Subject 5.27: How do I transform normals?
In 3D, the orientation of a plane in space can be given by a vector perpendicular to the plane, a “normal vector” or “normal” for short. Often it is convenient to keep that vector of unit length, or “normalized”; be careful of the different meanings of “normality”. A smooth surface has a plane tangent to each point, and by extension a normal to that plane is called a “surface normal”. Graphics code also cheats by associating artificial normal vectors with the vertices of polygonal models to simulate the reflection properties of curved surfaces; these are called “vertex normals”. The “orientation” of a plane has two meanings, both of which usually apply. Aside from the rotational tilting and turning meaning, there is also the sense of “side”. A closed convex surface made of polygons has two sides, an inside and an outside, and normals can be assigned to the polygons in such a way that they all consistently point outside. This is often desirable for shading and culling. When a model is d
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