Steps to re-created the worked out 3D example.
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With the example drawing <Summing Centroids v2.dxf> hide/freeze the layer 'Centroids'.
Add a new layer e.g. 'My Centroids'.

Front view:
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The hatch was created from 3 boundaries: The spline shape, the circular void and the rectangle.
  As if the rectangle is also a void what later is filled with steel & plywood.

Create 2 uniform density area 2D Centroids from:
- the hatched area. (1)
- the rectangle representing the steel insert. (2)
  By selecting one single entity at a time.
Create a point mass 2D Centroid at:
- the center of the circle representing the RVS rod. (3)
  And enter its known mass by equation 'PI*10*10*100*0.00793' in grams. (4)

Activate the 2D Centroids listener. (5)

Edit the custom property 'Density' of the plywood centroid marker to read '0.00068*19'. (6)
  This is the volumetric density of plywood in g/mm³ times its thickness in mm what is the areal density.
  -> Because of the listener, the marker its 'Point mass' property is also updated (601.066...grams).
Set the custom property 'Density' of the insert centroid marker to '(0.00785*8)+(0.00068*11)'. (7)
  As if the sum of an 8mm thick layer of steel and an 11mm layer of plywood their individual areal densities.

Draw a selection around these 3 markers, the tool only considers selected markers.
Combine all 3 in one overall point mass 2D Centroid by taking the weighted sum of the components. (8)

Side view:
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Remark that we don't create new 2D Centroids from an area in the side view.
  Those are unrelated to front view areas with their front view areal density.
Duplicate (DP) the Plywood centroid marker. (9)
- Move (MV) the duplicate restricted horizontally to the middle of the Plywood in the side view. (10)
  -> Because of the listener, the marker coordinate properties are updated, here only in Y.
Duplicate the RVS rod centroid marker. (11)
- Move the duplicate to the middle of the rod in the side view. (12)
  Snapping Middle Manual (SN) for the target point.
Duplicate the steel insert centroid marker. (13, 16)
- Move the duplicate restricted horizontally to the middle of the 8mm steel insert in the side view. (14, 17)
- Edit the custom property 'Density' of this marker to read '(0.00785*8)+0' ... Only the steel. (15, 18)
- Repeat this for the left over plywood with equation '0+(0.00068*11)'.

De-activate the 2D Centroids listener. (19)

Draw a selection around the 4 markers in the side view.
Combine all 4 in one overall 2D Centroid by taking the weighted sum of the components. (20)


Both overall results indicate where the center of mass is situated in 3D.
A point mass of 903.5646g situated @(224.0144, 233.8132, -25.6400) or 6.64mm 'behind' the 19mm plywood.
Obvious is that some X/Y values correlate when performed correctly.

The procedure is similar for the alternative representation in the lower section of the drawing.
(Refer to Layer State Y4 'Alternative')
Proof of concept by comparing the results with partial sums.
The weighted sum of two components is always situated on a line between both 2D markers.
(Refer to Layer State Y2 'Partials')

Regards,
CVH