Orbit displays are centered at the selected libration poimt. The x-y plane is the plane of motion of the primary (larger) body about the secondary (smaller) body. the positive x-asis points away from the primary body. The z-axis is normal to the orbit plane and completes the right-handed, rotating (synodic) coordinate system.
Reference - Analytic Contruction of Periodic Orbits about the Collinear Points, Celestial Mechanics 22 (1980), 241-253.
Here is a typical user interaction with this MATLAB script.
< halo orbit design using Richardson's algorithm>
please select the libration point of interest
<1> halo orbit about L1
<2> halo orbit about L2
<3> halo orbit about L3
selection (1, 2, or 3)
please input the class type (1 = class I, 2 = class II)
please input the three-body system (1 = Earth-Moon, 2 = Sun-Earth
please input the z-amplitude in kilometers