# surface normal

## English

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### 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 TP(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.