So a while ago I saw a video for a 4D puzzle game (Miegakure). I thought it was really neat, but it got me thinking... What would an actual 4D renderer look like? What's the best way to represent the fourth dimension? I thought about using 4D tetrahedral models, rendered with a shader to select the current 3D "slice", but that seemed too unwieldy. The most straight forward way, in my mind, was to take the "ray-casting 3D voxels" concept and just add a fourth dimension.
My program uses a 4D sparse voxel octree (I call it a hypertree) which acts exactly the way you'd expect: each dimension splits into two, which means that a node has up to 16 four dimension children volumes. I copied the ray casting algorithm from the Laine and Karras SVO paper (minus the contours), and added in an extra dimension to everything. To visualize the fourth dimension (W), I leave Z as up and down, but rotate the viewer's other three dimensions so that W replaces X or Y. Mathematically it works quite nicely, and doesn't look too bad.
One of the biggest issues that I had with it is that a 4D hypertree can get very big very quickly. Since every node can have 16 children, if I were to store all the leaf nodes I'd only be able to work with relatively shallow trees (e.g. at 4 bytes per node, seven levels is 1 GB). Since it's a sparse tree I don't store all this, but the potential is there. I also came up with two other solutions to this size problem. The first is to have portal nodes, which store a transformation matrix to teleport viewing rays, or object positions, from that node to some other node (and orientation). So even if the entire world is only 128 leaf nodes on a side, you can make larger environments by hijacking other (unused) dimensions seamlessly. The portal transformation does incur a performance hit though for every ray-portal intersection.
My second solution to the size problem is to not store unique geometry at the bottom of the tree. Using a palette of premade leaf node "tiles", you can give the environment more detail without having to store it all uniquely. Or at least that's how it would work... I haven't actually implemented this yet. I got the idea from watching that Unlimited Detail video, which looks like it uses a similar idea with 3D tiles nodes.
My other issue with a 4D renderer is that generating interesting content is difficult to do without an editor. I stopped working on it about the time I realized that I'd need to make an editor to get the full potential out of it as a concept. I'll probably pick it up again one of these days though.
So that's my experience with "voxels". If anyone wants me to go into more detail about anything I can, but I don't want to post the program right now.
BuzzyMember Since 30 Jan 2000
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