WSEAS Transactions on Circuits and Systems
Print ISSN: 1109-2734, E-ISSN: 2224-266X
Volume 20, 2021
How Accurately Can Spherical Caps Be Represented by Rational Quadratic Polynomials?
Author:
Abstract: This paper discusses the incapability of a tensor product rational quadratic patch to accurately represent a spherical cap. It was analytically found that there is no combination of control points and associated weights to accurately represent the spherical cap. On top of that, an optimization technique has revealed that for a unit sphere the computed radii in the parametric space may reduce within the interval [0.999999994, 1.000104146]. This study makes sense as a preparatory stage in relation with the isogeometric analysis (IGA), which may be applied in conjunction with either the Finite Element Method (FEM) or the Boundary Element Method (BEM).
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Keywords: Systems Theory, Dynamical Systems, Distributed Systems, Computational geometry, Spherical cap,
Bernstein polynomials, Rational interpolation, Weights, Control points, Isogeometric analysis, FEM, BEM.
Pages: 139-146
DOI: 10.37394/23201.2021.20.17