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Integration benchmark report

A reproducible measurement of BRepAX's volume paths and face-level metric coverage on the project's standard STEP fixture set.

The report below is the output of one command, regenerated from the same commit this documentation was built from (so the numbers shown here and the version of BRepAX you are reading docs for are guaranteed to be in sync):

uv run python -m benchmarks.integration_report.run_benchmark

What this report does not claim

  • No "first" or "unique" claim about any BRepAX path.
  • No quantitative speed comparison against external systems.
  • No claim that BRepAX outperforms any external system on tasks those systems were designed for.

The competitor landscape section below is qualitative feature coverage only, not a numerical head-to-head; cells are marked "hypothesis" where they reflect best-effort reading of public documentation.

The report

BRepAX Integration Benchmark Report

Reproducible measurement of the BRepAX volume paths and face-level metric coverage on the project's standard STEP fixture set.

This report is the output of one benchmark command — uv run python -m benchmarks.integration_report.run_benchmark. No claim of novelty is made beyond what the tables below directly show. Comparisons against external systems (Manifold, PyTorch3D, JAX-FEM) are qualitative; see competitor_landscape.md for the framing and its limitations.

Volume paths use a sigmoid grid integration at resolution=32 (per-axis cell count); the mesh divergence path uses the OCCT BRepMesh tessellation at the default deflection. OCCT BRepGProp is the reference and is computed analytically on the exact B-Rep, not on the mesh.

Volume accuracy

Fixture OCCT (ref) divergence mesh_sdf gwn CSG-Stump TrimmedCSG timings (s) Notes
sample_box 6000.0000 6000.0000 (0.00%) 5689.0195 (5.18%) 5900.4824 (1.66%) 5689.5962 (5.17%) 5689.5962 (5.17%) divergence=1.18 mesh_sdf=4.30 gwn=0.92 csg_stump=4.19 trimmed_csg=2.67
sample_cylinder 1178.0972 1176.5602 (0.13%) 1184.0016 (0.50%) 1164.7401 (1.13%) 1186.0311 (0.67%) 1186.0311 (0.67%) divergence=1.16 mesh_sdf=2.70 gwn=1.22 csg_stump=1.77 trimmed_csg=2.16
sample_sphere 113.0973 112.5589 (0.48%) 117.7642 (4.13%) 111.8235 (1.13%) 118.4262 (4.71%) 118.4262 (4.71%) divergence=1.52 mesh_sdf=15.60 gwn=6.31 csg_stump=0.62 trimmed_csg=0.66
sample_cone 54.9779 54.6540 (0.59%) 60.3504 (9.77%) 56.6688 (3.08%) 60.8456 (10.67%) 60.8456 (10.67%) divergence=3.44 mesh_sdf=4.04 gwn=2.04 csg_stump=2.58 trimmed_csg=2.46
sample_torus 222.0661 220.6733 (0.63%) 241.2626 (8.64%) 221.0463 (0.46%) 242.5633 (9.23%) 242.5633 (9.23%) divergence=1.83 mesh_sdf=23.25 gwn=8.83 csg_stump=0.05 trimmed_csg=0.31
box_with_holes 22429.2037 22432.0938 (0.01%) 20694.4512 (7.73%) 21917.6699 (2.28%) 20692.2324 (7.74%) 20692.2324 (7.74%) divergence=1.63 mesh_sdf=3.73 gwn=1.70 csg_stump=1.27 trimmed_csg=1.25
box_with_pocket 23214.6018 23215.6230 (0.00%) 21492.3789 (7.42%) 22700.0762 (2.22%) 20293.1797 (12.58%) 20293.1797 (12.58%) divergence=1.46 mesh_sdf=6.72 gwn=1.29 csg_stump=0.86 trimmed_csg=1.10
box_with_slot 20800.0000 20800.0000 (0.00%) 19218.2852 (7.60%) 20331.0352 (2.25%) 17470.7598 (16.01%) 17470.7598 (16.01%) divergence=1.49 mesh_sdf=2.72 gwn=0.58 csg_stump=4.31 trimmed_csg=2.99
l_bracket 12000.0000 12000.0000 (0.00%) 11267.1504 (6.11%) 11729.4434 (2.25%) 11025.0674 (8.12%) 11025.0674 (8.12%) divergence=0.64 mesh_sdf=1.69 gwn=0.57 csg_stump=1.78 trimmed_csg=1.91
nurbs_box 480.0000 480.0000 (0.00%) 481.2567 (0.26%) 497.4170 (3.63%) 481.2568 (0.26%) 481.2568 (0.26%) divergence=0.66 mesh_sdf=1.01 gwn=0.49 csg_stump=55.30 trimmed_csg=44.21
nurbs_revol 40.8856 — — — — — divergence=0.00 mesh_sdf=0.00 gwn=0.00 csg_stump=0.00 trimmed_csg=0.00 shell (volume paths require closed solid)
nurbs_saddle -0.0000 — — — — — divergence=0.00 mesh_sdf=0.00 gwn=0.00 csg_stump=0.00 trimmed_csg=0.00 shell (volume paths require closed solid)

How to read this table.

