The 3D cones trajectory has been employed for various applications. In this work we transform the task of designing the cones trajectory into a generic procedure of discretizing an analytic coordinate. We present a new discretization scheme with a spiral path on a unit sphere, which enables allocation of readout interleaves on distinct conic surfaces for any given number of readouts. Subsequently, we derive the relationship between the sampling density of each interleaf and that of overall interleaves, which allows us matching the sampling density of the cones trajectory to the 1/f-model of 3D images.
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