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Polytope compound generation

 
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Jabe



Joined: 12 Jan 2008
Posts: 46
Location: Somewhere between Texas and the Fourth Dimension

PostPosted: Mon Jan 14, 2008 7:42 am    Post subject: Reply with quote

Another idea would be to make a 'duplicate object by rotation about the center' feature - for example: Lets say you wanted to make a compound of 5 icoes - start with ico (vertex centered), (rotate xy 36 degrees rotate zw 36 degrees) duplicate ico, (rotate xy and zw another 36 degrees) duplicate ico, continue for remaining icoes and you have a swirl-compound of 5 icoes.
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robertw
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Joined: 10 Jan 2008
Posts: 395
Location: Melbourne, Australia

PostPosted: Wed Jan 16, 2008 2:33 pm    Post subject: Reply with quote

Maybe sometime. You'd probably be one of the only people who'd know how to use that feature! Laughing

Rob.
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Dinogeorge



Joined: 13 Jan 2008
Posts: 71
Location: San Diego, California

PostPosted: Sat Jan 19, 2008 7:43 am    Post subject: Reply with quote

One thing that might not be too difficult to implement would be an option for the "ADD/BLEND from Memory" feature: Allow the user to select a vertex in the target polytope (3D or 4D) and in the memorized polytope, and when the ADD operation is done, the memorized polytope is placed so that its selected vertex coincides with the target's selected vertex, sized/oriented so that their centers also coincide and as many other vertices as possible also coincide. Ambiguity would be resolved with arrows that allow the user's choice.

That way I could, for example, build the compound of 120 pentachora by clicking on 120 of the 120-cell's 600 vertices and adding a pentachoron at each, deleting the 120-cell once all the pentachora have been added. I could also build lots of other uniform compounds presently unreachable from their vertex figures.
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robertw
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Location: Melbourne, Australia

PostPosted: Mon Jan 21, 2008 3:47 am    Post subject: Reply with quote

Dinogeorge wrote:
One thing that might not be too difficult to implement would be an option for the "ADD/BLEND from Memory" feature: Allow the user to select a vertex in the target polytope (3D or 4D) and in the memorized polytope, and when the ADD operation is done, the memorized polytope is placed so that its selected vertex coincides with the target's selected vertex, sized/oriented so that their centers also coincide and as many other vertices as possible also coincide. Ambiguity would be resolved with arrows that allow the user's choice.


Interesting idea, but how often would it be useful? I'm thinking of 3D. This would be no help to make the compound of 5 cubes, for example. After the first vertex is aligned, no others would be shared by the first two cubes in the arrangement.

Maybe it happens more often in 4D?

Rob.
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robertw
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Joined: 10 Jan 2008
Posts: 395
Location: Melbourne, Australia

PostPosted: Mon Jan 21, 2008 3:51 am    Post subject: Reply with quote

Jabe wrote:
Another idea would be to make a 'duplicate object by rotation about the center' feature - for example: Lets say you wanted to make a compound of 5 icoes - start with ico (vertex centered), (rotate xy 36 degrees rotate zw 36 degrees) duplicate ico, (rotate xy and zw another 36 degrees) duplicate ico, continue for remaining icoes and you have a swirl-compound of 5 icoes.


There's a problem here: which way are the X,Y,Z,W axes? Since Stella4D generates polychora from vertex figures, there's no standard orientation in the result. That is, the axes are not aligned how you'd be expecting them. Stella4D does not yet determine symmetry groups in 4D like it does in 3D, so it can not guess which way to point the axes.

Would another solution be to select a face and ask for a rotation either in that plane or around that plane? Or might there not always be a face in the plane you need?

Rob.
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Dinogeorge



Joined: 13 Jan 2008
Posts: 71
Location: San Diego, California

PostPosted: Mon Jan 21, 2008 4:05 am    Post subject: Reply with quote

robertw wrote:
Interesting idea, but how often would it be useful? I'm thinking of 3D. This would be no help to make the compound of 5 cubes, for example. After the first vertex is aligned, no others would be shared by the first two cubes in the arrangement.

Maybe it happens more often in 4D?


Everything happens more often in 4D!

Here's how it would work for the compound of five cubes in a dodecahedron. Put the cube in memory. Select a corner of the dodecahedron and ADD the cube, concentric with the dodecahedron and sized/oriented with the other seven vertices at seven other dodecahedral corners. Arrows come up that say "1 of 2." You pick one and Stella4D finds the appropriate corners. Select the same corner again, and Stella4D puts the cube there the other way. Select a different corner with a cube at it, and Stella4D puts the cube there the other way. Select a corner with no cube at it, and Stella4D asks for your choice. Select a corner with two cubes and Stella4D says no new cubes may be added: Do you want to add one anyway (to coincide with one already there) or do you want to blend one out? Continue until all five cubes are in place.
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Jabe



Joined: 12 Jan 2008
Posts: 46
Location: Somewhere between Texas and the Fourth Dimension

PostPosted: Mon Jan 21, 2008 6:00 am    Post subject: Reply with quote

robertw wrote:
Jabe wrote:
Another idea would be to make a 'duplicate object by rotation about the center' feature - for example: Lets say you wanted to make a compound of 5 icoes - start with ico (vertex centered), (rotate xy 36 degrees rotate zw 36 degrees) duplicate ico, (rotate xy and zw another 36 degrees) duplicate ico, continue for remaining icoes and you have a swirl-compound of 5 icoes.


There's a problem here: which way are the X,Y,Z,W axes? Since Stella4D generates polychora from vertex figures, there's no standard orientation in the result. That is, the axes are not aligned how you'd be expecting them. Stella4D does not yet determine symmetry groups in 4D like it does in 3D, so it can not guess which way to point the axes.

Would another solution be to select a face and ask for a rotation either in that plane or around that plane? Or might there not always be a face in the plane you need?

Rob.


Your idea could work to some extent, but it would also be good to be able to select three vertices to establish a plane for rotation just in case there are no faces that work (i.e. need to rotate a pentagon symmetry, but there are only triangles in polychoron). Make it possible to rotate within the plane, as well as rotate the polychoron to move the plane in an orthogonal manner (while keeping the polychoron centered at origin).
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