surface normal

surface normal (plural surface normals)

1. (differential geometry) A unit vector at any given point P of a surface M which is perpendicular to the tangent plane T_P(M) of M at P. For a surface with parametrization ${\displaystyle {\vec {x}}(u,v)}$ , it is given by

${\displaystyle {\vec {n}}=\pm {{\vec {x}}_{u}\times {\vec {x}}_{v} \over \lVert {\vec {x}}_{u}\times {\vec {x}}_{v}\rVert }}$

where the sign can be chosen at will.