Re: Rotating a list of 3D point coordinates in one shot

• To: mathgroup at smc.vnet.net
• Subject: [mg100019] Re: Rotating a list of 3D point coordinates in one shot
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Fri, 22 May 2009 01:42:25 -0400 (EDT)
• References: <gv2k0e\$9gs\$1@smc.vnet.net>

```Bill wrote:
> Hi:
>
> I have a list of 3D coordinates:
>
> list={{1., 0., 0.}, {0.987688, 0.156434, 0.},
> {0.951057, 0.309017, 0.}, {0.891007, 0.45399, 0.}, {0.809017, 0.587785, 0.}, {0.707107, 0.707107, 0.},
> {0.587785,0.809017, 0.}, {0.45399, 0.891007, 0.}, {0.309017, 0.951057, 0.}, {0.156434, 0.987688, 0.},
> {0., 1., 0.}, {-0.156434, 0.987688, 0.},
> {-0.309017, 0.951057, 0.}, {-0.45399, 0.891007, 0.},
> {-0.587785, 0.809017, 0.}, {-0.707107, 0.707107, 0.},
> {-0.809017, 0.587785, 0.}, {-0.891007, 0.45399, 0.},
> {-0.951057, 0.309017, 0.}, {-0.987688, 0.156434, 0.},
> {-1., 0., 0.}}.
>
> I'd like to rotate all the coordinates in the list in one shot, using something like this:
>
> Rotate[list, 180 Degree, {-1, -2, -1}]}} (*Axis angle rotation.*)
>
> I haven't gotten this to work though. I can rotate a single point at a time using a similiar method, but
> that is very time consuming.
>
>  Question: Is there a way to rotate a list of numerous 3D coordinates such as in my example above, and if so, how do I code that using Mathematica 6.0.1?
>

Bill,

If you wish to rotate graphics, use

Graphics3D[Rotate[Point[list], 180 Degree, {-1, -2, -1}]]

If you need the coordinates transformed, use

RotationTransform[180 Degree, {-1, -2, -1}] /@ list

or even

RotationTransform[180 Degree, {-1, -2, -1}][list]

```

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