[OpenSCAD] Discuss manifoldness, co-incident faces edges etc

nop head nop.head at gmail.com
Sun Nov 17 15:15:27 EST 2019


So are two cubes meeting at an edge a 2-manifold?

Before this discussion I thought definitely not. People seem to imply it is
but only in file representations that keep two separate edges that are
actually coincident.

I have always thought that self intersections made an object not
2-manifold. People seem to imply that is only if the representation is a
polygon soup. Is a mesh with self intersections 2-manifold if it comes with
edge connection info but the same geometric shape without edge connection
info not? I am confused because I thought a manifold referred to a
geometric object not how it is represented on a computer.

If OpenSCAD used a PolySet representation with edges would it not matter if
the vertices where truncated and physically in the wrong place?



On Sun, 17 Nov 2019 at 19:58, adrianv <avm4 at cornell.edu> wrote:

> 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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>
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