A surface normal is by definition a three-dimensional vector which is perpendicular to that surface.

The surfaces (white or pial) generated by FreeSurfer are  represented in the form of triangular meshes. 
In this case, a normal vector can be computed for each face or triangle of a given surface mesh, using 
the vector cross-product of two edges of the face triangle. 

{{attachment:surface_normal1.jpg}}


In addition, the surfaces generated by FreeSurfer are considered to be oriented, and the direction of 
the surface normal follows the right-hand rule. In particular, each triangle face has three vertices
(V0, V1, and V2), which are ordered in such a way that the normalized cross-product of vector __''V0''``''V1''__ 
and vector __''V0''``''V2''__ gives the outward normal of the face. 

By convention, FreeSurfer defines the normal vector at a surface vertex as the normalized average of 
the normal vectors at all faces sharing this vertex.