Surface normal

Calculating the surface normal

For a polygon (such as a triangle), a surface normal can be calculated as the vector cross product of two edges of the polygon.

For a plane given by the equation , the vector
is a normal.

If a (possibly non-flat) surface S is parametrized by a system of curvilinear coordinates x(s, t), with s and t real variables, then a normal is given by the cross product of the partial derivatives
:

If a surface S is given implicitly, as the set of points satisfying
, then, a normal at a point on the surface is given by the gradient
:

If a surface does not have a tangent plane at a point, it does not have a normal at that point either. For example, a cone does not have a normal at its tip.

Uses

• Surface normals are essential in defining surface integrals of vector fields.

• Surface normals are commonly used in 3D computer graphics for lighting calculations, see Lambert's cosine law.
  

  External link

• An explanation of normal vectors from Microsoft's MSDN