surface normal

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English

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surface normal

Noun

surface normal (plural surface normals)

(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.

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