This scheme is based on the concept that a physical object is bounded by a set of faces. A solid model is created by combining faces and contains vertices, edges, loops, and bodies.

Only the boundary surfaces of the model are stored and the volumetric properties are calculated by the Gauss Divergence theorem, which relates volume integral to surface integrals. This scheme can model a variety of solids depending on the primitive surfaces (planar, curved, or sculptured). There are two types of solid models in this scheme:

1. Polyhedral solids

2. Curved solids

Polyhedral Solids: Polyhedral models consist of straight edges, e.g., a non-cylindrical surface: box, wedge, combination of two or more non-cylindrical bodies, etc. Polyhedral solids can have blind or through holes, and two or three-dimensional faces, with no dangling edges. A valid polyhedral abides by the Euler’s equation:

$F – E + V – L = 2 (B-G)$

Where,

F = Face

E = Edge

V = Vertices

L = Inner Loop

B = Bodies

G = Through holes

Primitives: In B-rep, a model is made up of the following primitives:

Vertex: A point in space

Edge: A finite, no-intersecting space curve bounded by two vertices that are not necessarily distinct.

Face: A finite connected, non-self-intersecting, region of a closed oriented surface, bounded by one or more loops.

Loop: An ordered alternating sequence of vertices and edges. A loop defines a non-selfintersecting closed space curve, which may be a boundary of a face.

Body: Entity that has faces, edges and vertices. A minimum body is a point.