  • divergence is the mesh divergence-theorem volume (Stokes' theorem on the BRepMesh tessellation). Differentiable through triangle vertex positions. Strongest production path.
  • mesh_sdf is the mesh-based signed distance field (unsigned distance to the nearest triangle, signed by generalized winding number) integrated with a sigmoid indicator on the same grid as the CSG paths. Differentiable through triangle vertex positions and the sigmoid integrator.
  • gwn is the generalized-winding-number indicator integrated directly: sigmoid((wn - 0.5) * GWN_SHARPNESS) summed over the grid. Sharpness is fixed at module level (the field is dimensionless 0..1, so the cell-width-based sharpness used by the SDF integrators is not appropriate here). This single fixed configuration is one operating point; sweeping sharpness / resolution / mesh deflection is out of scope for this PR.
  • CSG-Stump is the analytical primitive DNF, integrated with a sigmoid indicator. Differentiable through primitive parameters. Bounded by the BSpline half-space limitation (see project_bspline_halfspace.md in memory; concretely the CSG-Stump DNF cannot consume a finite trimmed BSpline patch as a half-space ingredient — ADR-0019, ADR-0020).
  • TrimmedCSGStump carries per-face trim metadata for standalone trimmed-face SDF queries; on the DNF path it is bit-equivalent to DifferentiableCSGStump per ADR-0019 / ADR-0020. Equality of the csg and trim columns is the expected outcome.

Face-level metric coverage

Each cell shows (finite / nan / inf) counts out of the fixture's total face count. Single-face shapes return +inf for min_wall_thickness_per_face (no other surface to measure against). mean_curvature_per_face returns NaN on cone, torus, and BSpline faces (analytical handler not yet added).

Fixture n_faces surface_area min_draft_angle mean_curvature min_wall_thickness
sample_box 6 6/0/0 6/0/0 6/0/0 6/0/0
sample_cylinder 3 3/0/0 3/0/0 3/0/0 3/0/0
sample_sphere 1 1/0/0 1/0/0 1/0/0 0/0/1
sample_cone 3 3/0/0 3/0/0 2/1/0 3/0/0
sample_torus 1 1/0/0 1/0/0 0/1/0 0/0/1
box_with_holes 8 8/0/0 8/0/0 8/0/0 8/0/0
box_with_pocket 8 8/0/0 8/0/0 8/0/0 8/0/0
box_with_slot 11 11/0/0 11/0/0 11/0/0 11/0/0
l_bracket 14 14/0/0 14/0/0 14/0/0 14/0/0
nurbs_box 6 6/0/0 6/0/0 0/6/0 6/0/0
nurbs_revol 0 0/0/0 0/0/0 0/0/0 0/0/0
nurbs_saddle 1 1/0/0 1/0/0 0/1/0 0/0/1

Qualitative competitor landscape

Important caveat. This is a qualitative feature-coverage table, not a head-to-head numerical benchmark. Numerical comparison would require running the same problem (e.g. volume of a Linkrods-class trimmed-BSpline shape with derivatives w.r.t. control points) through each system, which none of the listed competitors are directly designed to express. The table reports what each system is built to do, not who is faster on a shared benchmark. Cells marked "hypothesis" are best-effort observations from public documentation; treat them as starting points, not citations.

System / Path STEP / B-Rep input Per-face awareness Trimmed BSpline Differentiable volume Per-face metrics Notes
BRepAX divergence_volume yes (via OCCT) derived from face triangulation via OCCT BRepMesh yes — through triangle vertex positions yes (this PR's coverage table) strongest production path on this report
BRepAX evaluate_stump_volume yes (via OCCT + reconstruction) primitive-based weak (ADR-0020: BSpline patches are not a CSG-Stump DNF half-space ingredient) yes — through primitive parameters not directly analytical-dominant fixtures
BRepAX TrimmedCSGStump.volume yes per-face trim metadata stored metadata stored, not on DNF SDF path (ADR-0019, ADR-0020) yes — through primitive parameters not directly bit-equivalent to evaluate_stump_volume on the DNF path
Manifold (manifold3d) indirect (mesh only) mesh-level no (mesh) no (Boolean is exact, not differentiable) no hypothesis: robust mesh boolean, not a CAD-differentiable kernel
PyTorch3D mesh ops no (mesh only) mesh-level no (mesh) partial (mesh deformations are differentiable) no hypothesis: differentiable mesh operations, not B-Rep
JAX-FEM no (FE mesh) element-level no (mesh) yes — but for FE objectives, not CAD volume no hypothesis: physics solver, not a CAD geometry kernel

The framing BRepAX is built around — gradients flow from STEP / B-Rep through to a JAX scalar — does not have an obvious head-to-head counterpart in the listed systems, because they enter the pipeline at a different stage (mesh, or FE mesh). This is the BRepAX position to test, not assume; the right way to falsify it is to run a published benchmark that asks each system to solve the same B-Rep-rooted optimisation problem. No such benchmark is bundled with this PR.

What is not claimed by this report:

  • No "first" or "unique" claim about any BRepAX path. Other research projects exist on differentiable B-Rep, signed distance functions on trimmed surfaces, and topology-aware boolean differentiation; this report does not survey them.
  • No quantitative speed comparison against any external system.
  • No claim that BRepAX outperforms any competitor on tasks they were designed for. Manifold's exact mesh boolean and JAX-FEM's PDE solver are not in scope here.

What this report does assert:

  • The numbers in volume accuracy and face-level metric coverage are reproducible from the bundled command on the bundled fixtures.
  • The CSG-Stump and TrimmedCSGStump rows being equal is consistent with the negative-result ADRs (ADR-0019, ADR-0020).
  • Per-face metric NaN counts on cone / torus / BSpline faces in mean_curvature_per_face are the documented analytical-handler deferral, not failures.

Generated by benchmarks/integration_report/run_benchmark.py.