Struct PoincareDisk 

pub struct PoincareDisk {
    pub scale: f32,
}

Maps world positions into the Poincare disk model of the hyperbolic plane. Points inside the unit disk represent the entire hyperbolic plane.

Fields

scale: f32

Scale factor mapping world units to disk radius

Implementations

impl PoincareDisk

pub fn new(scale: f32) -> Self

pub fn to_disk(&self, world_pos: Vec2) -> Vec2

Convert a world position to Poincare disk coordinates. Uses the exponential map: disk_pos = tanh(|p|/2) * (p/|p|)

pub fn from_disk(&self, disk_pos: Vec2) -> Vec2

Convert a Poincare disk coordinate back to world position. Inverse of to_disk: world = 2 * atanh(|d|) * (d/|d|) * scale

pub fn hyperbolic_distance(&self, a: Vec2, b: Vec2) -> f32

Compute the hyperbolic distance between two points in the Poincare disk. d(a,b) = acosh(1 + 2|a-b|^2 / ((1-|a|^2)(1-|b|^2)))

pub fn geodesic(&self, a: Vec2, b: Vec2, steps: usize) -> Vec<Vec2>

Compute a geodesic (hyperbolic line) between two points on the disk. In the Poincare model geodesics are circular arcs orthogonal to the boundary, or diameters through the origin.

pub fn mobius_transform(&self, z: Vec2, a: Vec2) -> Vec2

Apply a Mobius transform (isometry of the Poincare disk). T_a(z) = (z + a) / (1 + conj(a)*z) treating Vec2 as complex numbers.