Stereogram projections

Ideas about how a world with more than three spatial dimensions would work - what laws of physics would be needed, how things would be built, how people would do things and so on.

Stereogram projections

Postby quickfur » Fri Jul 27, 2012 6:54 pm

Ovo suggested that I use stereograms for showing my polytope projections, so I decided to do a little test:

Image

This is a cross-eyed stereo pair image of the projection of the 120-cell into 3D, centered on a dodecahedron. I'm new to this, so I don't know if I chose the right the eye separation or the best image sizes, etc.. Suggestions are welcome. :)

I purposely left out edges and vertices, because they tend to clutter the image, and besides, I wanted to see how effective stereo pairs are at conveying the shapes of the cells just by pure stereopsis alone. I find that it's pretty good (even with me being a beginner at cross-eyed viewing). You should be able to see two layers of cells in front of the yellow cell quite clearly. The far side of the projection is much harder to see, though (I can't see it clearly at all), probably 'cos of the clutter of all the stuff in front. It's the disadvantage of our "crippled" 3D viewpoint that can only see the projection from the side. :\

If you're new to cross-eyed stereo viewing (as I am), try this tutorial. (Note: do not stare at the image for too long at a time; I found that my eyes tire out very quickly when I do cross-eyed viewing. If you feel discomfort please stop immediately and rest your eyes. I don't want to be held responsible for eye injuries!)

What do you guys think of this?
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Re: Stereogram projections

Postby Ovo » Fri Jul 27, 2012 9:59 pm

The size is perfect for me but if it tires your eyes out fast you should probably reduce it a bit.
The impression of depth is rather faint, you can increase the distance between the two POV by a half at least, maybe double it.
It's also too homogenous, I don't clearly see the shape of the cells because there's almost no difference in the shading of their faces. Is it too transparent?

I think that maybe with a better depth impression and less transparency, adding edges shouldn't be so confusing and would help to see the shapes. But probably better if they are rather subtle, in a mid-tone grey and thin.

Last point, the colors are close to each other (but even more because they blend). I'm not sure, but maybe if they where more different it would help a little.
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Re: Stereogram projections

Postby quickfur » Fri Jul 27, 2012 11:33 pm

Ovo wrote:The size is perfect for me but if it tires your eyes out fast you should probably reduce it a bit.

It could be because this is my first time learning to see stereo cross-eyed. :) Now that I'm starting to get the hang of it, I don't have to strain so hard and my eyes are less tired with the same image size.

The impression of depth is rather faint, you can increase the distance between the two POV by a half at least, maybe double it.

OK, I doubled it. It does look better now, I think.

It's also too homogenous, I don't clearly see the shape of the cells because there's almost no difference in the shading of their faces. Is it too transparent?

OK, I'll try to reduce transparency a bit. It gets a bit harder to see inside the 3D structure, though.

I think that maybe with a better depth impression and less transparency, adding edges shouldn't be so confusing and would help to see the shapes. But probably better if they are rather subtle, in a mid-tone grey and thin.

Last point, the colors are close to each other (but even more because they blend). I'm not sure, but maybe if they where more different it would help a little.

OK, what about this:

Image

The edges are a bit thicker than I'd like, but povray has this annoying tendency to start breaking them up (aliasing artifact) if they are too thin. I could try rendering at higher resolution then reducing it, but it's a bit more inconvenient, so I'll leave it as is for now. I think they do help a little in seeing where the volumes are, especially in the green cells, which are a bit too homogenous to tell apart otherwise. (I could color them individually instead; maybe that'll help?)
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Re: Stereogram projections

Postby Ovo » Sat Jul 28, 2012 7:13 am

It's much better !

I think you can increase the distance between the POVs even more. :)

The edges are as thin as they can be, they are one-pixel wide ! They do add a little confusion to the global picture but they help me to see the individual cells' shape.

(I could color them individually instead; maybe that'll help?)
Certainly.

Now, with such a complex shape, you can only go so far with a fixed point of view, anyway. Without navigating in and around the 3D projection, it's hard to see every thing precisely. The stereoscopy just helps a bit.

Here is the best 4D app I've found, there are many settings you can change on the fly, including stereoscopy related settings (the Roundness slider changes the POVs distance). You can train and try a few things with it. But it lacks volume coloring and hidden surface removal.
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Re: Stereogram projections

Postby quickfur » Thu Aug 02, 2012 4:25 am

Ovo wrote:It's much better !

I think you can increase the distance between the POVs even more. :)

OK I'll keep that in mind when I do the next test.

The edges are as thin as they can be, they are one-pixel wide ! They do add a little confusion to the global picture but they help me to see the individual cells' shape.

Yeah it's an unfortunate side effect that edges play such a big role in our 3D-centric vision, whereas in 4D, they are only marginally important! The main problem is that they overlap each other too much when seen from our disadvantaged viewpoint. I had initially hoped to only use ridges (polygons) to indicate where the volumes are, but as you can see, that doesn't work very well with very complex shapes without some other aid.

(I could color them individually instead; maybe that'll help?)
Certainly.

Now, with such a complex shape, you can only go so far with a fixed point of view, anyway. Without navigating in and around the 3D projection, it's hard to see every thing precisely. The stereoscopy just helps a bit.

Yes, my original goal was to write an interactive program for manipulating these things. I kinda got side-tracked for quite a few years 'cos the shapes themselves were so interesting to study. :)

Here is the best 4D app I've found, there are many settings you can change on the fly, including stereoscopy related settings (the Roundness slider changes the POVs distance). You can train and try a few things with it. But it lacks volume coloring and hidden surface removal.

For me, the biggest obstacle with these apps is that they only show edges, which in 4D only play the role of peaks (analogous to vertices in 3D). It's like trying to see a cube by looking at a rotating set of 8 points. Edges are slightly better in the sense that at least they connect to each other, but still, I usually can't make any sense of edge projections as far as 4D visualization is concerned.

Hidden surface removal, I find, is also essential, mainly because 4D shapes are so complex that only in very simple cases one can visualize the shape without hidden surface removal. Having hidden surface removal means the projected polygons do not intersect each other (as long as the object itself is convex, of course) -- a big plus when trying to visualize where the volumes are. When the volumes intersect each other (no HSR), it's non-trivial to figure out where they are.

Maybe one of these days I should get over my aversion of Java applets, and write something that uses Java3D for rendering ridges with HSR. And if the JVM can handle it, maybe I'll even do stereoscopic projections too. :) The biggest obstacle on this front is, how to render transparent faces in real-time. Transparent things are hard to see unless they have certain visual qualities -- which is where povray shines, but the usual shortcuts used by real-time 3D renderers generally do not work very well with transparent things.
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