[OpenSCAD] Discuss manifoldness, co-incident faces edges etc
adrianv
avm4 at cornell.edu
Sun Nov 17 15:11:16 EST 2019
cacb wrote
> Ok, but in practice we determine manifoldness for an edge by counting
> how many faces refer to it. That's what we are talking about, and in
> this case having 4 faces referring to an edge is not a problem.
"Manifoldness of an edge"? All edges are 1-manifolds...unless they have end
points. A given object either is a 2-manifold or is not. If somewhere on
the object, N faces meet at an edge where N is not 2 then the object is not
a 2 manifold. Note that if you construct 3-manifolds by sticking together
tetrahedra then the condition is the same: if two tetrahedra meet at a face
then everything is good and you have a valid 3-manifold. But if the number
of tetrahedra that meet at a face is not two then the resulting object is
not a 3-manifold. The magic of the number 2 (as the number of faces that
meet at an edge) is not that we are trying to make 2-manifolds, but that
dividing an object in half creates two halves. Similarly if you go to the
1-d case then the non-manifold figure 8 has four segments meeting at a point
whereas a valid 1-manifold will always have two segments meet at a point.
I suggest that using terminology correctly, or devising and clearly laying
out new terminology as needed, is better than abusing existing terminology
to mean something completely different than what it actually customarily
means. If people are confused about what a 2-manifold is already, using the
terminology incorrectly isn't going to help. It could really confuse
somebody who doesn't know what a 2-manifold is and thinks your use has
something to do with the customary meaning of the term. It sounds like you
want to talk about the face count of an edge, perhaps, the number of faces
meeting at an edge.
--
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