ConformalMaps is a package for approximating the Riemann map from a
simply connected planar domain to a disk. It uses the zipper algorithm as
described in
Convergence of the zipper algorithm for conformal mapping
by Don Marshall and Steffen Rohde.
The domain (approximated by a polygon) is specified as an array which lists
the vertices of the domain in counterclockwise order. A conformal
map from domain to the unit disk which maps center to the origin
is initialized as ConformalMap(domain,center). The keyword argument
resolution=n inserts n equally spaced points along each side of
the polygon. Higher values of n give greater accuracy but require
longer to compute.
using Graphics2D
using ConformalMaps
vertices = [1.0 0.0;
0.0 1.0;
-1.0 0.0;
0.0 -1.0]
f = ConformalMap(vertices,0.0;resolution=100)f supports function call syntax: f(0.1im)
The inverse of f is obtained as inv(g) and is of type
InverseConformalMap.
If Graphics2D is installed,
then visualize may be used to display the images of certain polar
coordinate level lines under the inverse conformal map (if called on
an InverseConformalMap) or grid lines (if called on a ConformalMap).
g = inv(f)
showgraphics([visualize(g;rays=24,rings=12,innerradius=0.2)[2];domain(f)])
