Scaling

Scaling is a basic transformation used in computer graphics to resize an object. It involves changing the size of an object by multiplying its coordinates by a scale factor. Scaling can be performed in 2D or 3D graphics.

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

```

[ sx 0  0 ]

[ 0  sy 0 ]

[ 0  0  1 ]

```

where `sx` and `sy` are the scaling factors in the x and y directions, respectively.

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

```

[ x' ]   [ sx 0  0 ]   [ x ]

[ y' ] = [ 0  sy 0 ] * [ y ]

[ 1  ]   [ 0  0  1 ]   [ 1 ]

```

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

In 3D graphics, scaling is performed using a 4x4 transformation matrix:

```

[ sx 0  0  0 ]

[ 0  sy 0  0 ]

[ 0  0  sz 0 ]

[ 0  0  0  1 ]

```

where `sx`, `sy`, and `sz` are the scaling factors in the x, y, and z directions, respectively.

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

```

[ x' ]   [ sx 0  0  0 ]   [ x ]

[ y' ] = [ 0  sy 0  0 ] * [ y ]

[ z' ]   [ 0  0  sz 0 ]   [ z ]

[ 1  ]   [ 0  0  0  1 ]   [ 1 ]

```

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

Scaling is a useful transformation in computer graphics that can be used to resize objects, change their proportions, and create special effects.