Boundary representation

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Boundary representation (B-rep) describes a 3D shape by its boundary. A solid is shown as a set of connected surface pieces that separate inside from outside. A B-rep model includes the building blocks: faces (bounded patches of surfaces), edges (segments of curves), and vertices (points), plus how they connect. The main topological groups are shells (connected faces), loops (edges that bound a face), and edge links (winged-edge or half-edge structures) that manage edge circuits.

Compared with constructive solid geometry (CSG), which uses primitive objects and Boolean operations, B-rep is more flexible and supports a larger set of operations. In addition to Boolean operations, B-rep can do extrusion or sweeping, chamfers, blending, drafting, shelling, tweaking, and other shape-editing tasks.

B-rep was developed independently in the early 1970s by Ian C. Braid (Cambridge) for CAD and Bruce G. Baumgart (Stanford) for computer vision. Braid helped create BUILD, the precursor to many solid-modelling systems, and worked on early commercial kernels like ROMULUS (the forerunner of Parasolid) and ACIS. Parasolid and ACIS now underpin many modern CAD systems. Other important contributors came from Sweden (Torsten Kjellberg) and Finland (Martti Mäntylä with GWB), as well as the USA (Eastman and Weiler) and Japan (Fumihiko Kimura), who advanced B-rep ideas further, including hybrids of wireframes, sheets, and volumes.

B-rep can also use “features”—logical groups of sub-elements that support high-level reasoning about shapes, manufacturing, and processes. This idea has enabled many advanced modeling techniques.

Non-manifold models extend B-rep to include non-solid cases, such as sheet objects, which blend surface modeling with solid modeling. These are useful for representing thin objects and complex boundaries.

Standardizing B-rep for data exchange took time. In 1979, IGES attempted to handle solid models but wasn’t ideal for B-rep. Later work led to STEP (the Standard for the Exchange of Product Model data), a widely used neutral format for boundary representations. STEP, together with ISO 10303-42, defines common geometric and topological models, and Application Integrated Resources (AICs) specify boundary-model constraints within that framework.