Convert electrode positions form 3D to 2D

Sometimes you have 3D montage but you need 2D montage. How to convert one to another? The function to_positions should help.

using UnfoldMakie
using CairoMakie
using TopoPlots
using PyMNE

    CondaPkg Found dependencies: /home/runner/.julia/packages/PyMNE/HGgbW/CondaPkg.toml
    CondaPkg Found dependencies: /home/runner/.julia/packages/PythonCall/S5MOg/CondaPkg.toml
    CondaPkg Dependencies already up to date

Get positions from MNE

Generate an MNE structure taken from mne documentation

biosemi_montage = PyMNE.channels.make_standard_montage("biosemi64")
n_channels = length(biosemi_montage.ch_names)
fake_info =
    PyMNE.create_info(ch_names = biosemi_montage.ch_names, sfreq = 250.0, ch_types = "eeg")
data = rand(n_channels, 1) * 1e-6
fake_evoked = PyMNE.EvokedArray(data, fake_info)
fake_evoked.set_montage(biosemi_montage)

pos = to_positions(fake_evoked)

64-element Vector{Point{2, Float64}}:
 [0.34935274876763384, 0.8914697618166454]
 [0.2285454515991697, 0.8299153694246765]
 [0.3239207434789678, 0.8210416675361911]
 [0.38009721906796695, 0.7346772379558053]
 [0.28116929732806945, 0.7288908776450373]
 [0.19598811803244962, 0.729048111114921]
 [0.13267223773863893, 0.7340421555641459]
 [0.07111784534666996, 0.6132348583956815]
 [0.1381378125628734, 0.6118022611559795]
 [0.2400936018380034, 0.6086174147856195]
 ⋮
 [0.612772564740614, 0.34981504242270145]
 [0.5864401194985318, 0.2239606378043266]
 [0.6853680412384293, 0.2297469981150946]
 [0.7705492205340492, 0.22958976464521094]
 [0.8338651008278599, 0.22459572019598625]
 [0.8710458357539724, 0.19758233504967118]
 [0.7379918869673291, 0.12872250633545543]
 [0.6426165950875308, 0.13759620822394072]
 [0.6171845897988648, 0.06716811394348651]

Projecting from 3D montage to 2D

pos3d = hcat(values(pyconvert(Dict, biosemi_montage.get_positions()["ch_pos"]))...)

pos2 = to_positions(pos3d)

f = Figure(size = (600, 300))
scatter(f[1, 1], pos3d[1:2, :], axis = (title = "Dropping third dimension",))
scatter(f[1, 2], pos2, axis = (title = "Projection form 3D to 2D",))
f

As you can see, the "naive" transformation of simply dropping the third dimension does not really work (left). Instead, we have to project the channels onto a sphere and unfold it (right).

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