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

Jordan Brown openscad at jordan.maileater.net
Thu Nov 14 19:25:40 EST 2019


On 11/14/2019 11:39 AM, Carsten Arnholm wrote:
> On 14.11.2019 19:42, Jordan Brown wrote:
>> 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?

Good question, but you don't need self-intersection to have to answer
that question.  What color do you get if you have two independent
strokes of different color that overlap?

> 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.

Yes.  (It need not be vertices.  Strictly, I think it's that one or more
edges penetrate one or more faces.)

> 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.

Indeed, two material objects cannot occupy the same space.  But again
you don't have to get self-intersection to have that problem; you can't
have two independent steel rods overlap either.  We *do* allow two
cylinders to overlap, via union, so our cylinders are not steel rods. 
Two independent cylinders are allowed to occupy the same space, so why
isn't a bent cylinder allowed to have two parts that occupy the same space?

(Klein bottles are an obvious problem case, though I think they can be
looked at as either a winding problem or a self-intersection problem. 
They don't have well-defined interiors and exteriors, *and* they
self-intersect.)
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