By Anthony A. Apodaca
This is often pretty well the bible for someone 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 speak about :)
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Extra info for Advanced RenderMan: Creating CGI for Motion Pictures
The resulting value is a scalar that equals the cosine of the angle between the vectors times the length of each of the vectors. 0, so the result is just the bare cosine. This function is really useful because it converts directions into relative angles. 0. This means that dot product can be used to quickly test whether two vectors are perpendicular to each other, regardless of their magnitude (that is, as long as the vectors do not have 0 length to start with). Moreover, because cos(6) is positive for angles between -90 and 90 degrees, and negative for angles outside that range, the dot product can be used to quickly determine if two vectors point roughly in the same direction or roughly oppositely.
For example, the image might be computed in layers, with the objects close to the camera rendered in one image and the images in the background rendered separately. In conventional special effects photography, optically combining the images is known as matting or composite photography and is done on a device called an optical printer. However, 46 2 Review of Mathematics and Computer Graphics Concepts only three operations are available on an optical printer: adjusting the exposure or focus of an image, multiplying two images together (often used to cut a piece out of an image), and multiple exposure (adding two images together).
With palm up, point your fingers right along x. You can then bend (curl) them to point up along y (we often say "rotate x into y"). The thumb then points along z. Same-handedness result: left hand gives you z away from the viewer, right hand gives you z toward the viewer. Transformations that change the handedness of a coordinate system are called mirror transformations. Scaling by a negative value on one (or three) axes does this, as does exchanging any two axes. Now we can answer the most probing question in all of human history.