square2disk function

Square to disk

Conformal map from the unit square to the unit disk. The function is vectorized.

square2disk(z)

Arguments

• z: a complex number in the unit square $[0,1] \times [0,1]$

Returns

A complex number in the unit disk.

Examples

x <- y <- seq(0, 1, length.out = 25L)
Grid <- transform(
  expand.grid(X = x, Y = y), 
  Z = complex(real = X, imaginary = Y)
)
u <- square2disk(Grid$Z)
plot(u, pch = 19, asp = 1)