Notes on Affine Transformations

October 16, 2019

Previously: Notes on Linear Transformations

Affine 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:

m11 m12 xt
m21 m22 yt

This single matrix implements a linear transformation followed by a translation, and this kind of transformation is an affine transformation.

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