Following yesterday's post here are the 'five rules' which aren't rules in Mathematica. Basically there is only one rule where the affine transformation consisting of invertible matrix $A$ and vector $t$ are mapped to a 3-by-3 matrix after which composition of affine transformations ( including translations only ) can be done by multiplying matrices.
f[A_, t_] := ArrayFlatten[{{A, Transpose[{t}]}, {0, 1}}]
 |
| Click to enlarge size. |
To understand these affine transformation rules, first we discuss it's definition, an affine transformation is any transformation that preserves col-linearity and ratios of distances. In this sense, affine indicates a special class of projective transformations that do not move any objects from the affine space to the plane at infinity or conversely. An affine transformation is also called an affinity.
ReplyDelete