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I have the 2D transformation A->B in the design below, with the homogeneous transformation matrix as the answer enter image description here

As i understand there 2 transformations performed: a Rotation by 180 degrees and a Translation of 4 at X Axis

With the homogeneous Matrices

enter image description here

The transformation Matrix should be this:

enter image description here

Can someone explain what im i doing wrong?

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You are not performing a 180-degree rotation, but a reflection with respect to the $x$-axis. Thus, your matrix $A$ is correct, but $B$ is not. Try to use this one instead $$B=\left(\begin{array}{c} 1 & 0 & 0 \\ 0 & -1 & 0 \\ 0 & 0 & 1 \end{array}\right)$$ That way you will obtain the transpose of the answer you have. It seems that the answer matrix is given to perform transformations by post-multiplying, instead of the most usual pre-multiplication. In other words, a point $(x,y)$ will have coordinates $(x',y')$ such that $$\left(\begin{array}{c} x' & y' & 1 \end{array}\right) = \left(\begin{array}{c} x & y & 1 \end{array}\right)\left(\begin{array}{c} 1 & 0 & 0 \\ 0 & -1 & 0 \\ -4 & 0 & 1 \end{array}\right) $$

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  • $\begingroup$ Thank you for the explanation. Do you mind explaining why i dont get the correct answer matrix by multiplication of the given A and B matrices? unsee.cc/zobemipu $\endgroup$
    – iamIcarus
    Commented Oct 22, 2015 at 7:59
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    $\begingroup$ Well, first of all you need to use the correct $B$—the one in AugSB’s answer. On top of that, as AugSB points out, the matrix in the given solution appears to be set up for post-multiplication, so it’ll be the transpose of the matrix you’re probably getting. $\endgroup$
    – amd
    Commented Oct 22, 2015 at 9:13
  • $\begingroup$ Ohhh now i get it! Thank you both $\endgroup$
    – iamIcarus
    Commented Oct 22, 2015 at 9:16

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