B-rep

What is a B-rep?

Boundary representation, almost always shortened to B-rep, describes a solid by its boundary: the faces, edges and vertices that enclose it, and the topological relationships between them (which faces share which edge, which edges meet at which vertex). The underlying method was developed independently in the early 1970s for CAD and for computer vision, and the theoretical framework that gave it mathematical rigour was formalised by Requicha and Voelcker in their widely cited historical and technical survey of solid modelling.¹

A face in a B-rep is not just a flat polygon: it can be a plane, a cylinder, a cone, a sphere, a torus or a free-form (spline) surface, trimmed by its bounding edges. That is what lets a B-rep model represent a part exactly, at any zoom level, rather than as an approximation.

B-rep versus a mesh

A mesh, such as the triangulated surface in an STL file, approximates a shape with flat facets and throws away exact geometry and the relationships between surfaces. A B-rep keeps both: the precise mathematical definition of each face, and the topology connecting them. That is the reason B-rep, not a mesh, is the representation most CAD and CAM systems build on internally, and the reason a STEP file exchanged between CAD systems typically carries a B-rep model rather than a mesh.

Why B-rep structure matters for manufacturing software

Recognising a manufacturing feature, such as a pocket, a hole or a thin wall, generally means reasoning over the B-rep: which faces bound a cavity, at what angle they meet, whether a cylindrical face is concave (a bore) or convex (a boss). That structural information is exactly what a tessellated mesh discards, which is one reason feature recognition and manufacturability reasoning work from B-rep-carrying formats such as STEP rather than from mesh formats. Newer research also explores learning directly over B-rep structure with machine-learning methods, sometimes called B-rep learning, as a way to recognise features or predict manufacturability from the native CAD representation rather than from a derived mesh.

Is a STEP file the same as a B-rep?

A STEP file typically contains a B-rep model, but STEP is the exchange format; B-rep is the underlying way the solid is represented.

Why not just use a mesh for everything?

A mesh has no exact geometry, tolerances or face relationships, which makes precise manufacturing reasoning and re-editing much harder.

Do all CAD systems use B-rep internally?

Most mainstream CAD systems use B-rep as their core solid representation, though some also support constructive solid geometry (CSG) at the modelling-operation level.