  Spherical harmonics are a favorable technique for 3D representation,
employing a frequency-based approach through the spherical harmonic transform
(SHT). Typically, SHT is performed using equiangular sampling grids. However,
these grids are non-uniform on spherical surfaces and exhibit local anisotropy,
a common limitation in existing spherical harmonic decomposition methods. This
paper proposes a 3D representation method using Fibonacci Spherical Harmonics
(FSH). We introduce a spherical Fibonacci grid (SFG), which is more uniform
than equiangular grids for SHT in the frequency domain. Our method employs
analytical weights for SHT on SFG, effectively assigning sampling errors to
spherical harmonic degrees higher than the recovered band-limited function.
This provides a novel solution for spherical harmonic transformation on
non-equiangular grids. The key advantages of our FSH method include: 1) With
the same number of sampling points, SFG captures more features without bias
compared to equiangular grids; 2) The root mean square error of 32-degree
spherical harmonic coefficients is reduced by approximately 34.6\% for SFG
compared to equiangular grids; and 3) FSH offers more stable frequency domain
representations, especially for rotating functions. FSH enhances the stability
of frequency domain representations under rotational transformations. Its
application in 3D shape reconstruction and 3D shape classification results in
more accurate and robust representations.
