The Riemann mapping theorem states that a simply connected domain of the complex plane (except for the plane itself) can be conformally mapped to a standard region, such as the unit circle, the square, or the upper-half plane. Conformal mapping is important in several applications, including the Laplace equation and mesh generation, but its use is limited to problems in two dimensions. Usually, the map must be found numerically. An important exception is a polygon; in this case, the map is given by the Schwarz-Christoffel formula.

Driscoll has written a MATLAB toolbox that allows for the creation of Schwarz-Christoffel maps through the command line and a graphical user interface. The toolbox was introduced in 1994; this paper discusses several enhancements since its initial release. For example, it now contains an object-oriented command line model that enables overloading functions of similar purpose into one command. In addition, algorithmic improvements have been made for handling high aspect ratios and multiply connected regions. The graphical interface is intuitive, and conformal mappings can be created easily.