Hi Speedy,
For the center 16 triangles, the centroid point is being found.
The remaining 32, 4 sided closed curves are not planar. This centroid node works for planar polygons.
(The Planar command does not work on the 32, 4 sided closed curves either.)
The center of mass of half of a solid sphere is at 3/8 of the distance from the sphere's center to the hemisphere's pole, as shown by Max's cVolume2.
For a hollow hemisphere, the distance is 1/2.
https://en.wikipedia.org/wiki/Centroid
The centroid node does not work for hemispheres either.
Wolfram gives a formula for center of mass for spherical caps.
Also Wolfram gives a formula for the centroid of a quadrilateral as the midpoint of the line between the midpoints of the diagonals.
Or "The centroid of the vertices of a quadrilateral occurs at the point of intersection of the bimedians."
http://mathworld.wolfram.com/GeometricCentroid.html
(Usually I find Wolfram math difficult to understand, and do not plan on doing integrals:-)
So the centroid for quadrilaterals, (4 line segments forming a closed quad), planar or non-planar, could be easily calculated.
The closed quads could be tested for planarity (somehow), and the calculation added to the centroid node. (I think.)
Is there a MoI method to test for planarity?
- Brian
