Translation

Translation is a basic transformation used in computer graphics to move an object from one position to another in a straight line. It involves changing the coordinates of an object by adding or subtracting values from its x and y coordinates.

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

```

[ 1 0 tx ]

[ 0 1 ty ]

[ 0 0 1  ]

```

where `tx` and `ty` are the translation 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' ]   [ 1 0 tx ]   [ x ]

[ y' ] = [ 0 1 ty ] * [ y ]

[ 1  ]   [ 0 0 1  ]   [ 1 ]

```

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

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

```

[ 1 0 0 tx ]

[ 0 1 0 ty ]

[ 0 0 1 tz ]

[ 0 0 0 1  ]

```

where `tx`, `ty`, and `tz` are the translation 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' ]   [ 1 0 0 tx ]   [ x ]

[ y' ] = [ 0 1 0 ty ] * [ y ]

[ z' ]   [ 0 0 1 tz ]   [ z ]

[ 1  ]   [ 0 0 0 1  ]   [ 1 ]

```

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

Translation is a simple and useful transformation that can be used to create animations and move objects around a scene in computer graphics.