Open AccessHow Accurately Can a Spherical Cap be Represented by Rational Quadratic Polynomials?
Author(s) -
Christopher G. Provatidis
Publication year - 2021
Publication title -
wseas transactions on circuits and systems/wseas transactions on circuits
Language(s) - English
Resource type - Journals
eISSN - 2224-266X
pISSN - 1109-2734
DOI - 10.37394/23201.2021.20.17
Subject(s) - mathematics , finite element method , quadratic equation , parametric statistics , mathematical analysis , tensor product , simplex , boundary element method , rational function , boundary (topology) , quadratic function , element (criminal law) , pure mathematics , geometry , physics , statistics , political science , law , thermodynamics
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 [0.4, 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).