We are given three 3-vectors
,
,
,
defining the three points vertices of the triangle. Using elementary vector
subtraction, we find two edges of the triangle,
and
,
using Equations 1 and 2.

The definition of the surface normal vector is a unit-length vector which is
perpendicular to any vector in the plane of the surface. Thus an unnormalised
surface normal vector can be obtained by taking the cross-product of any two
vectors in the plane of the surface. As
and
are both vectors in the plane of the surface, Equation 3
gives one such unnormalised surface normal vector.

If the points , and are defined in a clockwise order and the surface normal is required to be in the ``upward'' direction, as depicted in Figure 9, then the vectors , and form a right-handed set, as is usually desired.

2000-08-22