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

• To: mathgroup at smc.vnet.net
• Subject: [mg100072] Re: Rotating a list of 3D point coordinates in one shot
• From: Nicholas <physnick at gmail.com>
• Date: Fri, 22 May 2009 23:38:10 -0400 (EDT)
• References: <gv2k0e\$9gs\$1@smc.vnet.net>

```On May 21, 12:06 am, Bill <WDWNORW... at aol.com> 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 som=
ething 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 ti=
me using a similiar method, but
> that is very time consuming.
>
>  Question: Is there a way to rotate a list of numerous 3D coordinates s=
uch as in my example above, and if so, how do I code that using Mathematica=
6.0.1?
>
>
> Bill

Bill,

You can rotate all at once by matrix multiplication using the rotation
matrix.  For example, if you wanted to rotate 45 degrees
counterclockwise about the {0,0,1} axis, you would use:

RotationMatrix[\[Pi]/4, {0, 0, 1}].Transpose[list] // Transpose

As long as the dimensions of list are nx3, n can be any positive
integer.

Nick.

```

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