Boolean Exact Volume

A runnable example that cuts a 2 m cube with a 2 × 1 × 1 m slab using the Boolean modifier on the EXACT solver, in all three operations (UNION, DIFFERENCE, INTERSECT), then proves that each result has the closed-form volume and is a closed 2-manifold. The hard part is deliberate: the slab's top face lies in the cube's top plane, the coplanar case where floating-point booleans go wrong. The results are read through the depsgraph lifetime contract from depsgraph-and-evaluated-data (evaluated_get → to_mesh → to_mesh_clear), and the operands are built with bmesh and freed in try/finally as mesh-editing-and-bmesh requires.

What it witnesses: with A = [0,2]³ and B = [1,3] × [0.5,1.5] × [1,2], the overlap is A ∩ B = [1,2] × [0.5,1.5] × [1,2], so the closed forms are V(A ∪ B) = 8 + 2 − 1 = 9, V(A − B) = 8 − 1 = 7 and V(A ∩ B) = 1 cubic metre. Each operand pair sits in an object matrix that is translated and turned 18° about Z, so the modifier has to carry B into A's space. For every result the check:

• sums the signed volume over the evaluated mesh's own triangles (divergence theorem, world space) and requires the closed form to 1e-6 relative (measured 8.999999, 6.999999 and 1.000000 — float32 coordinates through a rotation). A positive volume also means the normals point outward;
• requires a closed 2-manifold: every edge borders exactly two faces, with no loose verts or edges;
• requires that the result's volume differs from V(A) by at least 0.5 m³, so the modifier really acted and the witness cannot pass vacuously.

The trap it exposes: the floating-point solver is faster and is right in general position, but it mishandles coplanar faces. --float-solver runs the same three operations on it and gets a union of 7.708 m³ against the closed form 9, so check 3 fails with the measured error. That solver was 'FAST' through 4.5 LTS and is 'FLOAT' from 5.0, so a script that hard-codes either name breaks on the other series (fast_solver_id() branches on bpy.app.version). 'EXACT' is the same identifier on 4.5, 5.1 and 5.2.

The still shows the three operations side by side on a walnut plinth, each named by a brass plaque in front of it. On the left, the union in teal glaze, with the slab's free end grown out of the cube. In the middle, the difference in machined bronze, with the notch cut down through the top face and the removed slab drawn as frosted amber glass. On the right, the intersection: the 1 m³ overlap cube in orange glaze, inside frosted ghosts of both operands. Thin rods trace the operands' edges (steel for the cube, amber for the coplanar slab).

Everything shown is render-only and is built after the check has run. The results on display are frozen copies of the checked meshes with a 12 mm chamfer; the measured modifier objects and the cutter objects never render. The ghosts are grown 2 mm and 4 mm so none of their faces is coplanar with a result or with each other.

Run#

# Cheap correctness check (no render) — the CI check:
blender --background --python boolean_exact_volume.py --

# Falsifier: the floating-point solver (FLOAT / FAST) on the coplanar case. Must exit 3.
blender --background --python boolean_exact_volume.py -- --float-solver

# Also render a still (EEVEE on a GPU host; use --engine cycles on GPU-less hosts):
blender --background --python boolean_exact_volume.py -- --output boolean.png --engine cycles

Version notes#

BooleanModifier.solver lists 'FAST', 'EXACT', 'MANIFOLD' on 4.5 LTS and 'FLOAT', 'EXACT', 'MANIFOLD' on 5.1 and 5.2 LTS: the floating-point solver was renamed in 5.0. Measured identically on 4.5.11, 5.1.2 and 5.2.1: EXACT union 8.999999 (12 faces), difference 6.999999 (10 faces), intersection 1.000000 (6 faces), all closed 2-manifolds; --float-solver union 7.708379.

Exit codes#

The blender-smoke workflow runs the check on Blender 5.2 LTS and 4.5 LTS (5.1 on the weekly cron, the needs-5.1 PR label, or manual dispatch). Smoke does not pass --output. Its catalog falsifier is --float-solver (expects exit 3).