Trajectory design

k-space trajectories of one base interleaf, and their conversion to gradient waveforms. k-space coordinates are in 1/m, that is cycles per metre, gradient amplitudes in Hz/m and slew rates in Hz/m/s, on the channel axes; Storage, deduplication and file revisions describes how one interleaf is reused for every shot through rotation extensions.

Trajectories and gradient conversion

The trajectory functions return geometry as a polyline, with no time parameterization. traj_to_grad() assigns the timing within the vector gradient amplitude and slew-rate limits of the system.

Object	Input	Returns	Purpose
calc_radial_trajectory	FOV (m), matrix, number of points	k-space points (num_points, 2)	Full radial spoke through the k-space centre.
calc_spiral_trajectory	FOV (m), matrix, design interleaves, density	k-space points (num_points, 2) from the origin	Spiral-out interleaf.
calc_rosette_trajectory	FOV (m), matrix, petals, frequency ratio	k-space points (num_points, 2), closed at the origin	Rosette interleaf.
traj_to_grad	k-space trajectory, time last (n,), (2, n), (3, n)	Gradient waveform (Hz/m); slew rate (Hz/m/s)	Time-optimal trajectory-to-gradient conversion.