Editing Normal (geometry) (section)

==Normal to planes and polygons==
[[File:Plane equation qtl3.svg|thumb|Plane equation in normal form]]

For a [[Convex set|convex]] [[polygon]] (such as a [[triangle]]), a surface normal can be calculated as the vector [[cross product]] of two (non-parallel) edges of the polygon.

For a [[Plane (mathematics)|plane]] given by the general form [[plane equation]] <math>ax + by + cz + d = 0,</math> the vector <math>\mathbf n = (a, b, c)</math> is a normal.

For a plane whose equation is given in parametric form 
<math display=block>\mathbf{r}(s,t) = \mathbf{r}_0 + s \mathbf{p} + t \mathbf{q},</math>
where <math>\mathbf{r}_0</math> is a point on the plane and <math>\mathbf{p}, \mathbf{q}</math> are non-parallel vectors pointing along the plane, a normal to the plane is a vector normal to both <math>\mathbf{p}</math> and <math>\mathbf{q},</math> which can be found as the [[cross product]] <math>\mathbf{n}=\mathbf{p}\times\mathbf{q}.</math>