# surface normal

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