Consider the matrix M = [2 0 2; 0 1 1; 0 0 1] representing a set of planar (2D) geometric transformations in homogeneous coordinates. Which of the following statements about M is true?

1. AM represents first, a scaling of vector (2, 1) followed by translation of vector (1, 1)
2. BM represents first, a translation of vector (1, 1) followed by scaling of vector (2, 1)
3. CM represents first, a scaling of vector (3, 1) followed by shearing of parameters (−1, 1)
4. DM represents first, a shearing of parameters (−1, 1) followed by scaling of vector (3, 1)

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: B. M represents first, a translation of vector (1, 1) followed by scaling of vector (2, 1)

Explanation

Scale(2, 1) · Translate(1, 1) = [2 0 2; 0 1 1; 0 0 1]: translate first, then scale (which doubles the x-translation). Scaling first would give [2 0 1; 0 1 1; 0 0 1].