Hi,
For some modeling problem, I need to sample as uniformly as possible the surface of an ellipsoid
http://mathworld.wolfram.com/Ellipsoid.html
Obviously, sampling uniformly the parametric equations do not result in uniform surface point distribution and I used some awkward rules of thumb to get more uniformly distributed points but that is sub-optimal as well as ungratifying intellectually.
Does anybody know of an algorithm, the simpler the better, which would uniformly sample the surface of an ellipsoid (or more generally a superquadric)? An implementation in C, C++, Python would be welcome as well.
Regards,
Bruno
Note: Ideally, I would like something simpler and more specific than algorithms like electric charges equi-distributions on a surface, etc. With the parametric equations of the ellipsoid known, I guess there must be much more explicit approaches...
Don't know if this can help you out: https://link.springer.com/article/10.1007/s10851-016-0700-6
Hello Nek,
My problem is not directly related to fitting. I really need to uniformly sample surface points on a known ellipsoid which is different than fitting. I need these points to be well distributed in another part of my process...
Thanks,
Bruno
Algorithms for fitting the ellipsoid would not really work in my case and here is why.
What I did not explain first is that I already have an optimization algorithm (Downhill simplex) in place in which it was easy to include constraints like major/minor axis direction, major/minor axis length, etc and that these combinations of constraints are difficult to include in the vast majority of the other more more theoretically grounded methods...
That's why I'm using a more "brute force" approach based on having my modified Downhill-Simplex generating the non constrained ellipsoid parameters, sampling points from 1/4 of this analytic surface (hopefully more uniformly) and fitting these points to the scan of a human heel I want to "symmetrize"...
Hope this precision can help people understanding my need for sampling rather than fitting.
Regards,
Bruno
Hi Bruno, Maybe my previous project can help you solving the problem. If this is still unsolved problem. you can contact with me : [email protected]. I will give you more details.
Simon
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