Struct MobiusTransform 

pub struct MobiusTransform {
    pub a: Complex,
    pub b: Complex,
    pub c: Complex,
    pub d: Complex,
}

A Möbius transformation f(z) = (az + b) / (cz + d) with ad - bc ≠ 0.

Fields

a: Complex

Numerator coefficient of z.

b: Complex

Numerator constant.

c: Complex

Denominator coefficient of z.

d: Complex

Denominator constant.

Implementations

impl MobiusTransform

pub fn new(a: Complex, b: Complex, c: Complex, d: Complex) -> Option<Self>

Create a new Möbius transformation. Returns None if det = ad - bc = 0.

pub fn identity() -> Self

Identity transformation z ↦ z.

pub fn apply(self, z: Complex) -> Option<Complex>

Apply the transformation to z. Returns None at the pole cz + d = 0.

pub fn compose(self, other: Self) -> Option<Self>

Compose two Möbius transformations: (self ∘ other)(z) = self(other(z)).

pub fn invert(self) -> Option<Self>

Invert the transformation: f^{-1}(z) = (dz - b) / (-cz + a).

pub fn fixed_points(self) -> Vec<Complex>

Fixed points of the transformation: solutions to f(z) = z. Solves cz² + (d - a)z - b = 0.

Trait Implementations

impl Clone for MobiusTransform

fn clone(&self) -> MobiusTransform

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for MobiusTransform

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Copy for MobiusTransform