Rotation:
It is a process of changing the angle of the object. Rotation can be clockwise or anticlockwise. For
rotation, we have to specify the angle of rotation and rotation point. Rotation point is also called a
pivot point. It is print about which object is rotated.
Types of Rotation:
1. Anticlockwise
2. Counterclockwise
The positive value of the pivot point (rotation angle) rotates an object in a counter-clockwise (anti-
clockwise) direction.
The negative value of the pivot point (rotation angle) rotates an object in a clockwise direction.
When the object is rotated, then every point of the object is rotated by the same angle.
Reflection:
It is a transformation which produces a mirror image of an object. The mirror image can be either
about x-axis or y-axis. The object is rotated by180°.
Types of Reflection:
1. Reflection about the x-axis
2. Reflection about the y-axis
3. Reflection about an axis perpendicular to xy plane and passing through the origin
4. Reflection about line y=x
Reflection about x-axis: The object can be reflected about x-axis with the help of the
following matrix
In this transformation value of x will remain same whereas the value of y will become
negative. Following figures shows the reflection of the object axis. The object will lie another
side of the x-axis.
2. Reflection about y-axis: The object can be reflected about y-axis with the help of following
transformation matrix
Here the values of x will be reversed, whereas the value of y will remain the same. The object
will lie another side of the y-axis.
The following figure shows the reflection about the y-axis
3. Reflection about an axis perpendicular to xy plane and passing through origin:
In the matrix of this transformation is given below
In this value of x and y both will be reversed. This is also called as half revolution about the
origin.
4. Reflection about line y=x: The object may be reflected about line y = x with the help of following
transformation matrix
First of all, the object is rotated at 45°. The direction of rotation is clockwise. After it reflection is
done concerning x-axis. The last step is the rotation of y=x back to its original position that is
counterclockwise at 45°.
Shearing:
It is transformation which changes the shape of object. The sliding of layers of object occur. The
shear can be in one direction or in two directions.
Shearing in the X-direction: In this horizontal shearing sliding of layers occur. The homogeneous
matrix for shearing in the x-direction is shown below:
Shearing in the Y-direction: Here shearing is done by sliding along vertical or y-axis.
Shearing in X-Y directions: Here layers will be slided in both x as well as y direction. The sliding will
be in horizontal as well as vertical direction. The shape of the object will be distorted. The matrix of
shear in both directions is given by:
