Better rendering of infinite duals

[senkoquartz]

Here are two issues with how the duals of hemipolyhedra look in Stella:
1) They are usually cut off after a very short distance, often failing to show how the polyhedron would look in reality where it extends out further. I would recommend and an option to change how far out it extends, and maybe even an option to gradually fade out instead of being abruptly cut off
2) The faces themselves tend to have wonky degenerate-looking edges, I usually can't tell what's going on with them when the face is complex or moderately complex

[senkoquartz]

Well, bizarrely, minutes after I posted this, I interacted with Skilling's Figure's dual for a few seconds and then it changed, and all the uniform infinite duals are properly far-extended now. I've never seen that before.

[senkoquartz]

Complex faces are still wonky though

[robertw]

Wonky how? Which one?

You can adjust the extent of the infinite dual faces using Ctr+Left-drag in the Dual view.

Hold Ctrl and you'll see the cursor change and the tip in the corner tell you what it does.

[senkoquartz]

Wonky how? Which one?

For example many (most?) of the duals of hemipolyhedron facets of the icosidodecahedron have faces I can't make sense of. I don't have access to stella at the moment to check

[guy]

I recall discussing this many years ago.
The fundamental issue is that the "interior" of an infinite face is not defined. Polyhedral reciprocation is only equivalent to projective reciprocity for convex solids. Non-convexity introduces anomalies as to the filled-in bits of the face plane, and the software has to figure the interiors of faces a slightly different way - essentially choosing the finite region and ignoring the rigorous projective solution which crosses infinity.
Reciprocating hemi elements to infinity makes matters even worse, as there is no finite region. I suggested that Great Stella should follow Wenninger's approach of choosing infinite faces such that they form long tubes (see for example my avatar here). I am not sure if that was ever introduced?

[robertw]

I recall discussing this many years ago.
The fundamental issue is that the "interior" of an infinite face is not defined. Polyhedral reciprocation is only equivalent to projective reciprocity for convex solids. Non-convexity introduces anomalies as to the filled-in bits of the face plane, and the software has to figure the interiors of faces a slightly different way - essentially choosing the finite region and ignoring the rigorous projective solution which crosses infinity.
Reciprocating hemi elements to infinity makes matters even worse, as there is no finite region. I suggested that Great Stella should follow Wenninger's approach of choosing infinite faces such that they form long tubes (see for example my avatar here). I am not sure if that was ever introduced?

I think there's only an issue when the centre of reciprocation lies in a facial plane (ie hemi faces). You'd get this issue even with convex polyhedra if you decide to put the centre of reciprocation on one of the faces. Nonconvex polyhedra work fine as long as they don't have hemi-faces.

Isn't your suggestion already what Stella has done all along? Or at least since very early on? It renders long prisms like in your avatar, and like in the screenshots in earlier posts above. You can also interactively control how long the prisms are.

[guy]

I think there's only an issue when the centre of reciprocation lies in a facial plane (ie hemi faces). You'd get this issue even with convex polyhedra if you decide to put the centre of reciprocation on one of the faces. Nonconvex polyhedra work fine as long as they don't have hemi-faces.

Isn't your suggestion already what Stella has done all along? Or at least since very early on? It renders long prisms like in your avatar, and like in the screenshots in earlier posts above. You can also interactively control how long the prisms are.

I have a hazy recollection that it may have worked OK for faces passing through the centre, but not when edges pass through. Some faceted dodecahedra have such edges.

Even more hazily, placing multiple superimposed vertices at the centre crashed the program. For example, treating the squares of thah as sets of coplanar triangles.

I just wondered if something like this might have been the case with senkoquartz.

[robertw]

I tried thah with vertex at centre (squares split into 4 triangles) and the dual worked fine.

I also tried faceting the thah to create something with edges through the centre. It worked OK, and a dual appeared, but I'm not sure how such a dual should appear. It did not offer the option to adjust the infinite parts as it would with a vertex at the centre. I probably don't care too much about such duals, as long as it doesn't crash.

[guy]

Looks good. Sorry to have fed you a red herring.