Game Development Reference
In-Depth Information
Just as it is with rotations, it is useful to describe translation as an affine transformation
matrix, however, recall that the rotation matrices we derived were all done around a fixed
point, the origin. A translation has no fixed point which would make it impossible to per-
form using matrices were it not for homogeneous coordinates.
Foracomplete,andwellwrittendescriptionofhomogeneouscoordinates,see (Chen,n.d.).
For our purposes we will limit the explanation on the part that is relevant for game trans-
formations.Homogeneouscoordinatesaddanotherdimensiontoapoint,whileinitiallyour
point in 3D was described by:
Adding a new dimension, we introduce the
w
component
We introduce homogeneous coordinates to allow us to represent translations as a matrix in
the form:
When multiplied by a point in homogeneous coordinates with the
w
component as 1, the
resulting point will be translated.
