I'm curious if anyone has any insight into how one might procedurally generate 4D objects, as showcased in Miegakure (or the developer's other game, 4D Toys ).
I built a program a while back to do this, basically using "shape definition" files that I found (and subsequently processed) for the regular polychora like the hypercube, 120-cell, 600-cell etc. Example shape files can be found on Paul Bourke's website.
Another way that I've recently discovered is, using a convex hull algorithm like Qhull to extract this information. You can first generate all of the vertices for your polytope (these are usually just even/odd permutations of certain 4-tuples). Then, you run Qhull to find how the vertices are connected to one another. The problem with this method is, it requires significant pre-processing, and the tetrahedral meshes that are generated aren't always very clean.
In 4D Toys, the author(s) are able to build shapes like a "hollowed out" 120-cell, so I'm curious if they are approaching this problem from a different angle - perhaps, one that is more flexible than the aforementioned approaches.
I'm curious if there are other ways of modeling and/or algorithmically generating shapes like those found in Miegakure that I haven't thought about? What are other ways of approaching this design challenge?
Thanks in advance for any help or guidance.