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Re: [OpenSCAD] Approximate a 3D object by an ellipsoid

S
Skonike
Wed, Jun 24, 2020 12:36 PM

Thanks a lot for your answers!
I see, getting an exact solution to this problem seems very complex. I will
look into Kenneth's idea then and try to get an approximate value based on
eigenvectors.

Thanks again :)

Le mar. 23 juin 2020 à 22:24, Kenneth Sloan kennethrsloan@gmail.com a
écrit :

There are several ways to get approximate answers to your question.

The method I prefer is to use principal component analysis (Eigenvectors).
First, you need a well-distributed set of points from the object.  Since we
are approximating, perhaps the set of vertices on the boundary is
sufficient.  Check wikipedia for the details on PCA, Hessian, and
Eigenvectors.  This will get you a set of 3 axes.  You can then scale these
to make the volume of the ellipsoid match the volume of the object.

Finding an exact solution looks extremely difficult.  I’m not even sure
the solution is unique.

--
Kenneth Sloan
KennethRSloan@gmail.com
Vision is the art of seeing what is invisible to others.


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Thanks a lot for your answers! I see, getting an exact solution to this problem seems very complex. I will look into Kenneth's idea then and try to get an approximate value based on eigenvectors. Thanks again :) Le mar. 23 juin 2020 à 22:24, Kenneth Sloan <kennethrsloan@gmail.com> a écrit : > There are several ways to get approximate answers to your question. > > The method I prefer is to use principal component analysis (Eigenvectors). > First, you need a well-distributed set of points from the object. Since we > are approximating, perhaps the set of vertices on the boundary is > sufficient. Check wikipedia for the details on PCA, Hessian, and > Eigenvectors. This will get you a set of 3 axes. You can then scale these > to make the volume of the ellipsoid match the volume of the object. > > Finding an exact solution looks extremely difficult. I’m not even sure > the solution is unique. > > -- > Kenneth Sloan > KennethRSloan@gmail.com > Vision is the art of seeing what is invisible to others. > > > _______________________________________________ > OpenSCAD mailing list > Discuss@lists.openscad.org > http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org >