Riemmanian metric of harmonic parametrization of geodesic quadrangles and quasi-isometric grids
✍ Scribed by Gennadii A. Chumakov
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 242 KB
- Volume
- 78
- Category
- Article
- ISSN
- 0378-4754
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✦ Synopsis
We consider the problem of generating a 2D structured boundary-fitting rectangular grid in a curvilinear quadrangle D with angles α i = ϕ i + π/2, where -π/2 < ϕ i < 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 α 1 , . . . , α 4 on surfaces of constant curvature K = 4 sin(ϕ 1 + ϕ 2 + ϕ 3 + ϕ 4 )/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 g jk , 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.