Conformal mapping and periodic cubic spline interpolation

Abstract

Previous studies have shown computation of conformal mapping in which the exact parameterization of the boundary of the region is assumed known. However there are regions whose boundaries have no known exact parameterization. Periodic cubic spline interpolation had been introduced to approximate and obtain the parameterization. We present a numerical procedure to generate periodic cubic spline from the boundary of a 2-dimensional object by using Mathematica software. First we obtain Cartesian coordinates points from the boundary of this 2-dimensional object. Then we convert them into polar coordinates form. Finally the cubic spline is generated based on this polar coordinate points. Some results of our numerical experiments are presented.