Rotation

Rotation is a basic transformation used in computer graphics to change the orientation of an object. It involves rotating the object around a fixed point, known as the pivot point or center of rotation. Rotation can be performed in 2D or 3D graphics.

In 2D graphics, rotation is performed using a 3x3 transformation matrix:

```

[ cosθ -sinθ 0 ]

[ sinθ  cosθ 0 ]

[   0     0   1 ]

```

where `θ` is the angle of rotation in radians.

To apply this matrix to a 2D point `(x, y)`, we multiply it by the matrix as follows:

```

[ x' ]   [ cosθ -sinθ 0 ]   [ x ]

[ y' ] = [ sinθ  cosθ 0 ] * [ y ]

[ 1  ]   [   0     0   1 ]   [ 1 ]

```

where `(x', y')` are the new coordinates of the point after rotation.

In 3D graphics, rotation can be performed around any axis using a 4x4 transformation matrix. The matrix depends on the axis of rotation and the angle of rotation. For example, to rotate around the x-axis by an angle of `θ`, we use the following matrix:

```

[ 1     0       0    0 ]

[ 0   cosθ  -sinθ  0 ]

[ 0   sinθ   cosθ  0 ]

[ 0     0       0    1 ]

```

To rotate around the y-axis or z-axis, we modify the matrix accordingly.

To apply the matrix to a 3D point `(x, y, z)`, we multiply it by the matrix as follows:

```

[ x' ]   [ 1     0       0    0 ]   [ x ]

[ y' ] = [ 0   cosθ  -sinθ  0 ] * [ y ]

[ z' ]   [ 0   sinθ   cosθ  0 ]   [ z ]

[ 1  ]   [ 0     0       0    1 ]   [ 1 ]

```

where `(x', y', z')` are the new coordinates of the point after rotation.

Rotation is a useful transformation in computer graphics that can be used to create animations and simulate the movement of objects in a scene.