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

Carsten Arnholm arnholm at arnholm.org
Thu Nov 14 14:39:46 EST 2019


On 14.11.2019 19:42, Jordan Brown wrote:
> On 11/14/2019 7:32 AM, arnholm at arnholm.org wrote:
>> I think self-intersections are almost always a sign of something else 
>> gone wrong, it is typically a body that overlaps itself and and not a 
>> result of a boolean operation. A self-overlapping volume is physically 
>> impossible. There are lots of ways to use bodies that are not 
>> 2-manifold, but a self overlapping volume seems like an obvious mistake.
> 
> Is it?
> 
> Consider the 2D case.  I'm drawing with a paintbrush, and so I'm drawing 
> areas, not lines.  I draw a figure-8.  It's self-intersecting, but it's 
> clearly not impossible.  The two parts of the stroke are unioned.

So if you changed paintbrush colour along the way, what would the colour 
of the intersecting area be?

What I was thinking of was the case in 3D where the topology is well 
defined and closed, but where the geometry (i.e. the coordinates) are 
such that some vertices fall within the volume of another part of the 
body. What I meant it by physically impossible was if you took a steel 
rod and bent it such that it would overlap itself. You cannot have two 
instances of material occupying the same volume even though you can 
formulate it with a polyhedron.

Your paintbrush example is kind of equivalent.

Carsten Arnholm




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