This paper synthesizes a theory from industrial best practices codified in recent standards. Recent editions of ASME and ISO standards codify the evolving industrial best practices in defining and modeling the information about products made from fibrous composite materials. A theory of constructive composite geometry and topology is synthesized from these practices. Major features of this theory include (1) a constructive composite geometry tree that is equivalent to the ply/laminate tables of the standards, (2) an adjacency graph that captures a crucial aspect of the topology of the geometric cell complex structure of composite products, and (3) conformal mapping of ply surfaces using rosettes in the lay-up process. It also addresses the geometrical and topological structure of fiber arrangements inside the plies. The goal of the theory is to provide a scientific basis for standards that enable the digital transformation of composite product manufacturing.

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