[OpenSCAD] Discuss manifoldness, co-incident faces edges etc
Carsten Arnholm
arnholm at arnholm.org
Sun Nov 17 14:23:02 EST 2019
On 17.11.2019 15:00, adrianv wrote:
> Standard mathematical terminology is that a 2-manifold is an object that is
> locally equivalent to 2-dimensional Euclidean space, meaning that if you
> take any point of a 2-manifold, it has a neighborhood that can be
> continuously mapped to the plane.
>
> A 1-manifold is an object where every point has a neighborhood that can be
> continuously mapped to a line. A 4-manifold, on the other hand, is an
> object where every point has a neighborhood that can be continuously mapped
> to Euclidean four-dimensional space. It does not make sense to talk about a
> "4-manifold edge", and 4-manifolds have no relevance to OpenSCAD. Edges are
> 1-dimensional objects. They can't be a 4-manifold, only a 1-manifold. I
> don't know a name for the points of an object that fail the test of being
> locally Euclidean, but "1-manifold" or "4-manifold" does not describe those
> points. It means something completely different.
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.
Carsten Arnholm
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