User question: How to find the combined center of gravity of 2 shapes

[CVH]

Regarding a consulting question offline.

Given: 2 arbitrary shapes at some distance apart, different mass per unit squared (Areal density)
Question: Position of the combined centers of gravity (Weighted sum of the 2D Centroids)

The method is explained regarding the attached drawing.

HowToSum2DCentroids.dxf

Arbitrary example

(103.53 KiB) Downloaded 1372 times

Ensure that both shapes are drawn CCW (=positive), are perfectly closed and without self-intersections.
Define the 2D Centroid of both shapes individually.

• Select only shape 1 or 2 >> Misc .. Information .. 2D Centroids .. Area Centroid
  (Or use the action buttons on the Misc Information Toolbar)

The areal density is considered to be uniform for the whole shape, 'undefined' on creation what falls back on =1.000.
If considered as flat, it would have no third dimension, furthermore, zero would reduce everything to zero.
For changing this we must bind the textual Centroid custom properties listed in the Property Editor.

• Activate the 2D Centroids transaction listener when not active.
  See: Misc .. Information .. 2D Centroids .. Centroids Listener

• Select the first Centroid marker (1) and define its mass per unit squared by editing the custom property 'Density'.
  For example 2.000 (All is unitless).

With the listener active, the 'Point mass' property is recalculated. (2.0 x area or about 3808.35)
The selection will be cleared. With custom properties I found no other way to avoid a recursive nature.

• Select the second Centroid marker (2) and also define its specific mass per unit squared, for example 1.200.
  In the same units of mass and the same unit squared. (Expressions are supported)

The listener is no longer required beyond this point.
When active it keeps on checking for Centroids property changes on any transaction.


For finding the system center of gravity we need to sum these Centroids weighted.
'Weighted' or not only based on their geometrical position.

• Select both Centroid markers >> Misc .. Information .. 2D Centroids .. Sum 2D Centroids weighted

A third Centroid marker is created, in this case of the 'Point mass' type. (The typical density is most likely no longer uniform)
-> Its position is the combined center of gravity.
-> See Command History for further details.
Select this marker for textual details in full floating point notation stored as custom properties.
=> At about (71.163, 18.806) for this example.
=> Combined mass is about 7757.522 in the unit of mass used to express 'Density'.


It took only a few messages forth and back ...
The user is now summing centers of gravity of various shapes, with holes, with virtual extrusions ....
It almost exceeded my comprehension with the sparsely given details.
The tools suits him/her very well so it seems.
Accuracy is reported to be near flawless.

Regards,
CVH