surface normal

English

Noun

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 ${\vec {x}}(u,v)$, it is given by
   ${\vec {n}}=\pm {{\vec {x}}_{u}\times {\vec {x}}_{v} \over \lVert {\vec {x}}_{u}\times {\vec {x}}_{v}\rVert }$
   where the sign can be chosen at will.