Is the freesurfer surface tesselation consistent with the "right-hand" rule? That is, if we have a triangle of three vertex points (P1, P2 & P3), we can find 2 edges,

E1 = P3 - P2 E2 = P2 - P1

and we can find the normal to this triangle surface by taking the cross product of the edge vectors

N = E1 x E2

and the unit normal from this, of course.

The question is, then, wether N is directed outside of the surface. Note that

E1 x E2 = -1 * ( E2 x E1 )

That is, the order of the cross product is important. Also, now note that the order of the points (P1, P2 & P3) in the triangle is important. Without a consistent convention for their order, we cannot know whether the surface normal is directed inside or outside the closed brain surface.

Best, Darren

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