Fracture-Event-Driven 3D Generation: A Generative Framework for Crack Propagation, Fragmentation, and Topology-Changing Shape Synthesis

Three-dimensional generation methods commonly synthesize shapes through implicit fields, point sets, volumetric representations, or collections of Gaussian primitives. Although these representations can describe complex geometry, generating a fractured object introduces an additional challenge: the final geometry is the result of a sequence of structural events that create cracks, divide material regions, expose internal surfaces, and produce a variable number of fragments. This paper proposes Fracture-Event-Driven 3D Generation (FED3D), a candidate framework that represents three-dimensional fracture as a structured generative process jointly involving fracture-event sequences, fragment partitions, and fracture-surface geometry. Given an intact object, material descriptors, initial defects, and optional loading conditions, the framework generates a fracture-event graph whose nodes represent geometric states and whose edges encode crack initiation, propagation, branching, intersection, and separation. A geometry decoder then constructs a variable-cardinality set of fragments while enforcing partition consistency, interface correspondence, and material-boundary constraints. A probabilistic event model represents alternative plausible fracture outcomes, while optional mechanics-based losses encourage compatibility with energy, loading, and material constraints. Unlike a formulation that predicts only a final fracture pattern, FED3D explicitly treats the causal organization of fracture events as a generative variable. The proposed framework is intended for rock fragmentation, shattered glass, impact damage, geological structures, and topology-changing three-dimensional content creation. This paper defines the architecture, mathematical formulation, training objectives, and experimental protocol. Its effectiveness and novelty remain hypotheses requiring implementation and empirical validation.