Notes on Affine TransformationsOctober 16, 2019
Previously: Notes on Linear Transformations
So far you have used a matrix to perform transformations on a vector, but you cannot use such transforms to translate objects, and there's no such way to do it with a 2x2 matrix.
We can use a clever trick to get a single matrix muiltiplication to do both operations together. The idea is simple: represent the posint by a 4d vector and use 3x3 matrices of the form:
This single matrix implements a linear transformation followed by a translation, and this kind of transformation is an affine transformation.