Let s(x, y, z) and t(x, y, z) be differentiable scalar functions defined at all points on a surface S. In computer graphics, the functions s and t 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 p = (p_x, p_y, p_z) element S so that they are aligned with the direction in which the derivative of s(p_x, p_y, p_z) or t(p_x, p_y, p_z) is zero. In this context, the tangent vector T(p_x, p_y, p_z) is specifically defined to be the unit vector lying in the tangent plane for which del _T t(p_x, p_y, p_z) = 0 and del _T s(p_x, p_y, p_z) is positive. The bitangent vector B(p_x, p_y, p_z) is defined to be the unit vector lying in the tangent plane for which del _B s(p_x, p_y, p_z) = 0 and del _B t(p_x, p_y, p_z) is positive. The vectors T and B are not necessarily orthogonal and may not exist for poorly conditioned functions s and t. The vector N(p_x, p_y, p_z) given by N(p_x, p_y, p_z) = (T(p_x, p_y, p_z)xB(p_x, p_y, p_z))/( left bracketing bar T(p_x, p_y, p_z)xB(p_x, p_y, p_z) right bracketing bar ) is a unit normal to the surface S at the point p. For a closed surface S, this normal vector can be characterized as outward-facing or inward-facing. The basis vectors of the local tangent space at the point p are defined to be T, B, and ± N, with N negated in the case that it is inward-facing.

bitangent | tangent vector