## How hard would it be to compute true filling?

For general discussion of polyhedra, not necessarily Stella-specific.
metachirality
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Joined: Fri Dec 20, 2019 10:02 pm

### How hard would it be to compute true filling?

True filling is filling regions of a polytope if they can be continuously transformed into a region of odd density. How feasible is this in practice?

robertw
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### Re: How hard would it be to compute true filling?

Wouldn't that mean they are already odd density? Can an even-density region ever be transformed to an odd density?

Did you already find "Display->Polygon Filling Options" from the menu? What you want is similar to the Modulo-2 method.

metachirality
Posts: 12
Joined: Fri Dec 20, 2019 10:02 pm

### Re: How hard would it be to compute true filling?

No, I mean if you had a four-shaped thing and transformed it so that it didn't intersect itself, you would've transformed the even density region in the four's intersection into an odd density region.

robertw
Posts: 535
Joined: Thu Jan 10, 2008 6:47 am
Location: Melbourne, Australia
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### Re: How hard would it be to compute true filling?

Do you mean something like this, with arms that cross over each other?

And then pull the arms apart so there's no more overlap?

I guess the region of space that was once density 2 is now density 1, but you could simply move the whole object to transform any region of space between odd and even density. So maybe I'm still not sure what you mean.

My way of thinking about density would be as follows. As the shape is transformed, the region 2 density shrinks until it disappears. It can never transform to an odd-density region without faces crossing over it.

metachirality
Posts: 12
Joined: Fri Dec 20, 2019 10:02 pm

### Re: How hard would it be to compute true filling?

The empty space around the polyhedron is also considered as a region. For orientable polyhedra, this is the same as density filling, for non-orientables its more complicated. For uniform polyhedra I think that binary filling works, but for other polyhedra which are non-orientable but not uniform, it's different.

robertw