Grid generation using lemniscates with two foci

We consider the approximation of planar curves by pairs of two-foci lemniscates that are stitched together continuously. Lemniscates are level curves of the absolute value of an univariate complex polynomial. We want to build orthogonal grids on offshore areas, and on elongated regions with changing width using lemniscates with two foci. Such grids have many advantages in the numerical modeling of problems such as contaminant transport in rivers and also in areas of 3D visualization such as terrain modeling. The main application is in the areas of numerical solution of PDEs and computer aided geometric design. We report on the results of numerical experiments performed with MATLAB®using data from the San Andrés island and the Guajira peninsula in Colombia and the Orinoco river. In this paper we compare the exact distance between a point and a lemniscate with the estimate that we have used in this paper and previous work.