Verteses around cylinter screw


I would like to move some vertices around cylinder, but how… thats the question.
I want transform path around cylinder like tihs:
The maker says he
Text was divided into 200-300 reference points, each point translated into polar coordinates around the cylinder. Don’t yet understand how… I managet to get the vertices and “transform” them to "polar coordinates, but doesn’t look right. Green one is the original path.
The code so far:

import bpy
from bpy import context
import numpy as np
import bmesh

def pol2cart(rho, phi):
    x = rho * np.cos(phi)
    y = rho * np.sin(phi)
    return(x, y)

def cart2pol(x, y):
    rho = np.sqrt(x**2 + y**2)
    phi = np.arctan2(y, x)
    return(rho, phi)

mesh =
bm = bmesh.from_edit_mesh(mesh)
for vert in bm.verts:
    kala = cart2pol(, = kala[0] = kala[1]

and if I get the right shape, how to rotate it round 0,0,0?