A CAD model is not stored as a single mathematical object. A mechanical part that appears to be one continuous shape is usually represented internally by many interconnected entities, each carrying a specific role. Boundary Representation, or B-Rep, provides a way to organize those entities so that engineering software can understand not only the shape of a model, but also how its individual regions are connected.
B-Rep Describes the Boundary, Not the Interior
The basic idea behind B-Rep is straightforward: a three-dimensional body can be defined by the boundary separating its interior from exterior space.
For a simple block, that boundary consists of planar faces. A more realistic component may combine planar, cylindrical, conical and freeform surfaces. Rather than filling the volume with geometric data, the CAD system stores the surfaces forming the boundary and the relationships between them.
This representation is particularly suitable for solid modeling because many engineering operations act directly on faces, edges and their connections.
The Model Has Two Interdependent Layers
B-Rep separates geometry from topology.
Geometry provides mathematical definitions. A line or spline may define a curve. A plane, cylinder or NURBS surface may define a surface. These objects describe shape and can generally be evaluated independently of the complete model.
Topology provides structure. It records how geometric elements participate in a particular body.
A vertex represents a topological location. An edge normally references a curve and connects vertices. One or more edges form loops that bound faces. Faces are associated with surfaces, while connected faces form shells. A properly closed shell can represent the boundary of a solid.
This distinction has an important consequence: a mathematical surface may extend far beyond the visible face that uses it. The face represents only a trimmed region of that surface, with its limits defined topologically.
Why Edges Are More Complicated Than They Look
An edge displayed in a CAD viewport might appear to be nothing more than a curve between two points. Inside a B-Rep, its meaning is richer.
An edge can represent the intersection or common boundary of neighboring faces. Those faces may each describe the edge within their own surface parameter space as well as refer to its three-dimensional curve representation.
The consistency of these representations matters during geometric operations. If neighboring faces disagree significantly about their common boundary, later calculations may fail even though the rendered model still appears acceptable.
A geometric kernel must therefore maintain relationships between curves, surfaces and their topological use within the body.
Changing Geometry Means Rebuilding Structure
Consider cutting a slot through an existing solid.
The operation introduces intersections between the cutting body and the original part. Existing faces may be divided into several regions. Some regions disappear, while others remain. New faces appear inside the slot, and the connectivity of surrounding edges changes.
The geometric modeling kernel cannot simply modify the pixels or triangles displayed on screen. It has to calculate intersection curves, trim surfaces and construct a new topological arrangement describing the resulting body.
The same structural changes occur during many familiar operations, including Boolean unions, hole creation, filleting, chamfering and shelling.
This explains why topology is not static metadata attached to geometry. It is actively reconstructed as a model evolves.
Model Validity Depends on Connectivity
A B-Rep solid is useful only when its structure is internally consistent.
Faces intended to form a closed volume must connect correctly. Edges must have valid relationships with their neighboring faces. Loops must form meaningful boundaries, and the orientation of entities must allow the system to distinguish the inside of the body from the outside.
Numerical tolerances complicate these requirements. Two vertices expected to coincide may have slightly different coordinates. Imported surfaces may contain small gaps, short edges or mismatched boundaries.
The modeling system therefore evaluates geometric relationships within defined tolerances when constructing and validating the model.
Why B-Rep Structure Matters to Developers
In CAD application development, B-Rep entities are often exposed through an API or SDK because application logic frequently needs to work with specific parts of a model.
A CAM module may inspect faces to determine machining regions. CAE preprocessing software may extract selected surfaces for boundary conditions. A CAD feature can modify selected edges, while measurement tools can analyze distances, areas or geometric relationships between model entities.
This would be difficult if a 3D model were represented only as a visualization mesh.
B-Rep gives engineering software a structured description of shape. Geometry defines the mathematical objects; topology explains how those objects form a model. Maintaining both layers together is what allows a CAD system to treat a displayed shape as an editable and computationally meaningful engineering object.