If matrix $M$ represents rotation around the origin, how to represent rotation about another point in terms of $M$?

Asked Mar 25 '14 at 07:51

Active Aug 07 '14 at 19:48

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For homework from school I have to made some tasks. There are no lessons because it is a second change.

my question is: Multiplication by matrix $M$ represents rotation around the origin. If we do not want to rotate, to the origin, but to a point $p$ which is obtained by translation of the origin of vector $t$ and use is made of column vectors, which of the four products below shows the matrix of the required rotation around $p$ (circle the correct answer).

$T ^ {-1} M T$
$T M T ^ {-1}$
$M ^ {-1} T M$
$M T M ^ {-1}$
None of the above product matrices

I really don't have an idea how to do this question. Can someone help me with this question.

edited Aug 07 '14 at 19:48

asked Mar 25 '14 at 07:51

Richard Lindhout

2

What happens to the universe, if you first translate point $p$ to the origin, then rotate it about origin, and then translate origin back to $p$? – Jyrki Lahtonen Mar 25 '14 at 07:59
@JyrkiLahtonen the universe is in the same position ? – Richard Lindhout Mar 25 '14 at 08:08
You only cancelled the translation - you didn't cancel the rotation. – Jyrki Lahtonen Mar 25 '14 at 08:11
@JyrkiLahtonen So it is only rotated about the origin ? – Richard Lindhout Mar 25 '14 at 08:26
No. It was rotated about the point that happened to reside in the origin at the time of the rotation. – Jyrki Lahtonen Mar 25 '14 at 08:27
@JyrkiLahtonen okay, but can you tell me what the answer of my question is ? – Richard Lindhout Mar 25 '14 at 08:49
I think I already did! Do you know how the composition of affine transformations is done using the matrices? – Jyrki Lahtonen Mar 25 '14 at 10:06
@JyrkiLahtonen sorry, but i dont get it. i dont know how the composition of affine transformations is done. – Richard Lindhout Mar 25 '14 at 12:03
See my question here: http://math.stackexchange.com/questions/2093314/rotation-matrix-and-of-rotation-around-a-point – Dschoni Jan 11 '17 at 13:41

If matrix $M$ represents rotation around the origin, how to represent rotation about another point in terms of $M$?

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