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Hi

Not quite: The sampled direction is always compared to the traveling direction and flipped if their dot product is negative, so the cosine is always between 0 and 1. 

Cheers
Saad



On 9 Dec 2015, at 16:40, Jackson Smith <[log in to unmask]> wrote:

Dear FSL Community,

Sadly, I always get trumped in interpreting the definition of curvature threshold – which is "the cosine of the minimum allowable angle between two steps."

If I understand this properly, then increasing the threshold towards 1 will allow new steps in the streamline to fold increasingly back upon the previous step. At 1, we even allow the next step to overlap the previous step completely, but in the opposite direction. In other words, increasing the threshold allows more backtracking. Thus, the default value of ~80 degrees allows a small amount of folding back.

On the other hand, lowering the threshold forces streamlines to go more and more in the same direction as the last step. However, the minimum allowable curvature threshold is cosine 0, corresponding to 90 degrees. Thus, the new step direction can always range from the same direction as the old step up to any perpendicular direction. In theory, if negative curvature thresholds were allowed, then a value of -1 would force every new step to travel in exactly the same direction as the old.

Is this the correct interpretation?

Kind regards,
Jackson Smith

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Saad Jbabdi, PhD
Associate Professor
MRC Career Development Fellow

FMRIB Centre, University of Oxford,
John Radcliffe Hospital, Oxford, OX3 9DU, UK. 
tel (+44)1865-222466  (fax 717)
www.ndcn.ox.ac.uk/team/researchers/saad-jbabdi