The three basic transformations of scaling, rotating, and translating are the most useful and most common. There are some other transformations which are useful in certain applications. Two such transformations are reflection and shear.
A reflection is a transformation that produces a mirror image of an object relative to an axis of reflection. We can choose an axis of reflection in the xy plane or perpendicular to the xy plane.
A transformation that slants the shape of an object is called the shear transformation.Two common shearing transfor-mations are used.One shifts x co-ordinate values and other shifts y co-ordinate values. However, in both the cases only one co-ordinate (x or y) changes its co-ordinates and other preserves its values.
The x shear preserves the y co-ordinates, but changes the x values which causes vertical lines to tilt right or left as shown in the figure below . The transformation matrix for x shear is given as
The y shear preserves the x coordinates, but changes the y values which causes horizontal lines to transform into lines which slope up or down, as shown in the figure below. The transformation matrix for y shear is given as