showing 4 related works from this author
Annihilation Operators for Exponential Spaces in Subdivision
2022
We investigate properties of differential and difference operators annihilating certain finite-dimensional subspaces of exponential functions in two variables that are connected to the representation of real-valued trigonometric and hyperbolic functions. Although exponential functions appear in a variety of contexts, the motivation behind this work comes from considering subdivision schemes with the capability of preserving those exponential functions required for an exact description of surfaces parametrized in terms of trigonometric and hyperbolic functions.
On the reconstruction of discontinuous functions using multiquadric RBF–WENO local interpolation techniques
2020
Abstract We discuss several approaches involving the reconstruction of discontinuous one-dimensional functions using parameter-dependent multiquadric radial basis function (MQ-RBF) local interpolants combined with weighted essentially non-oscillatory (WENO) techniques, both in the computation of the locally optimized shape parameter and in the combination of RBF interpolants. We examine the accuracy of the proposed reconstruction techniques in smooth regions and their ability to avoid Gibbs phenomena close to discontinuities. In this paper, we propose a true MQ-RBF–WENO method that does not revert to the classical polynomial WENO approximation near discontinuities, as opposed to what was pr…
G1 rational blend interpolatory schemes: a comparative study
2012
Interpolation of triangular meshes is a subject of great interest in many computer graphics related applications, as, for example, gaming and realtime rendering. One of the main approaches to interpolate the positions and normals of the mesh vertices is the use of parametric triangular Bezier patches. As it is well known, any method aiming at constructing a parametric, tangent plane (G^1) continuous surface has to deal with the vertex consistency problem. In this article, we propose a comparison of three methods appeared in the nineties that use a particular technique called rational blend to avoid this problem. Together with these three methods we present a new scheme, a cubic Gregory patc…
A comparison of local parametric C0 Bézier interpolants for triangular meshes
2011
Parametric curved shape surface schemes interpolating vertices and normals of a given triangular mesh with arbitrary topology are widely used in computer graphics for gaming and real-time rendering due to their ability to effectively represent any surface of arbitrary genus. In this context, continuous curved shape surface schemes using only the information related to the triangle corresponding to the patch under construction, emerged as attractive solutions responding to the requirements of resource-limited hardware environments. In this paper we provide a unifying comparison of the local parametric C^0 curved shape schemes we are aware of, based on a reformulation of their original constr…