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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.

• Shear offsets a set of points a distance proportional to their x and y coordinates. ... represented by a matrix multiplication of a point represented as a vector, " x0 y0 # = " ax+ by dx+ ey # = " a b d e #" x y #; ... 0s y 0 0 1 3 77 77 77 5;Rotate: 2 66 66 66 4 cos sin 0 sin cos 0 0 0 1 3 77 77 77 5;Shear: 2 66 66 66 4 1 h x 0 h y 1 0 0 0 ...

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