Schwarz–Christoffel mapping

Summary

A Schwarz–Christoffel mapping is a conformal map from the upper half-plane onto the interior of a polygon. Such maps have an explicit integral form, in which the derivative is a product of powers of linear factors, one for each vertex. The exponents come from the angles of the polygon, while the positions of the preimages of the vertices must usually be found numerically. The formula is one of the few cases where the Riemann mapping theorem comes with a concrete map. It is much used in engineering and in numerical conformal mapping.