Define the Boundary Representation of solids
Boundary model or b-rep model is based on the topological notion that a physical object is bounded by a set of faces. These faces are regions or subsets of closed and orientable surfaces.
Boundary Representation, or b-rep for short, can be considered as an extension to the wire-frame model. The merit of a b-rep is that a solid is bounded by its surface and has its interior and exterior. The surface of a solid consists of a set of well-organized faces, each of which is a piece of some surface (e.g., a surface patch). Faces may share vertices and edges that are curve segments. Therefore, a b-rep is an extension to the wire-frame model by adding face information to the latter. The geometry of the object can be described by its boundaries, namely vertices, edges and surfaces. An example of b-rep is a closed surface is one that is continuous without breaks. An orientable surface is one in which it is possible to distinguish two sides by using the direction of the surface normal to point to the inside or outside of the solid model under construction.
Each face is bounded by edges and each edge is bounded by vertices. Thus, topologically, a boundary model of an object is consisted of faces, edges, and vertices of the object linked together in such a way as to ensure the topological consistency of the model.