BRepAX

JAX-native differentiable B-Rep kernel with NURBS support.

BRepAX loads STEP files into a JAX computation graph, enabling gradient-based optimization of CAD geometry through Boolean operations. It provides stratum-aware differentiation that handles topological transitions at Boolean boundaries, and supports both analytical primitives and freeform B-spline surfaces.

Installation

pip install brepax

Quick Start

import jax
import jax.numpy as jnp
from brepax.io.step import read_step
from brepax.brep.triangulate import (
    triangulate_shape, divergence_volume,
    mesh_surface_area, mesh_center_of_mass,
)

# Load STEP file and compute volume via divergence theorem
shape = read_step("part.step")
tris, params = triangulate_shape(shape)

vol = divergence_volume(tris)           # exact for watertight mesh
area = mesh_surface_area(tris)          # sum of triangle areas
com = mesh_center_of_mass(tris)         # surface integral (Eberly 2002)

# Gradient of volume w.r.t. all triangle vertices
grad = jax.grad(divergence_volume)(tris)

Parametric Optimization

from brepax.brep.triangulate import extract_mesh_topology, evaluate_mesh

# Separate topology (one-time) from evaluation (differentiable)
topology = extract_mesh_topology(shape)

def volume_fn(radius):
    tris = evaluate_mesh(topology, {"radius": radius}, uv_scale_param="radius")
    return divergence_volume(tris)

# Gradient flows from volume through vertices to design parameter
grad = jax.grad(volume_fn)(jnp.array(5.0))

Speeding up cold starts

BRepAX compiles one XLA artifact per surface type and per unique B-spline signature on the first triangulation. On busy parts (e.g. NIST CTC-02, 664 faces) this is ~10 seconds of one-shot work per Python process. Enabling the persistent compilation cache lets later process starts reuse those compiled artifacts from disk:

import brepax
from brepax.io.step import read_step
from brepax.brep.triangulate import triangulate_shape

brepax.enable_compilation_cache()  # defaults to ~/.cache/brepax/jax-compile

# First run populates the cache on disk, later runs load from it.
shape = read_step("part.step")
tris, _ = triangulate_shape(shape)

The cache directory can also be set explicitly or via the BREPAX_COMPILATION_CACHE_DIR environment variable. In-process repeat calls are unaffected — they already hit JAX's in-memory JIT cache.

Features

Primitives

9 geometric types with differentiable SDF interface: Plane, Cylinder, Sphere, Cone, Torus, Box, FiniteCylinder, Disk, and BSplineSurface (rational NURBS with weights).

STEP Pipeline

• Read STEP files via OCCT (cadquery-ocp-novtk)
• Convert all face types to primitives (100% conversion on 4,080 faces across 28 test files)
• PMC-based CSG-Stump reconstruction (tested up to 664 faces)
• OCCT mesh hybrid triangulation with JAX-native vertex re-evaluation

Volume and Mass Properties (Divergence Theorem)

Mesh-based computation via the divergence theorem, working for all surface types including freeform B-spline. Validated on 32 models (< 0.5% error vs OCCT GProp). All are polynomial in vertex positions, giving exact gradients with no grid artifacts or singularities.

Function	Formula	Degree
divergence_volume	(1/6) sum(v0 . (v1 x v2))	3
mesh_surface_area	(1/2) sum(norm(cross(e1, e2)))	--
mesh_center_of_mass	First moments via surface integral	4
mesh_inertia_tensor	Second moments (Tonon 2004)	5

Differentiable Metrics

10 metrics, all differentiable via jax.grad. 8 of 10 work for all surface types; wall thickness metrics require analytical surfaces via CSG-Stump.

Metric	Method	BSpline
divergence_volume	Divergence theorem on mesh	Yes
mesh_surface_area	Triangle area sum	Yes
mesh_center_of_mass	Divergence theorem variant	Yes
mesh_inertia_tensor	Divergence theorem variant	Yes
draft_angle_violation	SDF gradient near surface	Yes
mean_curvature / max_curvature	AD Hessian of SDF	Yes
thin_wall_volume	Sigmoid indicator on SDF grid	Analytical only
min_wall_thickness	Soft-argmax on SDF grid	Analytical only

Parametric Optimization

extract_mesh_topology + evaluate_mesh separate watertight mesh topology (from OCCT, one-time) from vertex evaluation (JAX-native, differentiable). Design parameters flow through surface evaluation to volume:

• Sphere radius: Newton convergence in 4 steps
• Cylinder radius: Multi-face with disk cap tracking, 4 steps
• BSpline control points: Exact gradient, Newton convergence in 1 step

Boolean Operations

Union, subtract, intersect with stratum-dispatched gradients. Analytical exact gradients for bounded primitive pairs in 3 of 4 topological configurations.

Documentation

Full documentation: lv416e.github.io/brepax

License

Apache License 2.0. See LICENSE for details.