Matrix Tutorial

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# Transformation Matrices

## Translation Matrix

A translation matrix moves a point along specified axis by specified amount. It is easily constructed from an identity matrix.

So lets say we have 2d point ***x,y*** defined as a vertical vector, 

|***x***|\
|***y***|\
|***w***|

We can multiply the 2d point by this matrix to move ***x*** by 2, ***y*** by 3:

|1 0 **2**| \
|0 1 **3**| \
|0 0 1|

We clearly see a ressemblance with the identity matrix.

The inverse is easily calculated by inverting the sign in front of the translation values like so:

|1 0 **-2**| \
|0 1 **-3**| \
|0 0  1|

#### What is ***w*** for?
>if 0, cancels the translation. \
if 1, makes the translation. \
if in between 0 and 1, makes partial translation

Usually, you would like to leave ***w*** at 1 and that may be the only thing you need to know about ***w***. Just leave it at 1.

© Paul Caron, aka ChillPill
Transformation Matrices - Translation
