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The method of boundary curve reparametrization is applied to construction ofthe approximate analytical conformal mapping of the unit disk onto an arbitrarygiven finite domain with a boundary smooth at every point but fininte number ofacute angle points. The method is based on both the Fredholm equation solutionand spline-interpolation. This approach consists of approximate solution of alinear system with unknown Fourier coefficients and construction of correctionsplines. The approximate mapping function has the form of a Cauchy integral.The method presentation is supported by demonstration of some examples. Thismethod is applicable to the case of multiply connected domains with boundaryangle points.

The approximate conformal mapping of a disk onto domain with an acute angle