Layered Spatial Articulation and Base Spatial Graph: Formalizing Structural Preconditions of Architectural Spatial Analysis

Graph-based spatial analysis formalizes relations among spatial units, but the formation of these units and their boundary correspondences remains under-specified. This study defines the structural stage preceding relational abstraction and establishes the conditions under which spatial units and boundary correspondences become analytically determinate. It then develops a layered spatial articulation procedure that derives spatial objects from plan-encoded architectural information by differentiating topographic substrate, building frame, spatial enclosure, and relational boundary conditions. These are organized into a base spatial graph. The topology of this graph is fixed by articulation, and its edges encode admissible relational mode combinations. Using traditional Korean housing (hanok) as an illustrative reference for the proposed methodology, the study shows that heterogeneous spatial conditions can be consistently articulated into a unified structural domain prior to relational abstraction. The resulting base spatial graph defines a finite but combinatorially extensive space of admissible relational configurations. Within this domain, graph-domain operations act without expanding the articulated structure, while certain operations may reduce it through structural transformation. The study shows that spatial units cannot be treated as pre-given entities but must be structurally constituted. By formalizing this prior stage, the study establishes explicit structural preconditions for graph-based spatial analysis and provides a consistent analytical domain for subsequent spatial interpretation.