On 2D quasi-isometric regular grids that are orthogonal far from corners (Q1405131)

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