The bitangent vector 
for differentiable scalar functions 
and 
on a surface 
is the unit vector lying in
the tangent plane for which 
and 
is positive. 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 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.
