To transform a normal to eye
coordinates, we use the normal
It is also used to transform direction vectors (for example, a spotlight
The normal matrix N
is the transpose of the inverse of
the upper left 3x3 submatrix of the modelview matrix (denoted this as M
This part of the matrix represents rotation and scaling (translations
don’t affect the orientation of a normal vector)
- Consider the triangle below. The normal n is orthogonal to any vector in the plane of the
triangle, including its edges, for example edge e = p2 – p1
is, n ·
0. We did something just like this in
the vector mathematics worksheet.
that the dot product can be written as a matrix multiplication, that is: n ·
e = nT e = 0
going to apply the modelview matrix M
the points on the triangle.
like to find a transformation N
applied to the normal, so that the transformed normal is still orthogonal to
the triangle after transformation.