Skip to content

Why B-Rep

Why BRepAX operates on true Boundary Representation geometry rather than implicit (SDF) representations alone.

The Limitation of Implicit Representations

SDF-based and implicit shape representations are powerful for differentiable geometry, but they cannot capture:

  • Parametric surfaces: NURBS, Bezier patches, and analytic surfaces (planes, cylinders, cones, tori) with exact evaluation
  • Trim curves: The boundaries that define which portion of a surface is active in a face
  • Tolerance handling: Manufacturing tolerances that determine whether edges are coincident or distinct
  • Face/edge/vertex incidence: The combinatorial structure that encodes how geometric entities connect

These are precisely the structures that manufacturing cost analysis depends on (undercuts, wall thickness, rib detection, mold direction, bend analysis).

Existing Work in the Implicit Space

Several projects already address differentiable implicit geometry:

  • Marschner et al.'s pseudo-SDF correction
  • DreamCAD and related neural implicit CAD methods
  • MeshSDF and DMTet for differentiable mesh extraction

BRepAX's differentiation from these approaches comes from operating directly on B-Rep topology, not from JAX-nativeness alone.

OCCT as the Foundation

Open CASCADE Technology (OCCT) is the industry-standard open-source B-Rep kernel, used by FreeCAD, CadQuery, build123d, and many commercial systems. By building on OCCT, BRepAX gains:

  • Exact parametric surface evaluation (no tessellation artifacts)
  • Standard STEP file I/O for interoperability with industrial CAD systems
  • Robust Boolean operations as a reference implementation
  • Access to the full vocabulary of B-Rep topology