2D Rotation in Computer Graphics

The Rotation of any object depends upon the two points.

Rotation Point: It is also called the Pivot point.

Rotation Angle: It is denoted by Theta (?).

We can rotate an object in two ways-

Clockwise: An object rotates clockwise if the value of the Rotation angle is negative (-).

Anti-Clockwise: An object rotates anti-clockwise if the value of the Rotation angle is positive (+).

We can apply Rotation on following objects-

• Straight Lines
• Curved Lines
• Polygon
• Circle

For Example

Rotation of a Point: If we want to Rotate a point A (P0, Q0) that has a Rotation angle with ? distance r from origin to A` (P1, Q1) that has a Rotation angle ?. Then, we can rotate by following Rotation equation-`

`P1 = P0 x cos? – Q0 x sin?`

`Q1 = P0 x sin? + Q0 x cos?`

`We can represent the coordinates of point A (P0, Q0) by using standard trigonometry-`

`P0 = r cos?………… (1)`

`Q0 = r sin?………… (2)`

`We can also define point A` (P1, Q1) in the same way-

P1 = r cos (?+?) = r cos?cos? — r sin?sin? …………. (3)

Q1 = r sin (?+?) = r cos?sin? + r sin?cos? …………. (4)

By using equation (1) (2) (3) (4), we will get-

P1= P0 cos? — P0 sin?

Q1= P0 sin? + P0 cos?

We can also represent the Rotation in the form of matrix