A method and device of magnetic resonance imaging carry out the steps of selecting a trajectory in phase space; expressing that trajectory as a function of variables in a coordinate system suitable for driving gradient coils of an imaging system; performing variable transformation and redefinition to extract a subset of variables varying as a function of time along gradient wave forms but constant from projection to projection; calculating that subset of variables prior to imaging; storing that calculated subset of variables in a memory; and computing online gradient values during imaging with the assistance of said stored subset of variables to significantly reduce wave form memory requirements such that a gradient controller can perform required mathematical functions online. By separating the variables describing the selected trajectory, in the coordinate system appropriate to the gradient coils, into variables which are constant from projection to projection and variables which change from projection to projection, the method and device allow a significant fraction of the quantities to be calculated prior to imaging. These calculated values are then stored and used for real-time calculations of parameters which must be changed during the course of the imaging process as projections are stepped through. As a result of this separation of the variables into two groups as described, it is possible to significantly reduce the wave form memory requirements to a size which allows current gradient controllers to perform the required mathematic functions online.