ijouk(x; halfplane=Val(false), branch=Val(true)) -> z

Inverse Joukowsky map z = x ± √(x^2-1). The branch to evaluate is seleced as follows.

+–––––-+–––––––-+––––––––+ | | !halfplane | halfplane | +–––––-+–––––––-+––––––––+ | branch | abs(z) >= 1 | imag(z) >= 0 | | !branch | abs(z) <= 1 | imag(z) <= 0 | +–––––-+–––––––-+––––––––+

jouk(z)

Joukowsky map (z+z^-1)/2.

radius(x; kwargs...) = abs(ijouk(x; kwargs...))

rsmo(x)

Evaluate √(x^2-1) with branch cut along [-1,1].

The function name is the abbreviation of "root of square minus one".

semimajor(x; kwargs...)

Semi-major axis of the Bernstein ellipse through x.

See ijouk regardings kwargs.

semiminor(x; kwargs...)

Semi-minor axis of the Bernstein ellipse through x.

See ijouk regardings kwargs.

semiminor(x,xr)

Imaginary component of the point in the upper half-plane where the line { x̃ | real(x̃) = xr } intersects the Bernstein ellipse through x.