   Next: 4.2 Scalar treatment Up: 4 Surface Normal Vector Previous: 4 Surface Normal Vector

## 4.1 Vector treatment

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. (1) (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. (3)

The unnormalised surface normal vector of Equation 3 is now normalised in Equation 4, where is used to denote the magnitude of the vector . (4) 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.   Next: 4.2 Scalar treatment Up: 4 Surface Normal Vector Previous: 4 Surface Normal Vector
Kevin Pulo
2000-08-22