FIELD_GAUSSIAN Function

Note

The $\phi$ modulation is weighted by $\sin\theta$ so the field stays single-valued at the poles: at $\theta=0$ (or $\pi$), every $\phi$ maps to the same physical point, so any legitimate smooth field must be $\phi$-independent there. An earlier version of this field used a bare $\cos\phi$ term with no such weighting -- it was multi-valued at the pole (1.5 approaching along $\phi=0$, 0.5 along $\phi=\pi$), and no finite spherical harmonic series can converge to a discontinuous function; the reconstruction error plateaued at exactly 0.5 (the size of the discontinuity) instead of shrinking with $\ell_{max}$. Caught by comparing this driver's convergence curve against an isolated, single-$\ell_{max}$ reconstruction check, which did not show the plateau.