on which we form approximative spline functions are determined by solving equation systems that are formed from treshold conditions. For Gaussian source at the input of the quantizer, using the obtained approximate spline functions a com...

In this paper, we propose a fragment-based evaluation method for non-uniform B-spline surfaces using recent programmable graphics hardware (GPU). A position on a non-uniform Bspline surface is evaluated by the linear combination of both control points and B-spline basis functions. Hence the computational costs can be reduced by pre-computing a knot interval of a parameter from a knot vector. We...

In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.

A number of criteria exist to select the penalty in penalized spline regression, but the selection of the number of spline basis functions has received much less attention in the literature. We propose to use a maximum likelihood-based criterion to select the number of basis functions in penalized spline regression. The criterion is easy to apply and we describe its theoretical and practical pr...

In this paper, nonlinear integral equations have been solved numerically by using B-spline wavelet method and Variational Iteration Method (VIM). Compactly supported semi-orthogonal linear B-spline scaling and wavelet functions together with their dual functions are applied to approximate the solutions of nonlinear Fredholm integral equations of second kind. Comparisons are made between the var...

The Hybrid Spline method (H-spline) is a method of density estimation which involves regression splines and smoothing splines methods. Using basis functions (B-splines), this method is much faster than Smoothing Spline Density Estimation approach (Gu, 1993). Simulations suggest that with more structured data (e.g., several modes) H-spline method estimates the modes as well as Logspline (Kooperb...

Capability to manage the performance of a shared resources environment relies on the model estimation of all dynamics in the system. The main challenge is to capture the nonlinear characteristic which inherently exists in software system applications. Hammerstein-Wiener block structural model is widely regarded as a basis for description of nonlinear systems. This paper extends the existing wor...