相关论文: Construction of $C^2$ cubic splines on arbitrary t…
We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology. Since prevalent…
Probability density functions form a specific class of functional data objects with intrinsic properties of scale invariance and relative scale characterized by the unit integral constraint. The Bayes spaces methodology respects their…
Under consideration methods of constructing trigonometric interpolation splines of two variables on rectangular areas. These methods are easily generalized to the case of trigonometric interpolation splines of several variables on such…
A new representation of splines that targets efficiency in the analysis of functional data is implemented. The efficiency is achieved through two novel features: using the recently introduced orthonormal spline bases, the so-called {\it…
Reachable Minimally supported (RM) B-splines have been recently introduced as a novel B-spline--like basis. They feature local linear independence and admit a fast de Boor--like evaluation algorithm. These properties make them particularly…
The perimeter and area generating functions of exactly solvable polygon models satisfy q-functional equations, where q is the area variable. The behaviour in the vicinity of the point where the perimeter generating function diverges can…
Motivated by applications in architecture and design, we present a novel method for increasing the developability of a B-spline surface. We use the property that the Gauss image of a developable surface is 1-dimensional and can be locally…
Compactly supported shearlets have been studied in both theory and applications. In this paper, we construct symmetric compactly supported shearlet systems based on pseudo splines of type II. Specially, using B-splines, we construct…
Approximating data points in three or higher dimension space based on cubic B-spline curve is presented. Representations for planar curves, are merged and extended to the higher dimension. The curve is fitted to the order of data points, or…
We constructed physically stable sp2 negatively curved cubic carbon structures which reticulate a Schwarz P-like surface. The method for constructing such crystal structures is based on the notion of the standard realization of abstract…
We present computational methods for constructing orthogonal/orthonormal polynomials over arbitrary polygonal domains in $\mathbb{R}^2$ using bivariate spline functions. Leveraging a mature MATLAB implementation which generates spline…
Box splines provide smooth spline spaces as shifts of a single generating function on a lattice and so generalize tensor-product splines. Their elegant theory is laid out in classical papers and a summarizing book. This compendium aims to…
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
In this paper we compute the distributions of various markings on smooth cubic surfaces defined over the finite field $\mathbb{F}_q$, for example the distribution of pairs of points, `tritangents' or `double sixes'. We also compute the…
Two triangle meshes are conformally equivalent if for any pair of incident triangles the absolute values of the corresponding cross-ratios of the four vertices agree. Such a pair can be considered as preimage and image of a discrete…
Shape preservation behavior of a spline consists of criterial conditions for preserving convexity, inflection, collinearity, torsion and coplanarity shapes of data polgonal arc. We present our results which acts as an improvement in the…
We study the product structure on the Chow ring (with rational coefficients) of a cubic hypersurface in projective space and prove that the image of the product map is as small as possible.
For any 3-monotone on $[a,b]$ function $f$ (its third divided differences are nonnegative for all choices of four distinct points, or equivalently, $f$ has a convex derivative on $(a,b)$) we construct a cubic 3-monotone (like $f$) spline…
Let Fq be a finite field with q=8 or q at least 16. Let S be a smooth cubic surface defined over Fq containing at least one rational line. We use a pigeonhole principle to prove that all the rational points on S are generated via tangent…
Abstract deformations of the CR structure of a compact strictly pseudoconvex hypersurface $M$ in $\mathbb{C}^2$ are encoded by complex functions on $M$. In sharp contrast with the higher dimensional case, the natural integrability condition…