Double ray tracing as an approach to visualise 4D objects a?

Discussions about how to visualize 4D and higher, whether through crosseyedness, dreaming, or connecting one's nerves directly to a computer sci-fi style.

Double ray tracing as an approach to visualise 4D objects a?

Postby Secret » Mon Aug 31, 2015 3:24 pm

Double ray tracing as an approach to visualise monochromic 4D objects arranged in layers (like a cloudscape)

This is directly extracted from a dream last night, thus it might not necessary make sense

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Consider cloud layers in the sky in 4D space

Here we picked out one of the clouds to focus our attention on. Note how the top cloud cast a shadow to the bottom cloud as expected, and the more and thicker the clouds are on top of the target cloud in question, the darker the shadow being cast
Now note how the cloud has a section (which extend into its 3D "interior" in the 3D projection shown that is in a bluer gradient.

Looking at the parallel projection of the 4D sky, we have a piece of cloud anwards to the target cloud in question. This cast a bluish "shadow" onto the cloud in question. Once again, the more clouds anwards to the target cloud, the bluer the cloud became

Now since we live in 3D, we can only see the top image, that is, we cannot see the clouds anwards to it, but we can infere it is there as the cloud moves by noting how the blueness moves and morphs due to clouds anwards to it casting the blusih "shadow" down to the cloud we are looking?

It seems easy to implement in POVray or other raytracing softwares, but will this help us in illustrating layered structures in 4D in real time?
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Re: Double ray tracing as an approach to visualise 4D object

Postby ICN5D » Tue Sep 01, 2015 8:21 pm

Interesting, but how do you mean double ray tracing? Are you trying to combine two different angles of the same thing into one image?
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Re: Double ray tracing as an approach to visualise 4D object

Postby Secret » Wed Sep 02, 2015 3:48 am

https://en.wikipedia.org/wiki/Ray_tracing_(graphics)

Unless I misunderstood something, the idea that there are effectively two different types of shadows suggests there are two light sources, one shining in the y (vertical) direction and another shining in the w direction

The result is then viewed on a 3D slab (viewing region) since we live in 3D space.

Therefore while the black shadows are 2D since the cloudscape only exists in one 3D "slab" at a time and the slabs are discretely arranged in an array, the blue shadow is 3D because it is cast by light passing through the 4D array of 3D cloudscapes onto the viewing region

Thus by adjusting some parameters such as xyz or polar coordinates, the viewer will obtain the appearance of the moving 4D cloudscape as it walked or turned around in 3D space

Screen Shot 2015-09-02 at 2.33.11 pm.png
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Here the pics told us where the red ball is relative to the white clouds by the presence of its 3D blue shadow cast onto the cloud layers katwards to it, and the black shadows told us where in 3D the white clouds are relative to each other

Both you and gonegahgah have developed viewers that can take slices (cartesian or polar) of nD objects, and quickfur has a rendering program on projections with hidden surface removal. The game Miegakure also has similar mechanics except there are no shadows shown for objects casting in the 4th direction. I am curious how will this idea be like combining all the resources here
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Re: Double ray tracing as an approach to visualise 4D object

Postby ICN5D » Wed Sep 02, 2015 2:59 pm

Ahh, that's more clear. I see what you're trying to do. I've thought about a similar technique using just slices, by superimposing different angle sections into one object. It would work best with toratopes. And, maybe set up some basic rotations, so you can see some kind of continuity, in the topology morphs.

But, I've been thinking more about projection rendering, lately. My knowledge is pretty limited to exploring through cross sections, but I still might be able to come up with something. Like, maybe put together a truss-tube model of a tesseract, defined as a product of 32 cylinders. Getting them to do the inside-out rolling of a 4D rotation is the hard part.
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Re: Double ray tracing as an approach to visualise 4D object

Postby quickfur » Thu Sep 24, 2015 10:37 pm

The 4D renderings I post here and on my website are all rendered via a two-step projection process, one is 4D->3D (sadly, my program is not sophisticated enough to work with 4D lighting), then the resulting 3D model has 3D-light artificially placed in the scene and rendered in 3D using povray to produce the 2D image.
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Re: Double ray tracing as an approach to visualise 4D object

Postby neverhood311 » Sat Dec 16, 2017 4:35 pm

A couple of years ago I did a 4D ray tracing research project. I made a few animations and posted them on YouTube.

Here's a link to the playlist: https://www.youtube.com/playlist?list=PLP1FVyLCCHYggAyB7QDor84Uj-rJL-6sF

I have a few more up my sleeve, but I can't make them public until after I publish a paper based on my MS Thesis research.
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