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What is a Brep?¤

A Brep (boundary representation) describes a 3D shape by its boundary — the surfaces, curves, and points that enclose it. Not a mesh of triangles, not a grid of voxels.

Take a cube. A mesh stores a pile of flat triangles that approximate its six faces. A Brep stores six exact, flat surfaces, meeting at sharp edges. That's why Breps stay exact through fillets, booleans, and zoom — there's no faceting to notice.

Building blocks¤

A Brep is built bottom-up from five kinds of entities:

Entity What it is
Vertex A 3D point.
Edge A 3D curve (line, arc, NURBS, ...), bounded by two vertices.
Trim The 2D curve an edge traces in a face's parameter space ("UV" space).
Loop A closed ring of trims: the outer boundary of a face, or an inner one that cuts a hole.
Face A trimmed patch of a surface (plane, cylinder, NURBS, ...), bounded by one outer loop and zero or more inner loops. 
graph LR
    F["Face<br/>(a trimmed surface patch)"] --> L["Loop<br/>(outer boundary, or a hole)"]
    L --> T["Trim<br/>(2D curve in the face's UV space)"]
    T --> E["Edge<br/>(3D curve)"]
    E --> V["Vertex<br/>(3D point)"]

A Brep is the set of faces — plus the edges and vertices they share — that together enclose, or partially bound, a shape.

In compas_brep, these map directly onto BrepVertex, BrepEdge, BrepLoop, BrepFace, and BrepTrim.

Further reading¤