Related papers: Constructing Explicit B-Spline
New differential-recurrence relations for B-spline basis functions are given. Using these relations, a recursive method for finding the Bernstein-B\'{e}zier coefficients of B-spline basis functions over a single knot span is proposed. The…
This study continues three recent papers in which barypolygonal sequences have been defined and their properties of convergence demonstrated. Any barypolygonal sequence $\mathcal{B}$ of a finite set $\mathcal{A}$ comprising $p\ge 2$ points…
A new global basis of B-splines is defined in the space of generalized quadratic splines (GQS) generated by Merrien subdivision algorithm. Then, refinement equations for these B-splines and the associated corner-cutting algorithm are given.…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
In the realm of computer-aided design (CAD) software, the intersection of B-spline surfaces stands as a fundamental operation. Despite the extensive history of surface intersection algorithms, the challenge of handling complex intersection…
The property of preserving the convexity and concavity of the Bernstein polynomial and of the B\'{e}zier curves is used to generate a method of approximating the reliability polynomial of a hammock network. The mutual behaviour of the…
In this paper, we propose a linear method for $C^{(r,s)}$ approximation of rational B\'{e}zier curve with arbitrary degree polynomial curve. Based on weighted least-squares, the problem be converted to an approximation between two…
We classify all possible local linear procedures over triangular meshes resulting in polynomial $C^1$-spline functions with affinely uniform shape for the basic functions at the edges, and fitting the 9 value- and gradient data at the…
B-splines of order $k$ can be viewed as a mapping $N$ taking a $(k+1)$-tuple of increasing real numbers $a_0 < \cdots < a_k$ and giving as a result a certain piecewise polynomial function. Looking at this mapping $N$ as a whole, basic…
The main result of the paper is the construction of explicit uniformly bounded basis in the spaces of complex homogenous polynomials on the unit ball of $C^3$, extending an earlier result of the author in the $C^2$ case
The aim of this paper is to write an explicit orthonormal parallelization for all parallelizable products of spheres, using an explicit isomorphism with a trivial vector bundle.
Inspired by shape constrained estimation under general nonnegative derivative constraints, this paper considers the B-spline approximation of constrained functions and studies the asymptotic performance of the constrained B-spline…
This paper provides a self-contained exploration of subdivisions of simplicial complexes, with emphasis on barycentric subdivision. We present formal definitions of subdivisions, show how the realization of a complex is preserved under…
We develop a discrete extension operator for trimmed spline spaces consisting of piecewise polynomial functions of degree $p$ with $k$ continuous derivatives. The construction is based on polynomial extension from neighboring elements…
Methods of constructing trigonometric fundamental splines with constant sign and sign-changing convergence factors are given. An example and graphics illustrating the concepts of convergence and interpolation grids are given. Some methods…
In this study, a new form of quadratic spline is obtained, where the coefficients are determined explicitly by variational methods. Convergence is studied and parity conservation is demonstrated. Finally, the method is applied to solve…
We explicitly construct infinite families of MSTD (more sums than differences) sets. There are enough of these sets to prove that there exists a constant C such that at least C / r^4 of the 2^r subsets of {1,...,r} are MSTD sets; thus our…
In this paper, we survey and refine several results -- some previously established in the literature -- that facilitate the construction of exponential bases on planar domains with explicit control over the associated frame bounds. We apply…
Polygonal slap maps are piecewise affine expanding maps of the interval obtained by projecting the sides of a polygon along their normals onto the perimeter of the polygon. These maps arise in the study of polygonal billiards with…
We describe a new, generally applicable strategy for the systematic construction of basis invariants (BIs). Our method allows one to count the number of mutually independent BIs and gives controlled access to the interrelations (syzygies)…