MakieSphericalHarmonics

MakieSphericalHarmonics.jl

using GSL
using Makie

struct Y
    l::Int
    m::Int
    function Y(l,m)
        @assert -l <= m <= l
        new(l,m)
    end
end

function (y::Y)(θ,φ)
    Plm = GSL.sf_legendre_sphPlm_e(y.l, abs(y.m), cos(θ)).val
    exp(im*y.m*φ) * Plm
end


θ = range(0,stop=π, length=50)
φ = range(0, stop=2π, length=100)

x = [sin(θ)*cos(φ) for θ in θ, φ in φ]
y = [sin(θ)*sin(φ) for θ in θ, φ in φ]
z = [cos(θ) for θ in θ, φ in φ]

function scale01(xs)
    mi, ma = extrema(xs)
    (xs .- mi) ./ (ma - mi)
end

function compute_color(l,m)
    vals = [Y(l,m)(θ, φ) for θ in θ, φ in φ]
    Float32.(scale01(imag.(vals))) * RGBf0(1,1,1)
end


scene = Scene(raw = false, resolution = (500, 500))
surface!(scene, x, y, z)

l = 1
m = 0

thm = Theme(raw = true, camera = campixel!)
sliderl = slider(thm, 1:10, start=l)
# sliderm = slider(thm, -10:10, start=m)
sliderm = slider(thm, 0:10, start=m)
on(sliderl[end][:value]) do l_new
    global l = l_new
    scene[end][:color] = compute_color(l,m)
end

on(sliderm[end][:value]) do m_new
    global m = clamp(m_new, -l, l)
    scene[end][:color] = compute_color(l,m)
end

scene[end][:color] = compute_color(l,m)
vbox(
    hbox(sliderl,sliderm), 
    scene)