Composite Rotation

Composite rotation refers to the combination of two or more rotation transformations to produce a more complex rotation in computer graphics.

To perform a composite rotation, we simply add the individual rotation angles together to obtain the total rotation angle. For example, if we want to rotate a point by `theta1` degrees about the origin, and then rotate it again by `theta2` degrees about the same origin, we can combine the two rotations into a single composite rotation by adding the angles:

```

theta = theta1 + theta2

```

We can then create a composite rotation matrix `M` using the total rotation angle as follows:

```

[ cos(theta) -sin(theta)  0 ]

[ sin(theta)  cos(theta)  0 ]

[     0           0       1 ]

```

To apply the composite rotation matrix `M` to a point `P = (x, y)`, we multiply it by `P` as follows:

```

P' = M * P

```

where `P' = (x', y')` is the transformed point.

Composite rotation is useful for combining multiple rotations into a single transformation, which can simplify the graphics pipeline and improve performance. It is often used in animations, where objects need to rotate along complex paths. It can also be used to rotate an object around an arbitrary point by first translating the object so that the point is at the origin, performing the composite rotation, and then translating the object back to its original position.