On 2D quasi-isometric regular grids that are orthogonal far from corners

Abstract

A special class of the quasi-isometric mappings for the generation of quasi-isometric regular coordinate systems is discussed. The base computational strategy of our approach is that the physical field is decomposed into five nonoverlapping sub-regions which are automatically generated by solving a variational problem. Four of these blocks containing four corners on the boundary of the physical region are conformal images of geodesic quadrangles on surfaces of constant curvature. Within each of these blocks a quasi-isometric grid is generated. Orthogonality of coordinate lines holds in the fifth block which is a conformal image of a non-convex polygon composed of several rectangles on the plane.