So to generalize, how would it be possible to copy a clothing button, and place it tangent to a surface, such as a sphere, or catenary of revolution, with the "center" at an on-surface point of the surface?

Using the ArrayGem script with a tiny line segment, instead of a point object does such a copy.

Is it possible to modify the ArrayGem factory, to use a PointObject, instead of a Curve?
Changing objectpicker.allowCurves() to objectpicker.allowPointObjects() in the script, does not work, so the change would have to be in the ArrayGem factory, (I think).