Is it possible to convert RotationMatrix to RotationTransform ?
I guess it should exist a function to do this
Thank you for your help
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1 Answer
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One only needs to apply AffineTransform[] to the result of RotationMatrix[]; e.g.
AffineTransform[RotationMatrix[π/3, Normalize[{1, 2, 3}]]] ===
RotationTransform[π/3, Normalize[{1, 2, 3}]]
True
An additional advantage to using AffineTransform[] is that one can put in other classes of rotation matrices, instead of just RotationMatrix[]; e.g. AffineTransform[RollPitchYawMatrix[{-π/4, π/6, 3 π/5}]] or AffineTransform[EulerMatrix[{π/2, -π/5, 2 π/3}]].
answered Sep 29, 2018 at 12:57
J. M.'s missing motivation♦J. M.'s missing motivation
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1$\begingroup$ TransformtionFunction works the same: 'TransformationFunction[ RotationMatrix[[Pi]/3, Normalize[{0, 0, 1}]]] == RotationTransform[Pi/3]' $\endgroup$– bill sCommented Sep 29, 2018 at 13:23
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$\begingroup$ @bill, since
TransformationFunction[]takes a homogeneous transformation matrix as an argument, in general one needs to augment the starting matrix beforehand. $\endgroup$ Commented Sep 29, 2018 at 13:42 -
$\begingroup$ The role of the Normalize[0,0,1] is exactly the augmentation, just as with AffineTransform $\endgroup$– bill sCommented Sep 29, 2018 at 18:21
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$\begingroup$ Right;
RotationMatrix[π/3, Normalize[{0, 0, 1}]effectively says "rotate by $\pi/3$ radians anticlockwise over the $z$-axis", which does correspond to a rotation in the $x$-$y$ plane. $\endgroup$ Commented Sep 29, 2018 at 18:23