Convert from x/y/z to eeg_topoplot positions

[behinger]

I converted some MNE code to convert form x/y/z to eeg_topoplot coordinates.

Now the big question is, can/should this be included here in TopoPlots.jl, or somehwere else?

using CoordinateTransformations

	"""
		convert x/y/z electrode montage positions to spherical coordinate representation. output is a matrix
	"""
	function cart3d_to_spherical(x,y,z)
		sph = SphericalFromCartesian().(SVector.(x,y,z))
		sph = [vcat(s.r,s.θ,π/2 - s.ϕ) for s in sph] 
		sph = hcat(sph...)'
		return sph
	end

		
"""
Projects 3D electrode positions to a 2D layout.

Re-implementation of the MNE algorithm.

If you put sphere to 
"""
function pos3D_to_layout(x,y,z;sphere=[0,0,0.])
	#cart3d_to_spherical(x,y,z)
	
# translate to sphere origin
	x .-= sphere[1]
	y .-= sphere[2]
	z .-= sphere[3]
	
	# convert to spherical coordinates
	sph = cart3d_to_spherical(x,y,z)

	# get rid of of the radius for now
	pol_a = sph[:,3]
	pol_b = sph[:,2]
	
	# use only theta & phi, convert back to cartesian coordinates
	p_x = pol_a .* cos.(pol_b)
	p_y = pol_a .* sin.(pol_b)

	# scale by the radius
	p_x .*= sph[:,1] ./(π/2)
	p_y .*= sph[:,1] ./(π/2)

	# move back by the sphere coordinates
	p_x .+= sphere[1]
	p_y .+= sphere[2]

  return Point2f.(p_x,p_y)
end
		  		



	  

---

(for full reproducibility)

begin
using CSV
	using LinearAlgebra
	using HTTP
	using CoordinateTransformations
	using WGLMakie
using StaticArrays
using DataFrames
end
begin
pos3d = CSV.read(download("https://raw.githubusercontent.com/lrkrol/SEREEGA/b5dec01e8b98260904906cc19c38853bfbb2ff19/leadfield/hartmut/chanlocs-hartmut-NYhead_small.xyz"),DataFrame,header=false)
rename!(pos3d,:Column1=>:ix,:Column2=>:x,:Column3=>:y,:Column4=>:z,:Column5=>:label)

	# remove some whitespace in the labels
transform!(pos3d,:label=>(x->strip.(x))=>:label)

	# remove some weird channels
	subset!(pos3d,:label=>ByRow(l -> l ∉ ["Nk1","Nk2","Nk3","Nk4"]));

out =   pos3D_to_layout(pos3d.x,pos3d.y,pos3d.z)

eeg_topoplot(1:size(out,1),pos3d.label;positions=out, interpolation=NullInterpolator(),label_text=true,enlarge=0.5)
end;