Approximation of meander-like regions by paths of lemniscatic sectors and the computation of orthogonal meshes

We consider the question of automatic generation of orthogonal meshes on meander-like regions (i.e. elongated regions with changing width, such as riverbeds, 2D profiles of arteries, sinuous roads). We model the boundaries by stitching together segments of lemniscates of three foci. Each portion of the meander-like region is approximated with a ‘sector’ of a region between two confocal lemniscates. We place an orthogonal mesh on each of these regions by transferring the mesh on a circular annulus, taking roots of cubic polynomials. We report on the results of numerical experiments performed with Matlab on data pertaining the Orinoco river.