Related papers: Trigonometric splines of several variables
We study the local approximation properties in hierarchical spline spaces through multiscale quasi-interpolation operators. This construction suggests the analysis of a subspace of the classical hierarchical spline space (Vuong et al.,…
Standard interpolation techniques are implicitly based on the assumption that the signal lies on a single homogeneous domain. In contrast, many naturally occurring signals lie on an inhomogeneous domain, such as brain activity associated to…
Given a permutation polynomial of a large finite field, finding its inverse is usually a hard problem. Based on a piecewise interpolation formula, we construct the inverses of cyclotomic mapping permutation polynomials of arbitrary finite…
A C++ software design is presented that can be used to interpolate data in any number of dimensions. The design is based on a combination of templates of functional collections of elements and so-called type lists. The design allows for…
We give an overview of recently implemented polymake features for computations in tropical geometry. The main focus is on explicit examples rather than technical explanations. Our computations employ tropical hypersurfaces, moduli of…
We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in $n$ variables. The main tool is combinatorial polarization, and the…
A $\textit{polygonal curve}$ is a collection of $m$ connected line segments specified as the linear interpolation of a list of points $\{p_0, p_1, \ldots, p_m\}$. These curves may be obtained by sampling points from an oriented curve in…
In the context of cubic splines, the authors have contributed to a recent paper dealing with the computation of nonlinear derivatives at the interior nodes so that monotonicity is enforced while keeping the order of approximation of the…
The local refinement of PHT-splines (polynomial splines over hierarchical T-meshes) is achieved by a simple cross insertion, which may introduce superfluous control points or coefficients. By allowing split-in-half in mesh refinement,…
A projective rectangle is like a projective plane that may have different lengths in two directions. We develop properties of the graph of lines, in which adjacency means having a common point, especially its strong regularity and clique…
Flow matching is a scalable generative framework for characterizing continuous normalizing flows with wide-range applications. However, current state-of-the-art methods are not well-suited for modeling dynamical systems, as they construct…
Let a polygon be composed of equal rectangles. We find all quadratic irrationals r for which the polygon can be tiled by similar rectangles with given side ratio r.
In CAGD the design of a surface that interpolates an arbitrary quadrilateral mesh is definitely a challenging task. The basic requirement is to satisfy both criteria concerning the regularity of the surface and aesthetic concepts. With…
A theory of spline quadrature rules for arbitrary continuity class in a closed interval $[a, b]$ with arbitrary nonuniform subintervals based on semi-classical orthogonal Jacobi polynomials is proposed. For continuity class $c \ge 2$ this…
The edge-to-edge tilings of the sphere by congruent polygons, where all edges are straight, have been completely classified. We classify the curvilinear version of the similar triangular tilings, where the edges may not be straight, and…
Many scientific fields and applications require compact representations of multivariate functions. For this problem, decoupling methods are powerful techniques for representing the multivariate functions as a combination of linear…
We discuss some applications of an intrinsic multipication in the space of simple loops in a surface.
Blending schemes based on circles provide smooth `fair' interpolations between series of points. Here we demonstrate a simple, robust set of algorithms for performing circle blends for a range of cases. An arbitrary level of G-continuity…
The primary objectives of this paper are to present the construction of bivariate fractal interpolation functions over triangular interpolating domain using the concept of vertex coloring and to propose a double integration formula for the…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…