surface normal
Noun
Meaning
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 TP(M) of M at P. For a surface with parametrization
x
→
(
u
,
v
)
{\displaystyle {\vec {x}}(u,v)}
, it is given by
n
→
=
±
x
→
u
×
x
→
v
‖
x
→
u
×
x
→
v
‖
{\displaystyle {\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.