B-Rep vs Mesh

If you have used Three.js, Babylon.js, or any other renderer-first 3D library, you have worked with meshes — bags of triangles. brepjs models shapes a fundamentally different way: as boundary representations (B-Rep). The difference is not cosmetic. It changes which operations are exact, which are approximate, what fillets are possible, and what file formats round-trip with desktop CAD tools.

The mental shift

A mesh describes a surface as a list of triangles. A cube is 12 triangles. A sphere is hundreds. The triangles approximate the surface; the surface itself has no first-class existence in the data structure.

A B-Rep describes a shape as a set of bounded mathematical surfaces stitched together along shared edges. A cube is six planes, each trimmed to a 2D rectangle, sharing twelve straight edges that meet at eight vertices. A sphere is one spherical surface trimmed to a full closed region. The surfaces are exact — x² + y² + z² = r² for the sphere, not 200 triangles approximating it.

Mesh:    triangles → visual approximation
B-Rep:   faces (bounded surfaces) + edges (curves) + vertices (points)
         → exact mathematical model

Every B-Rep operation can therefore be exact on the underlying mathematics rather than approximate on its triangulated rendering.

What you gain with B-Rep

Exact booleans

fuse, cut, intersect operate on the surface mathematics, not on triangle intersections. A cylinder cut from a box leaves an exact cylindrical hole — not a many-sided polygonal approximation. Re-export to STEP and another CAD tool sees the same exact geometry.

CSG-on-mesh libraries can produce visually plausible results, but they accumulate floating-point error every time you intersect triangles, and the more operations you stack the more degenerate edges and tiny slivers appear. B-Rep does not have this drift.

Real measurements

measureVolume(s) returns the exact volume — not a Riemann sum of tetrahedra. measureArea(face) returns the exact area of the trimmed surface. For a cylinder, the area is 2πrh + 2πr², and brepjs returns precisely that, rounded only to floating-point precision.

Real fillets and chamfers

A fillet replaces an edge with a curved blend surface. On a B-Rep this is a well-defined geometric construction — find the intersection of the offsets of the two adjacent faces, build a blending surface, trim the result. On a mesh, "fillet" means something fuzzy like "smooth this region" — there's no edge to find, just triangles.

brepjs's fillet, chamfer, and shell all rely on the B-Rep structure to do the right thing.

Industry-standard exports

STEP, IGES, and BREP files describe B-Rep shapes. They round-trip with SolidWorks, Fusion 360, FreeCAD, OnShape, Rhino — every mechanical CAD tool. Mesh exports (STL, glTF, OBJ) lose the B-Rep structure: a STEP-imported sphere is a single face; an STL-exported sphere is a thousand triangles.

What you give up

Memory ownership

WASM objects are not garbage-collected. brepjs gives you tools to manage this — the using keyword, DisposalScope, the fluent shape() wrapper that disposes intermediate results — but you must think about it for long-running apps. See Memory Management.

Speed for trivial operations

A single boolean on simple shapes is milliseconds. A single boolean on heavily-filleted swept assemblies can be hundreds of milliseconds. Mesh CSG, while less reliable, is often microseconds. If you need real-time interactivity over many operations per frame (e.g. a sculpting tool), B-Rep is too slow.

Shape diversity

B-Rep represents what the kernel can express: planes, cylinders, cones, spheres, tori, B-spline surfaces, swept and revolved surfaces. Hand-sculpted blobs and arbitrary deformations are out. For organic forms, use a SubD or implicit-surface library.

A direct comparison

Concept	Mesh (Three.js)	B-Rep (brepjs)
Storage	Triangles	Faces + edges + vertices + curves + surfaces
Sphere	~thousand triangles	One spherical surface, exact
Boolean reliability	Approximate (CSG hacks)	Exact (kernel operations)
Fillet support	None natively	Built-in, on real edges
Volume measurement	Approximate (sum of tets)	Exact
Surface area	Approximate (sum of triangles)	Exact
STEP export	Not possible	Native
Memory model	GC-managed	Explicit cleanup (using, scope)
Best at	Rendering, real-time CSG, organic	Mechanical parts, exact ops, parametric

When to convert between them

The two representations meet at meshing time:

import { shape, box } from 'brepjs/quick';

const part = box(20, 20, 20);
const m = shape(part).mesh({ tolerance: 0.1 }); // B-Rep → triangles
console.log('Triangles:', m.indices.length / 3);

mesh() triangulates the B-Rep surfaces with a configurable tolerance. Smaller tolerance → more triangles → better visual fidelity → more memory. The output goes straight to a Three.js BufferGeometry (see Three.js Integration).

You only convert in this direction. brepjs has importSTL for the reverse, but it produces a B-Rep approximation — useful for measurement and STEP conversion, not for further B-Rep work.

In one sentence

If you want rendering, you want a mesh; if you want manufacturing, you want a B-Rep. brepjs is built for the latter, with first-class export to the former.

Next steps

• The Topology Hierarchy — how B-Rep nests vertex inside edge inside wire inside face inside shell inside solid
• Types That Prove Geometry Is Valid — the brand-and-validity type system that catches errors at compile time
• Three.js Integration — meshing your B-Rep for in-browser rendering