Convert Poincare Disk Coordinates to Lorentz Coordinates

Convert two-dimensional Poincare disk coordinates to the upper sheet of the Lorentz hyperboloid. Input rows must satisfy rowSums(P^2) < 1.

Usage

poincare_to_lorentz(P, tol = 1e-10)

Arguments

P

An n x 2 numeric matrix of Poincare disk coordinates.

tol

Numerical tolerance used when checking the unit disk boundary.

Value

An n x 3 Lorentz coordinate matrix with columns z0, z1, z2.

Examples

P <- matrix(c(0, 0, 0.2, -0.1), ncol = 2, byrow = TRUE)
Z <- poincare_to_lorentz(P)
check_hyperboloid(Z)