By Anthony A. Apodaca
This is often pretty well the bible for an individual who makes use of renderman day-by-day. no matter if you're not a programmer this is a nice reference for these issues the programmers discuss :)
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Extra info for Advanced RenderMan: Creating CGI for Motion Pictures
Because of the way the lenses work, the image on the film plane is upside down. Narrowing the lens aperture blocks some light from reaching the film, and therefore dims the image. The primary characteristic of a lens is its focal length, which is the distance from the center of the lens to the point where light from an infinitely distant object will focus. The focal length of a simple lens is determined solely by how it is manufactured, the material, and the curvature of the lens, and so it is a constant.
Negative curvature means the surface curves down, drooping away from the surface normal. Zero curvature means the surface is flat. Just as there are infinitely many tangent vectors at a point on a surface, all radiating at different angles, so too there are infinitely many curvatures, corresponding to all the circles oriented at different angles around the point. Of these, a few in particular are interesting. On a parametric surface, the curvatures in the two parametric directions are interesting because they are easy to compute.
Negating a vector makes it point in the opposite direction. Vectors can be added together by adding the corresponding coordinates. We can visualize this as chaining the vectors together, the end of one attached to the start of the next. 3). Subtracting vectors is also legal; it is just like adding the negated vector. A vector can also be added to a point, again by adding the matching coordinates, which creates a new point that is displaced from the first by the distance and direction of the vector.
Advanced RenderMan: Creating CGI for Motion Pictures by Anthony A. Apodaca