Geometry & modeling
B-Rep
Boundary representation
Definition
B-Rep is the way professional CAD kernels describe a solid: by its boundary, made of exact surfaces (faces), the curves where they meet (edges), and the points where edges end (vertices). Because the geometry is exact and the topology is explicit, B-Rep models can be measured, filleted, dimensioned, and manufactured precisely.
Also known as: BRep, boundary representation, B-rep solid
Updated
Geometry and topology#
A B-Rep model has two layers. The geometry layer holds the mathematical surfaces and curves: planes, cylinders, cones, tori, and freeform NURBS surfaces. The topology layer records how those pieces connect: which faces bound a shell, which edges bound a face, and which vertices end an edge.
That connection data is what makes CAD operations possible. To fillet an edge, the kernel needs to know the two faces that meet at it. To shell a part, it needs to know which faces form the outside of the solid.
Where B-Rep is used#
Almost every mainstream mechanical CAD program is built on a B-Rep kernel. Siemens describes Parasolid as a B-rep modeling kernel with a data format shared by more than 350 applications. Open CASCADE is a common open-source alternative, used by FreeCAD and CadQuery.
B-Rep is also what neutral exchange formats carry. The CAx Interoperability Forum tests precise B-Rep geometry as one of the core parts of STEP AP242.
B-Rep compared with mesh#
A mesh approximates a shape with flat triangles. It has no concept of a face, an edge, or an exact radius, so a "hole" in an STL is a polygon tube whose diameter depends on how finely it was tessellated.
A B-Rep describes the same hole as a cylindrical face with a defined axis and radius. That difference decides whether a model can be dimensioned on a drawing, toolpathed accurately in CAM, or edited with normal CAD features. It is also the main line between text-to-CAD tools, which aim for B-Rep output, and text-to-3D tools, which generally produce meshes.
Limits#
B-Rep kernels have to keep geometry and topology consistent after every operation, which is why fillets, shells, and booleans sometimes fail on awkward geometry. Imported B-Rep models can also arrive with tiny gaps, sliver faces, or tolerance mismatches between systems, which show up later as failed features or leaky solids.
Sources
Related terms
Mesh
A mesh represents a shape as a surface of small flat polygons, almost always triangles, joined at shared edges and vertices. Meshes work well for rendering, games, and 3D printing, but they have no true faces, edges, or exact curves, so they are hard to dimension or edit as engineering geometry.
NURBS
NURBS are mathematical curves and surfaces that can represent both simple shapes, such as lines, arcs, and circles, and complex freeform surfaces exactly. CAD kernels use them for the faces and edges of B-Rep solids that are not simple planes or cylinders.
CAD kernel
A CAD kernel is the geometry engine inside a CAD program that creates and modifies solids: booleans, fillets, shells, intersections, and tessellation for display. Parasolid and Open CASCADE are common examples, and the kernel largely decides which operations are reliable and how exports behave.
STEP
STEP is the ISO 10303 family of standards for exchanging 3D product data between CAD systems, usually saved as .step or .stp files. A STEP file carries exact B-Rep solid geometry that another CAD program can measure and edit, but it normally does not carry the original feature history.