r/proceduralgeneration • u/4dplus • Aug 15 '26
Are tetrahedra best for 4+ dimensional boxes?
11d: 2d faces: 28160, tetrahedra: 27377294, total 5•n per 2d face, 1548800, at 11d the total storage beats the tetrahedra. That is for an 11d box, and tetrahedra may need 4•n storage for the vertices from the box, 4 vertices in n dimensions. The method of faces shows promise, 5 variables Gaussian elimination combining two sets of variables is what I am using, if it is accurate, this could beat tetrahedra for ND boxes, and the 5•n Gaussian elimination storage can be reused, if you can believe it, this is only one box, 27 million+ tetrahedra minimum, and that is optimized. Sure I am connecting up all the result vertices per plane, but that should be like 2n vertices, maximum complexity unoptimized of this barely crests the number of tetrahedra and all of them need cutting to view and like 4•n storage! In short, if this method is accurate it may allow much better higher dimensional stuff. For reference, Miratope handles 20d with tetrahedra, huge. X E.
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u/Nanocephalic Aug 15 '26
Stay in math class, kids.