[OpenSCAD] Discuss manifoldness, co-incident faces edges etc
adrianv
avm4 at cornell.edu
Sun Nov 17 09:00:16 EST 2019
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.
https://en.wikipedia.org/wiki/Manifold
cacb wrote
> I would say it is a misunderstanding to present this as a problem. There
> is nothing wrong with this model, it is just not 2-manifold everywhere.
> 1-manifold edges are a problem, but this 4-manifold edge is not.
--
Sent from: http://forum.openscad.org/
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