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how to calculate the 3D centre point of rotation given the angle of

  • To: mathgroup at smc.vnet.net
  • Subject: [mg132127] how to calculate the 3D centre point of rotation given the angle of
  • From: parr.will at googlemail.com
  • Date: Tue, 17 Dec 2013 04:42:50 -0500 (EST)
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Hi,

I've been looking at the Mathematica function: RotationTransform.

in the mathematica help it says: 	

RotationTransform[Theta,w,p]
gives a 3D rotation (Theta in radians/degrees) around the axis w anchored at the point p.

I have a problem where I have some 4 points in 3D space before and after a rotation is applied to them. I have the 3D rotation in radians/degrees and the axis (w), but want to find the point (p) around which the rotation occurs. 

eg: 
(*points before rotation*)
pts1{{-21.365, -1.61273, 2.41973}, {-41.0366, -4.33682, 
  4.78811}, {-18.1104, -20.673, 7.53}, {-19.804, 3.79904, 21.6102}};
(*points after rotation*)
pts2={{-17.9409, -3.2446, -7.46078}, {-35.9907, -7.76684, -14.7927},{-14.3971, -22.658, -4.21113}, {-25.7926, -1.61099, 10.8609}};

theta(*in degrees*)=29.3405

axis of rotation(*normalised*)={0.347494, -0.904472, 0.247341}

(*axis of rotation not normalised={19.9099, -51.8224, 14.1716}*)

can anyone help me find the centre point of rotation (p) please?

best wishes,

Will





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