Page 80 - DCAP504_Computer Graphics

Unit 6: 2-D Transformation

Figure 6.7 is a graphical representation of the triangle object before and after rotation.

Figure 6.7: Triangle Rotated by an Angle 90 Degree

(2, -1)

6.1.5 Shear Transformation

The shear transformation makes an object slant either in X or Y direction and is called as X-shear and Y-
shear respectively. In X-shear, the y-coordinate values of the object remain constant, but the x-
coordinate values are changed. This makes the vertical lines (lines that are parallel to Y-axis or lines that
are perpendicular to X-axis) to tilt left or right. Similarly, in Y-shear, the x-coordinate values of the
object remain constant, but the y-coordinate values are changed. This makes the horizontal lines (lines
that are parallel to X-axis or lines that are perpendicular to Y-axis) to transform up or down.
The X-shear transformation matrix is given by,
1  a
Sh x=Error! Bookmark not defined.    , where, ‘a’ is the X-shear factor.

 0 1 
The Y-shear transformation matrix is given by,

 1  0
Sh y=Error! Bookmark not defined.    , where, ‘b’ is the Y-shear factor.

 b 1 

The object transforms right during X shear and transforms up during Y shear, when the
value of ‘a’ and ‘b’ are positive. If the values are negative, the object tilts left during X-
shear and transforms down during Y-shear.

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