Let 
and 
be differentiable scalar functions defined at
all points on a surface 
. In computer graphics, the functions 
and 
often represent texture coordinates for a 3-dimensional polygonal
model. A rendering technique known as bump mapping orients the basis
vectors of the tangent plane at any point 
so that they are
aligned with the direction in which the derivative of 
or 
is zero. In this context, the tangent
vector 
is specifically defined to be the unit vector lying
in the tangent plane for which 
and 
is positive. The bitangent vector 
is defined to be the unit
vector lying in the tangent plane for which 
and 
is positive. The vectors 
and 
are not necessarily orthogonal and may not exist for poorly
conditioned functions 
and 
.
The vector 
given by
 |
is a unit normal to the surface 
at the point 
. For a closed surface 
, this normal vector can be characterized as outward-facing
or inward-facing. The basis vectors of the local tangent space at the point 
are defined to be 
, 
, and 
, with 
negated in the case that it is inward-facing.
