In computer-aided design, the term boundary representation — often abbreviated as B-REP or BREP, refers to storing information about how to make a model based on its geometric and often Euler topological boundaries.
Often, a user builds the model in CSG format, but stores it in BREP. In facetted BREP STEP format (part 42), the Euler topological representation is vertex, edge, half-edge, face loop, face, shell, and body and refer to the underlying geometric representations. The geometric representation is the point, line, and solid. Other formats like Mantayla's (Geometric Work Bench) GWB and ACIS's SAT use similar names.
Newer, parametric based CAD systems, store both (CSG & BREP) representations, which allow subsequent modifications and regeneration of the BREP. Due to the work of Braid, Euler boolean operations have gained favor because the operations generate an Euler consistent (satisfies the Euler characteristic) BREP at every stage of the constructions process. An Euler consistent BREP is one which satisfies Euler's equation at every stage. Often, this is implanted by capturing the representation in a change state, so that if a problem is encountered (e.g. programming exception) or the model is not Euler consistent, the model state is reverted back to its original state.
STEP ISO 10303 (Standardized Exchange of Product) is an ISO CAD standard introduced in the 1990's replacing and extending IGES.