Game Development Reference
In-Depth Information
Such that a point transformed by this scaling matrix would have the expected result.
Scale transformations can also be represented in homogeneous coordinates which allows
us to add the component to the scale vector, giving us a matrix of the form.
Now in this form, the scale matrix is in the same form as the translation matrix we de-
scribed earlier. This is useful because now we are able to combine all the transformations
we have developed giving us the ability to scale, translate and rotate a point or a collection
of points across any axis we may need.
1.3.7 Matrix Concatenation
When we discussed rotations, we established that in order to create a generalized rota-
tion matrix we could concatenate the rotation matrix around each axes in 3D. How the or-
der in which the matrices are multiplied determined the order in which the rotations are
applied. This is due to the non-commutativity property of matrix multiplication.
