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Elia Perry
2025-12-25 10:23:02 -06:00
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# Procedural Generation with Heterogeneous Polyhedral Units using pseudo-Boolean Satisfiability
> DO NOT TOUCH, FOR MATHEMATICAL DEFINITION ONLY
`Primitive Atom`: An indivisible volumetric unit whose geometry is a single convex polyhedron.
Atom Type: An equivalence class of primitive atoms under rigid motions of ℝ³.
`Adjacency Relation`: A symmetric binary relation over primitive atoms indicating admissible face-to-face contact.
`Aggregate`: A finite set of primitive atoms whose induced adjacency graph is connected and whose internal adjacencies are fixed.
`Placement instance:` A rigid motion mapping an aggregate’s atoms into the global adjacency graph such that all internal and external adjacency constraints are satisfied.