Systems and methods for determining lighting fixture arrangement information (e.g., position and/or orientation). A lighting beam from the lighting fixture is directed among three discrete locations on a reference surface (e.g., by a controller). The fixture's position is determined using perspective inversion based on angular changes of the lighting fixture and coordinate data of the discrete locations (e.g., determined using a camera and a reference point on the surface). Distances from the fixture to the three discrete locations are estimated based on perspective inversion. The position of the lighting fixture is trilateralized based on the distances. Spherical coordinates of the fixture's orientation relative to the reference surface are determined, and yaw, pitch, and roll of the fixture are extracted.