By Anthony A. Apodaca
This is often pretty well the bible for a person who makes use of renderman day-by-day. no matter if you're not a programmer it is a nice reference for these issues the programmers speak about :)
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Additional resources for Advanced RenderMan: Creating CGI for Motion Pictures
One of the most important theories of signal processing (known as the Nyquist theorem) says that representing a signal accurately takes twice as many regularly spaced discrete samples as the highest frequency in the signal. Rarely do computer graphics images have such high spatial resolution. Without enough samples, we get abasing. 10). There are two ways around this conundrum. First, our samples can be nondiscrete. That is, they can represent not the specific colors at particular points in the scene, but instead some average color over a region of the scene.
As is common in ancient fields of study, angles can be measured in a variety of different units, and in RenderMan two of these appear: degrees and radians. Degrees are probably very familiar to everyone. There are 360 degrees in a circle, a right angle is 90 degrees. Degrees are used whenever angles are needed in the geometric scene description part of RenderMan as in RenderMan Interface Bytestream (RIB) commands, for example. Radians, on the other hand, are familiar to mathematicians and programmers.
Conversely, you can multiply a matrix by a vector, M x V, resulting in a vector that is calculated by computing the dot products of the vector with each row of the matrix. In that case, the number of elements in the original vector must equal the number of columns in the matrix, and the number of elements in the result is equal to the number of rows. The first type of vector-matrix multiply, V x M, is called premultiplying the vector by the matrix, because the vector appears before the matrix. By convention, vectors that premultiply matrices are written horizontally, as rows, and are therefore known as row vectors.
Advanced RenderMan: Creating CGI for Motion Pictures by Anthony A. Apodaca