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Affine Transformations - Clemson University

A P P E N D I XCAffine The need for geometric Affine Matrix representation of the linear Homogeneous 3D form of the Affine THE NEED FOR GEOMETRIC TRANSFORMATIONSOne could imagine a computer graphics system that requires the user to construct ev-erything directly into a single scene. But, one can also immediately see that this wouldbe an extremely limiting approach. In the real world, things come from various placesand are arranged together to create a scene. Further, many of these things are themselvescollections of smaller parts that are assembled together. We may wish to define one objectrelative to another for example we may want to place a hand at the end of an arm.

transform into a set of simpler transforms. For example, suppose we want to scale an object up to a new size, shear the object to a new shape, and finally rotate the object. Let S be the scale matrix, H be the shear matrix and R be the rotation matrix. Then x0= R(H(Sx)) defines a sequence of three transforms: 1st-scale, 2nd-shear, 3rd-rotate ...

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