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