Schwarz-Christoffel Toolbox

Computes conformal maps to polygons, allowing easy solution of Laplace's equation.

The Schwarz-Christoffel transformation is a recipe for a conformal map to a region bounded by a polygon. They can be computed to very high accuracy in little time. These maps can make certain Laplace boundary value problems trivial to solve on such domains.

Example:

p = polygon([0 i -1+i -1-i 1-i 1]); % L-shaped region

f = diskmap(p); % find map

plot(f) % visualize it

phi = lapsolve(p,[1 nan 4 3 nan 2]); % solve a BVP

[t,x,y] = triangulate(p);

trisurf(t,x,y,phi(x+i*y)); % see it