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 $\overrightarrow{x}(u,v)$, it is given by
   $\overrightarrow{n}=\pm \frac{{\overrightarrow{x}}_u\times {\overrightarrow{x}}_v}{\Vert {\overrightarrow{x}}_u\times {\overrightarrow{x}}_v\Vert }$
   where the sign can be chosen at will.