# 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**–