Computational Topology, Boolean Algebras, and Solid Modeling

Abstract

The paper aims to unfold and clarify both the theoretical approach and the practical implementation of an original and unusual solution to geometric modeling of any expression of the Boolean algebras generated by computer representations of solid models (Paoluzzi et al., 2020; Paoluzzi et al., 2023). Starting from the integration of generative, decompositive, enumerative, CSG, and Boundary primitive representation schemes, the paper describes both the underlying topological theory and how to make practical and effective use of a complete set algebra isomorphic to the Constructive Solid Geometry (CSG) enlarged with $n$-ary operations and explicit consideration of external space, including possible holes inside and between the elements of any assembly of solid models. All examples in this paper are supported by the straightforward Domain Specific Language (DSL) Plasm.jl [1], [2] (Paoluzzi et al., 1995; Paoluzzi, 2003) , an extension to the geometry of FL (Function Level), by Backus and his group at IBM Almaden [3], [4] (Williams and Wimmers, 1988; Backus et al., 1990) , and recently ported to the Julia language [5] (Bezanson et al., 2017) . The cover, text, and appendices present a concise and functional implementation of

, demonstrating simple examples and generating images of geometric objects corresponding to each section of the paper. The software, with a liberal license MIT, is available at https://github.com/PlasmLanguage/Plasm.jl.