By Anthony A. Apodaca
This is often pretty well the bible for an individual who makes use of renderman day-by-day. whether 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
It is easy to generate a few points that are on the surface and then approximate the rest of the surface by linear approximation. We call this technique tesselation. Second, because we have an equation that converts a 2D pair of parametric coordinates into 3D, the surface has a natural 2D coordinate system. This makes it easy to map other 2D data onto the surface, the most obvious example being texture maps. 2 Tangents and Normals Having mathematical equations for our geometric primitives allows us to use the machinery of analytic geometry and calculus to compute important properties of the equations, which in turn are important properties of the geometric primitives.
Materials that appear rough tend to reflect light strongly in a wide range of directions. Transparent materials, such as plastic and glass, refract some light based on angle-dependent Fresnel equations, so they reflect more strongly at glancing angles and therefore appear glossy. Iridescent materials reflect different colors at different angles due to destructive interference in the reflection. In fact, these light reflection properties are actually components of a more comprehensive characteristic of the material known as the bidirectional reflection distribution function or BRDF.
The results are equivalent either way, but it is important to be consistent about your notation. Unfortunately, some of the popular computer graphics textbooks use one notation, and others use the other. In RenderMan texts and documentation, we always premultiply row vectors by transformation matrices. 6 Periodic Functions Some mathematical functions are naturally periodic, meaning that their values repeat at regular intervals. Two examples are sine and cosine: for all integers n.. Not all functions are periodic, of course, but sometimes it is very handy to create periodic versions of a segment of a function.