f[A_, t_] := ArrayFlatten[{{A, Transpose[{t}]}, {0, 1}}] |
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2-2024 Quran and mathematics
7 months ago
Thursday, January 26, 2012
Affine transformation rules - Revisited
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.
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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.
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