More correspondence between faceting and stellation criteria options

Suggest new features for Stella.
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senkoquartz
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More correspondence between faceting and stellation criteria options

Post by senkoquartz » Sun Oct 11, 2020 7:53 pm

Since stellation and faceting are dual processes of each other, it makes sense that if a faceting criteria is available, its dual stellation criteria should also be available.

The biggest issue is that the stellation options don't produce stellations with internal structure - they just create the outer pieces and don't care about the interior. But if you facet a polyhedron, and take that new polyhedron's dual, you can now have a stellated polyhedron with internal structure, intersecting faces, etc. So you can find new stellated polyhedra with internal structure by faceting the base's dual and taking the dual of that, but that's cumbersome and not always viable.

Also I think that generally, if Stella has the capacity to search for facetings or stellations in a certain way than that way should be an option. If there are more criteria that Stella has the capacity to search with besides the several ones you can choose in the faceting menu, than being select for those would really help with polyhedron finding.

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robertw
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Re: More correspondence between faceting and stellation criteria options

Post by robertw » Mon Oct 12, 2020 2:06 am

Thanks for the suggestions.

The current stellation criteria don't really make sense for faceting, since as you say, it's about the exterior shape, which has no meaning for the dual. Stellation was added first, and was more based on the approach of Coxeter et al in The 59 Icosahedra, ie Miller's Rules, as well as some other published papers which deal with stellation in a similar way. It makes sense because stellations can be built up in this way, using the stellation cells as building blocks.

Going the other way could work though, using the faceting criteria to step through stellations. I already had that on my to-do list somewhere, although not quite sure how to fit it in. The stellation view is based on combinations of stellation cells, as mentioned above, which doesn't fit in with this idea. I suppose it could have a completely separate purpose (separate in the code) to show the dual of the current faceting when a faceting-based criterion has been selected. Since it wouldn't tie into the current stellation process, it may mean that the Stellation Face, Stellation Diagram, and Cell Diagram views wouldn't work.

Some faceting criteria are still asymmetric though, eg "Tidy Facetings", but we could just leave those out as stellation criteria, just adding "Tide Facetings & Duals" instead.

senkoquartz
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Re: More correspondence between faceting and stellation criteria options

Post by senkoquartz » Mon Oct 12, 2020 10:04 am

robertw wrote:
Mon Oct 12, 2020 2:06 am
Since it wouldn't tie into the current stellation process, it may mean that the Stellation Face, Stellation Diagram, and Cell Diagram views wouldn't work.

Some faceting criteria are still asymmetric though, eg "Tidy Facetings", but we could just leave those out as stellation criteria, just adding "Tide Facetings & Duals" instead.
Yeah I think an additional version of the "view face"/"view stellation face"/"view stellation diagram" that shows the real face of the polyhedron would be good - as it is I can't tell from those views what the kind of edge and internal structure the face has, just its silhouette.
Here's another suggestion - what about a "stellation mode" where you can manually create stellated faces by interacting with the stellation diagram?

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robertw
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Re: More correspondence between faceting and stellation criteria options

Post by robertw » Mon Oct 12, 2020 1:40 pm

You can already interact with the stellation diagram and the cell diagram. Watch the bottom right corner for tips about what the mouse can do, and hold down Shift or Ctrl to see how they change.

With the mouse in the Stellation Diagram view, hold Shift:

Image

Or hold Ctrl:

Image

You can also display the stellation diagram attached to a selected face of the polyhedron, and still interact with it in the same way:

Image

senkoquartz
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Re: More correspondence between faceting and stellation criteria options

Post by senkoquartz » Mon Oct 12, 2020 5:35 pm

robertw wrote:
Mon Oct 12, 2020 1:40 pm
You can already interact with the stellation diagram and the cell diagram. Watch the bottom right corner for tips about what the mouse can do, and hold down Shift or Ctrl to see how they change.

Image
I didn't know about any of this, this is great! You can even use it with faceting mode, which is what I was specifically thinking of.

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