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? > > Thanks in advance, > > 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.