Download Advanced RenderMan: Creating CGI for Motion Pictures by Anthony A. Apodaca PDF

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 this is a nice reference for these issues the programmers speak about :)

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That is, Multiplying a matrix by the identity matrix leaves the matrix unchanged. Similarly for a vector. This is the reason that the identity matrix is called the identity. It is important to note that in matrix multiplication, the order of the matrices matters. Reversing the order of the matrices changes the result. That is, Another useful operation is taking the inverse of a matrix. The inverse matrix does the opposite of the original matrix and is often denoted M-1. 0. There are, of course, many other useful operations on matrices, such as computing the transpose or the determinant of a matrix.

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. However, these values are not necessarily the "most curved" directions on the surface. If we are interested in those, we need values known as the principal curvatures, Kmax and Kmin• The equations for computing K are somewhat complex and scary, so persons wearing Math-Sensitive SunglassesTM will see a large blank space next: The curvature in the a and v directions are Ku and Kv, respectively.

In 3D computer graphics, it is very common to use 4-row, 4-column (4 x 4) matrices for a variety of purposes. A 4 x 4 matrix therefore has 16 values, arranged in a square. There are only a small number of mathematical operations In the wider world of mathematics, other transformations exist that don't do either of these things, but we don't use them too often in computer graphics. 24 2 Review of Mathematics and Computer Graphics Concepts that make sense on matrices and are useful to us, but these turn out to be very important.

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