Transforming Normals
Normal vectors aren’t transformed in the same way as vertices or position vectors are. Mathematically, it’s better to think of normal vectors not as vectors, but as planes perpendicular to those vectors. Then, the transformation rules for normal vectors are described by the transformation rules for perpendicular planes.
A homogeneous plane is denoted by the row vector (a, b, c, d), where at least one of a, b, c, and d is nonzero. If q is a nonzero real number, then (a, b, c, d) and (qa, qb, qc, qd) represent the same plane. A point (x, y, z, w)T is on the plane (a, b, c, d) if ax + by + cz + dw = 0. (If w = 1, this is the standard description of a Euclidean plane.) In order for (a, b, c, d) to represent a Euclidean plane, ...
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