2.1 Two-Dimensional Case

Two of the parameters that specify a two-dimensional rigid-body transformation can be viewed as translations along the primary axes, and the third can be viewed as a pure rotation around the origin. Although this particular parameterization is not unique, translations along each axis and rotations around the origin will be referred to here as elementary transformations. If a two-dimensional point (x, y) is to be transformed by one of these elementary transformations to some new point (x', y'), the following equations describe the elementary transformations:

^-translation: x y y-translation: x y

Rotation: x y

= x * cos(0) + y * sin(0) = —x * sin(0) + y * cos(0),

0 0

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