VIII CONGRESO COLOMBIANO DE METODOS NUMERICOS: Simulación en Ciencias y Aplicaciones Industriales

We consider the approximation of planar regions by pairs of lemniscates that are stitched together continuously. Lemniscates are level curves of the absolute value of an univariate complex polynomial. We approximate coastal sides or 2D meander like regions such that profiles of arteries, rivers and sinuous roads using lemniscates of two foci and use confocal lemniscates to build orthogonal grids. The use of low degree polynomials gives some computational advantages which are exploited in the implementation. The main applications are numerical solution of PDE’s, computer aided surgical procedures and computer aided geometric design. We report on the results of numerical experiments performed with MATLAB® using data from the Orinoco River, the San Andrés Island and the Guajira Península. In this paper we compare the exact distance between a point and a lemniscates with the estimate we have used in previous works.