Topological consistency preservation with graph transformation schemes

Topology-based geometric modeling tackles the issue of representing objects with data structures that encode topological subdivision modeled in vertices, edges, faces, and volumes. Such subdivisions can be represented graphs labeled by dimensions on arcs, while operations used to edit formalized as graph transformations. Among existing models, we consider generalized oriented maps, defined constrained graphs, ensure well-formedness objects. Since a operation should provide correct object when applied object, transformations are provided conditions model consistency. Our approach exploits firmly established framework DPO implement operations. We enrich standard product construction ease design, enabling generic rule schemes. lift from rules this enriched framework, ensuring preservation consistency via static analysis syntactic • Double-pushout modeling. Unified for maps. Consistency analysis. Generalization using functors categorical products.