Projecting nodes on circumference divided into 36 parts

I am working on a task in which I have to project nodes (X and Y coordinates) of a point cloud to the circumference located exactly on the centre of gravity of the mesh (Geometry). My question is how can I create a circumference on the geometry and divvide it into 36 different parts and then how can I project the nodes on it.

What I have done? : I have found the centroid (Centre of Gravity) of the geometry. I moved the geometry with its centroid and placed it on the reference point (0, 0). Now I have the same geometry, but with different coordinates which I have shown here below.

node_number X_coordinate    Y_coordinate
    0            -1.0          -2.0
    1            -1.0          -1.0
    2            -1.0           0.0
    3            -1.0           1.0
    4            -2.0           1.0
    5            -2.0           2.0
    6            -1.0           2.0
    7             0.0           2.0
    8             1.0           2.0
    9             2.0           2.0
   10             2.0           1.0
   11             1.0           1.0
   12             0.0           1.0
   13             0.0           0.0
   14             0.0          -1.0
   15             0.0          -2.0

I would like to project the nodes (coordinates shown above) onto the circumference which is divided into 36 pixels (parts). I have shown an example of that below in the picture.

2022-08-20_20h03_01

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