Schwarz–Christoffel transformation

The Schwarz–Christoffel transformation is a mathematical tool used to map complex shapes, like irregularly shaped regions in the plane, onto simpler, more manageable ones, such as the upper half-plane or a rectangle. Imagine it as a way to "stretch" or "bend" a complicated polygonal area into a straight or regular shape without distorting angles at the corners. This transformation leverages complex analysis to effectively study and solve physical problems—like fluid flow or electromagnetic fields—in complex geometries by translating them into simpler, equivalent domains.