Affine transforms as 3x4 matrix (in 3D)


Is it true that all affine transformations have a last row of the form (0, 0, .., 0, 1), and therefore could be stored in a n by (n+1) matrix?


Hi! Yes, all affine transformations can be represented as n × (n + 1) matrices. However not all n × (n + 1) matrices can be interpreted as affine transforms. For example the matrix filled with zeros does not represent an affine transform because that would not be a bijection.


My motivation is to make composing them faster. Was wondering if you could reduce the number of ops required if you used an alternative repr.