In a 3D graphics engine, calculations can be performed in a multitude of different Cartesian coordinate spaces. Moving from one coordinate space to another requires the use of transformation matrices. We casually referred to matrices at various places in Chapter 2; and in this chapter, we acknowledge the importance of matrices in 3D graphics programming by presenting a more formal exposition of their properties. The process of transforming points and direction vectors from one coordinate space to another is described in Chapter 4.

An *n×m* matrix **M** is an array of numbers having *n* rows and *m* columns. If *n=m* =, then we say that the matrix **M** is *square*. We write *M*_{ij} to refer to the entry of **M** that resides at the ...

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