3D Cones Trajectory Design

Read the MRM paper: Design and Analysis of a Practical 3D Cones Trajectory

Note: A new, improved version of the algorithm has been implemented. Untar this file to get the latest version. Note that some of the interfaces have changed.

Here are the files you need to generate 3D Cones Trajectories:

findcone.m
- Generates a 3D Cone given the desired Resolution, FOV, waveform length, and range of polar angles.

gencone.m
- Generates a 3D Cone given the desired Resolution, FOV, number of interleaves, and range of polar angles.

wc.c
- The MEX-file which implements the core algorithm (compile with 'mex wc.c')

mrewind.m
- A support function which calculates rewinders (thanks to Brian Hargreaves!)

intlineellipse.m
- A support function which calculates the intersection of a line and an ellipse

Please e-mail ptgurney at mrsrl dot stanford dot edu if you have any questions. A brief note to say that you're using these functions would also be greatly appreciated so that I can let you know if any bugs/errors are found/fixed. Thanks!

Notes/Errata
There is a step missing in section "Designing Waveforms for a Range of Polar Angles" of the paper. In addition to passing in the substituted RESrange and THETArange values, Gtwist must be scaled by sqrt(1+sin(THETAlower)^2/sin(THETAupper)^2*tan(THETArange)^2)/sqrt(1+tan(THETArange)^2). The above MATLAB functions are correct. Questions? Please email me!

Updated July 1, 2007