## ConformalMaps.jl

A Julia package implementing the zipper algorithm for numerical conformal maps
Author sswatson
Popularity
2 Stars
Updated Last
7 Months Ago
Started In
April 2015

# ConformalMaps.jl

`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 ### Used By Packages

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