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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)
*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com
*Delivered-to*: l-mathgroup@wolfram.com
*Delivered-to*: mathgroup-outx@smc.vnet.net
*Delivered-to*: mathgroup-newsendx@smc.vnet.net
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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