spheres.coordinates.xyz_c

spheres.coordinates.xyz_c(xyz, pole='south')[source]

Reverse Stereographic projection from the unit sphere to the extended complex plane.

Given \((0,0,-1)\), returns \(\infty\).
Otherwise returns \(c = (\frac{x}{1+z}) + i(\frac{y}{1+z})\).
Parameters
  • xyz (list/np.ndarray) – Cartesian coordinates of point(s) on unit sphere.

  • pole (str, default 'south') – Whether to reverse project from the North or South pole.

Returns

Extended complex coordinate(s).

Return type

complex/inf or np.ndarray