boundaryrepresentation

Boundary representation, commonly abbreviated B-rep, is a method for representing shapes, especially solids, by their boundary. A B-rep model encodes the boundary as a collection of topological entities—faces, edges, and vertices—together with geometric descriptions of those entities. It is widely used in CAD/CAM, 3D modeling, and interoperability between software systems because it supports precise, editable surface boundaries and explicit topology.

In a B-rep model, the boundary of a solid is decomposed into faces (surface patches) connected along edges, which meet at vertices. Each face has an associated geometric surface; each edge has one or two incident faces; each vertex is the junction of edges. Topology is stored separately from geometry to maintain connectivity and enable operations such as shell extraction, filleting, and boolean operations. Data structures such as winged-edge, half-edge, or doubly connected edge list (DCEL) implement B-rep connectivity.

B-rep supports planar and curved surfaces (for example NURBS patches). A typical B-rep solid is a watertight boundary: every edge is shared by one or two faces and the overall topology forms a closed shell. This explicit boundary enables robust editing, accurate manufacturing representations, and easier exchange with standards such as STEP (ISO 10303).

The approach contrasts with constructive solid geometry (CSG), which represents solids as a tree of constructive operations, and with polygon meshes that approximate boundaries. B-rep can offer more exact representations for industrial modeling but is more complex to implement and maintain. Limitations include handling non-manifold geometries, tolerance robustness, and performance in large models.

History and usage: B-rep concepts date from CAD research in the 1970s and 1980s, with development of formal data structures for representing solids. Today, B-rep remains foundational in commercial CAD systems and in data-exchange standards for geometric information.