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MoeSzyslak12-Amethyst
12-Amethyst
Aug 27, 2014 1:50 AM UTC
Question

Spherical Harmonics and Optimization

Hi, All --

I am trying to use spherical harmonics to represent a surface in 3D. The worksheet calculates through without error, but the results are off by ~24 orders of magnitude (for 12th degree Legendre polynomials). I note also that the magnitude of the answer increases with the degree of the polynomials.

Anybody have any ideas? Maybe there's a better way to approach this altogether?

Thanks in advance.

Matt

4 replies

MoeSzyslak12-AmethystAuthor
12-Amethyst
Sep 2, 2014 7:54 PM UTC

All -- just thought I would give this a "bump" before allowing it to die a peaceful death. For what it is worth, I am attempting to implement the algorithm illustrated in Section 3.1 of this document:

http://www.stat.wisc.edu/~mchung/papers/3DPVT.2006.pdf

Again, thanks in advance.

MAtt

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AlanStevens19-Tanzanite
19-Tanzanite
Sep 4, 2014 8:31 AM UTC

I think you are just trying to fit a function with a degree that is far too big. Try setting Lmax to 1 or 2.

Alan

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    MoeSzyslak12-AmethystAuthor
    12-Amethyst
    Sep 4, 2014 7:06 PM UTC

    Alan -- genius! Thanks for the help -- that gets me quite a bit closer. That said, there are still a couple of issues that I can see:

    1. The fit isn't very good -- it almost looks as if one of the "clouds" is rotated relative to the other, but I am using sph2xyz and xyz2sph, so I would expect that the two coordinate systems are consistent.

    2. In the double sum [R(theta,phi)], 'm' is supposed to range from -l to l, but clearly, this doesn't work when accessing elements of the array 'a' via subscripting. My workaround is to take |m|, but this doesn't seem right. Thoughts?

    I've never really played with spherical harmonics much, so I am learning as I go.

    Matt

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