I can't get through to their website at the moment. But, from the description, this looks like it could be a nice tool for making pretty tesseract pictures.
http://freshmeat.net/projects/tesseracttrainer/?branch_id=58663&release_id=198451
southa wrote:In TT the hypercube displayed is officially transparent, so you see the whole thing and there are no hidden faces. An opaque one would be more tricky. I've a feeling that culling (hyper)faces based on their normals isn't enough because of expanded faces, and you need some sort of depth buffering or sorting as well.
As for other shapes, I tried a spherical shell made up of points. That was an interesting one - there's a weird pudding-stirring motion as the two rotation planes interact. Right now I'm moving on to a 4D environment, i.e. more cubes, and you can move about between them. Hopefully the renderer from that can be fed back into Tesseract Trainer.
(PS Tried the maze game a while ago - didn't stick at it though. Maybe I'll take another look)
quickfur wrote:Culling surfaces based on normals works for convex objects. But if you have non-convex objects, you'll have to do something more.
pat wrote:quickfur wrote:Culling surfaces based on normals works for convex objects. But if you have non-convex objects, you'll have to do something more.
??? Assuming you're not inside the object, then... [If you're inside the object, then swap "in front of" and "behind" in the following.]
For any given facet, it's on a hyperplane. Either you're in front of that hyperplane or you're behind it. If you're behind it, then your view of the objects in that hyperplane will be obscured by some other facet of the object.
[...]
pat wrote:Oh, sure.... I guess I didn't read enough above. I was thinking you were talking about back-face(t) culling. Occlusion culling is much thornier.
One possible way would be to extend the concept of z-buffering into z-w-buffering. For the discussion below, assume orthographic projection. You can do perspective projection with very little alteration... it's just easier to describe orthographically.
[...]
quickfur wrote:My personal opinion, though, is that we should consider it as though we are only projecting from 4D -> 3D.
pat wrote:quickfur wrote:My personal opinion, though, is that we should consider it as though we are only projecting from 4D -> 3D.
Sure... and that's what I try to convey with the multiple slices with my raytracer:
[...]
There, however, the occlusion culling happens easily because of the ray tracing.
If you were willing to take the slices approach, then you could adapt the above scheme more easily and make one slice per column. And do the occlusion culling as per row. I'll describe it more later.... family obligations now.
quickfur wrote:Anyway, there are different approaches to how this can be done, which depends on how you represent objects in the scene. There is an interesting page that describes an algorithm using the half-space representation for polytopes: http://www.flowerfire.com/ADSODA/. Only parallel projections are considered, but I think it should be simple to adapt to perspective projections. I'm not sure about how to do the same thing using the more common vertex or (N-1)-polytope representation of objects, though. Seems in that case that we would have to compute intersections of polyhedra directly, which is not fun.
pat wrote:That's the 600 cell. Here's the 120-cell.
And, yes... I also find it hard to piece together the facets from the slices. But, when I do... I feel like I have a much better understanding of "where" they really are than when they all get projected down to the same space.
In particular, someone above described swirling when rotating points on a sphere. With the slices view... you can actually see the separate rotations instead of seeing it as a swirl.
pat wrote:Yes... I have real trouble seeing the projection things as anything but the "turning inside out effect" which is so misleading.
Here's a duo-circle animation. The top one is radially striped in x-y. The bottom one is radially striped in z-w. The middle is both.
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