Related papers: A Note on Ribbon-based Biharmonic Surface Patches
Bicubic four-sided patches are widely used in computer graphics, CAD/CAM systems etc. Their flexibility is high and enables to compress a surface description before final rendering. However, computer graphics hardware supports only…
Three forms of representation of trigonometric interpolation splines are considered, in particular, the representation by the coefficients of the interpolation trigonometric polynomial, the representation by trigonometric B-splines, which…
We solve the following problem: given a polynomial of order $n$ and the corresponding $B\'ezier$ tensor product patches over an unstructured regular quadrilateral mesh of any valence, find a solution to the $G^{1}1$ or $C^{1}1$…
In this document we present the construction of a radial functions that have the objective of emulating the behavior of the radial basis function thin plate spline (TPS), which we will name as function TPS, we propose a way to partially and…
This paper derives strong relations that boundary curves of a smooth complex of patches have to obey when the patches are computed by local averaging. These relations restrict the choice of reparameterizations for geometric continuity. In…
We consider biharmonic submanifolds in both generalized complex and Sasakian space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature…
The main purposes of this article are to extend our previous results on homogeneous sprays to arbitrary (generalized) sprays, to show that locally diffeomorphic exponential maps can be defined for any (generalized) spray, and to give a…
We classify the space-like biharmonic surfaces in 3-dimension pseudo-Riemannian space form, and construct explicit examples of proper biharmonic hypersurfaces in general ADS space.
Recently the author and U. Reif introduced the concept of diversification of uniform tensor product B-splines. Based on this concept, we give a new constructive modification of non-uniform B-splines. The resulting spline spaces are…
The algebraic characterization of dual univariate interpolating subdivision schemes is investigated. Specifically, we provide a constructive approach for finding dual univariate interpolating subdivision schemes based on the solutions of…
In this article we study various analytic aspects of interpolating sesqui-harmonic maps between Riemannian manifolds where we mostly focus on the case of a spherical target. The latter are critical points of an energy functional that…
This document facilitates understanding of core concepts about uniform B-spline and its matrix representation.
This paper introduces a biharmonic interpolatory subdivision framework on Riemannian manifolds. In the Euclidean setting, the six-point Deslauriers-Dubuc stencil is characterised as the unique minimiser of a discrete curvature-variation…
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…
Using the orbicell decomposition of the Deligne-Mumford compactification of the moduli space of Riemann surfaces studied previously, a chain complex based on semistable ribbon graphs is constructed which is an extension of Konsevich's graph…
We propose and numerically validate a patch reflectarray modeling approach suitable for small patches that describes each patch as a pair of polarizable magnetic dipoles. We introduce an extraction technique to obtain the effective…
In this article we study the estimation of bifurcation coefficients in nonlinear branching problems by means of Rayleigh-Ritz approximation to the eigenvectors of the corresponding linearized problem. It is essential that the approximations…
We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The…
This paper contains a review of available methods for establishing improved interpolation inequalities on the sphere for subcritical exponents. Pushing further these techniques we also establish some new results, clarify the range of…
We present a simple combinatorial model for quasipositive surfaces and positive braids, based on embedded bipartite graphs. As a first application, we extend the well-known duality on standard diagrams of torus links to twisted torus links.…