python - How do I calculate a 3D centroid?

Question

Is there even such a thing as a 3D centroid? Let me be perfectly clear—I've been reading and reading about centroids for the last 2 days both on this site and across the web, so I'm perfectly aware at the existing posts on the topic, including Wikipedia.

That said, let me explain what I'm trying to do. Basically, I want to take a selection of edges and/or vertices, but NOT faces. Then, I want to place an object at the 3D centroid position.

I'll tell you what I don't want:

• The vertices average, which would pull too far in any direction that has a more high-detailed mesh.
• The bounding box center, because I already have something working for this scenario.

I'm open to suggestions about center of mass, but I don't see how this would work, because vertices or edges alone don't define any sort of mass, especially when I just have an edge loop selected.

For kicks, I'll show you some PyMEL that I worked up, using @Emile's code as reference, but I don't think it's working the way it should:

from pymel.core import ls, spaceLocator
from pymel.core.datatypes import Vector
from pymel.core.nodetypes import NurbsCurve

def get_centroid(node):
    if not isinstance(node, NurbsCurve):
        raise TypeError("Requires NurbsCurve.")
    centroid = Vector(0, 0, 0)
    signed_area = 0.0
    cvs = node.getCVs(space='world')
    v0 = cvs[len(cvs) - 1]
    for i, cv in enumerate(cvs[:-1]):
        v1 = cv
        a = v0.x * v1.y - v1.x * v0.y
        signed_area += a
        centroid += sum([v0, v1]) * a
        v0 = v1
    signed_area *= 0.5
    centroid /= 6 * signed_area
    return centroid

texas = ls(selection=True)[0]
centroid = get_centroid(texas)
print(centroid)
spaceLocator(position=centroid)

Answer 1

In theory centroid = SUM(pos*volume)/SUM(volume) when you split the part into finite volumes each with a location pos and volume value volume.

This is precisely the calculation done for finding the center of gravity of a composite part.