Riemmanian metric of harmonic parametrization of geodesic quadrangles and quasi-isometric grids

Gennadii A. Chumakov

Mathematics and Computers in Simulation (MATCOM), 2008, vol. 78, issue 5, 575-592

Abstract: We consider the problem of generating a 2D structured boundary-fitting rectangular grid in a curvilinear quadrangle D with angles αi=ϕi+π/2, where −π/2<ϕi<π/2, i=1,…,4. We construct a quasi-isometric mapping of the unit square onto D; it is proven to be the unique solution to a special boundary-value problem for the Beltrami equations. We use the concept of “canonical domains”, i.e., the geodesic quadrangles with the angles α1,…,α4 on surfaces of constant curvature K=4sin⁡(ϕ1+ϕ2+ϕ3+ϕ4)/2, to introduce a special class of coefficients in the Beltrami equations with some attractive invariant properties. In this work we obtain the simplest formula representation of coefficients gjk, via a conformally equivalent Riemannian metric of harmonic parametrization of geodesic quadrangles. We also propose a new, more robust method to compute the metric for all parameter values.

Keywords: Quasi-isometric mapping; Conformal mapping; Non-Euclidian geometries; Geodesic quadrangles (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:78:y:2008:i:5:p:575-592

DOI: 10.1016/j.matcom.2008.04.001

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