By a d-dimensional B-spline object (denoted as ), we mean a B-spline curve (d = 1), a B-spline surface (d = 2) or a B-spline volume (d = 3). By regularization of a B-spline object we mean the process of relocating the control points of such that they approximate an isometric map of its definition domain in certain directions and is shape preserving. In this paper we develop an efficient regul...

B-spline functions are widely used in many industrial applications such as computer graphic representations, computer aided design, computer aided manufacturing, computer numerical control, etc. Recently, there exist some demands, e.g. in reverse engineering (RE) area, to employ B-spline curves for non-trivial cases that include curves with discontinuous points, cusps or turning points from the...

We present a new strategy for constructing tensor product spline spaces over quadtree and octree T-meshes. The proposed technique includes some simple rules for inferring local knot vectors to define spline blending functions. These rules allows to obtain for a given T-mesh a set of cubic spline functions that span a space with nice properties: it can reproduce cubic polynomials, the functions ...

In this communication the advantages and drawbacks of the isogeometric analysis (IGA) are reviewed in the context of electromagnetic simulations. IGA extends the set of polynomial basis functions, commonly employed by the classical Finite Element Method (FEM). While identical to FEM with Nédélec’s basis functions in the lowest order case, it is based on B-spline and NonUniform Rational B-spline...

In many industrialized areas, the highest concentration of particulate matter, as a major concern on public health, is being felt worldwide problem. Since the air pollution assessment and its evaluation with considering spatial dispersion analysis because of various factors are complex, in this paper, GIS-based modeling approach was utilized to zoning PM2.5 dispersion over Tehran, du...

In this paper we derive optimal subspaces for Kolmogorov n-widths in the L2 norm with respect to sets of functions defined by kernels. This enables us to prove the existence of optimal spline subspaces of arbitrarily high degree for certain classes of functions in Sobolev spaces of importance in finite element methods. We construct these spline spaces explicitly in special cases. Math Subject C...

In this paper we propose a strategy for generating consistent hierarchical T–meshes which allow local refinement and offer a way to obtain spline basis functions with highest order smoothness incrementally. We describe the required ordering of line–segments during refinement and the construction of spline basis functions. We give our strategy for generating consistent hierarchical T–meshes over...

(For properties of box spline functions, see [3, 2]. For computation of these bivariate box spline functions, see [4, 13].) It is known that Bl,m,n generates a multi-resolution approximation of L2(R ) (cf. [14]). We are interested in constructing a compactly supported function B̃l,m,n generating a multi-resolution approximation of L2(R ) which is a biorthogonal dual to Bl,m,n in the following se...

A collocation method based on modified cubic B-spline functions has been developed for the valuation of European, American and barrier options of a single asset. The new approach contains discretization of temporal derivative using finite difference approximation of and approximating the option price with the modified B-spline functions. Stability of this method has been discussed and it is sho...