Project Spatial Coordinates to the Lorentz Hyperboloid

Map Euclidean coordinates (x, y) to (sqrt(1 + x^2 + y^2), x, y).

Usage

project_to_H2(S)

Arguments

S

An n x 2 numeric matrix.

Value

An n x 3 matrix on the upper hyperboloid.

Examples

S <- matrix(c(0, 0, 1, 0), ncol = 2, byrow = TRUE)
Z <- project_to_H2(S)
check_hyperboloid(Z)