Re: Problem using PrincipalComponents to rotate 3D model data

• To: mathgroup at smc.vnet.net
• Subject: [mg80875] Re: Problem using PrincipalComponents to rotate 3D model data
• From: Antti Penttilä@smc.vnet.net
• Date: Tue, 4 Sep 2007 06:38:45 -0400 (EDT)
• Organization: University of Helsinki
• References: <fbj2t7\$nk0\$1@smc.vnet.net>

```Will,

Principal components, or the principal vectors can be reversed
(mirrored) and still be valid principal vectors. If (j,k,l) are the
principal vectors, then (-j,-k,-l) or any other combination is also
possible.

Antti

will wrote:
> Dear Math Forum,
>
> I am using PrincipalComponents[] (in Mathematica 6) to perform a rotation operation on some 3D data (effectively to align my data so that the maximum length of my models runs down the x axis,the maximum width down the y axis, and height max on the z axis).
> However, i have noticed that mathematica repeatedly reverses the normal (flips inside out) of and/or mirrors my models. I find this very odd, and was wondering if anyone else had encountered this problem? it seems to happen consistently with certain models, but i cannot see what is different in these models to those (few) that work as they should. if this problem is to do with my data,
> can anyone think of a way to rotate the models not using
> PrincipalComponents[].
>
> below is the code i have been using on STL (3D points and surface polygon data).
>
> Needs["MultivariateStatistics`"];
>
> 3Dmodel = Import["3Dmodel.stl"];
>
> Rotated3Dmodel =
>   Graphics3D[{EdgeForm[],
>     Polygon[Partition[
>       PrincipalComponents[Flatten[3Dmodel[[1, 2, 1]], 1]], 3]]},
>    Boxed -> False];
>
> Export["Rotated3Dmodel.stl", Rotated3Dmodel];
>
> thank you,
>
> William
>

```

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