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
pointspacing=ϵ inserts equally spaced points along each side of
the polygon so that the spacing between consecutive points is
everywhere less than ϵ. Smaller values of ϵ give greater accuracy
but require longer to compute. The default value is 1% of the diameter
of the domain.
using AsyPlots, ConformalMaps
vertices = [1.0 0.0;
0.0 1.0;
-1.0 0.0;
0.0 -1.0]
f = ConformalMap(vertices,0.0)f supports function call syntax: f(0.1im)
The inverse of f is obtained as inv(f) and is of type
InverseConformalMap.
If AsyPlots is installed,
then visualize may be used to display the images of a hyperbolic
tiling of the disk (if called on an InverseConformalMap) or grid
lines (if called on a ConformalMap).
g = inv(f)
visualize(g) 
visualize returns a ConformalMapVisualization object, whose
fields domain and range contain AsyPlots.Plot2D objects.
combine returns a single plot with the domain and the range
