Functional Expansion Tallies for 3D

New Ideas
1

As introduced in the documentation,

“This filter allows scores to be multiplied by Legendre polynomials of the particle’s position along a particular axis.”

  1. Can this be extended to all three axial directions (without using the separation of spatial variables method)?

    This would allow using three Legendre polynomials as basis functions. A spatial variable in 3D could then be represented as:
    φ(x, y, z) = Σᵢ₌₀ᴵ Σⱼ₌₀ᴶ Σₖ₌₀ᴷ φᵢⱼₖ(x, y, z) = Σᵢ₌₀ᴵ Σⱼ₌₀ᴶ Σₖ₌₀ᴷ fᵢⱼₖ Pᵢ(x) Pⱼ(y) Pₖ(z)

    where I, J, K are the expansion orders for the x, y, z directions respectively, and fᵢⱼₖ are the function expansion coefficients.

    The estimator for fᵢⱼₖ could be obtained via the collision estimator.

  2. More generally, is it possible to specify basis functions other than Legendre or Zernike polynomials?