As discovered by the Gestaltists, in particular by Duncker, we often perceive motion to be within a non-retinotopic reference frame. For example, the motion of a reflector on a bicycle appears to be circular, whereas, it traces out a cycloidal path with respect to external world coordinates. The reflector motion appears to be circular because the human brain subtracts the horizontal motion of the bicycle from the reflector motion. The bicycle serves as a reference frame for the reflector motion. Here, we present a general mathematical framework, based on vector fields, to explain non-retinotopic motion processing. Using four types of non-retinotopic motion paradigms, we show how the theory works in detail. For example, we show how non-retinotopic motion in the Ternus–Pikler display can be computed.