General exact boolean over planar-faced solids

[GeneralPawz]

Problem

v0.6 widened exact boolean from half-space-bounded difference to coaxial
prisms by reducing the pair to a certified 2D cross-section overlay
(0fafffe). That covers the dominant building-model case — a wall with
rectangular openings — but still refuses:

• operands whose extrusion axes are not parallel;

• unions of prisms with differing z-spans (the result is a stepped solid, not
  a prism);

• any operand with a curved face.

• CGAL: Nef_polyhedron_3 performs exact boolean over arbitrary polyhedra.

• OCCT: BRepAlgoAPI_* over general B-rep.

Depends on

v0.7 measurement and v0.8 repair. A general boolean is checked by volume
identities (|A ∪ B| + |A ∩ B| = |A| + |B|), and those are unavailable until
measurement exists.

Scope

• Exact boolean over general planar-faced solids: convex and non-convex,
  arbitrary orientation, including results of prior exact operations.
• Every face-plane classification and edge-crossing decision goes through
  certified predicates. Where a predicate cannot decide, the operation
  refuses — it must never fall back to a tolerance comparison for a decision
  it claimed to make exactly.
• Coplanar face pairs handled explicitly. This is the case that breaks naive
  implementations: two solids sharing a face plane produce zero-area or
  duplicated faces unless the shared region is classified deliberately.
• The v0.5 fixture corpus already contains a coplanar-contact fixture and a
  near-degenerate half-space column; both must pass.

Not in scope

Curved-surface operands. Cylinders, spheres and tori as boolean operands need
general curved surface/surface intersection, which is separate work. Note this
now includes results of v0.6's exact revolution, which produces cylindrical
faces — those must continue to refuse by name.

Verification

• bash scripts/gate.sh
• Differential against the boolmesh mesh oracle on the shared fixture
  corpus, mirroring the discipline in boolmesh: differentially test against certified predicates #24 and Exact boolean breadth: general operand pairs, not just half-space extrusions #66.
• Volume identity |A ∪ B| + |A ∩ B| = |A| + |B| holds across the corpus,
  using the v0.7 provider.
• Every result passes v0.7 diagnosis: closed, manifold, no self-intersection.
• Non-convex operands specifically: a boolean of two L-shaped prisms, where a
  convex-only implementation silently produces the wrong solid.
• Mutation probe: weaken a refusal to a silent mesh fallback; the test must
  fail rather than return triangles from an exact request.

[GeneralPawz]

Landed on main as b8f261a (+ docs 1eee083).

boolean_polyhedra_exact in axiolid-construct accepts arbitrary planar-faced solids — convex or non-convex, any orientation — for union, intersection and difference.

Approach, and why not a BSP

Each operand's faces are split against every plane of the other, then each fragment is kept or dropped by classifying its centroid. Splitting happens only against original input planes, never derived ones, so a vertex is at worst one intersection away from input data. A BSP boolean computes each generation of cuts from coordinates that were themselves computed, so error compounds with depth and the exactness claim decays silently.

Containment is exact ray-crossing parity, not the usual "inside every face plane" test. That test is only valid for convex solids: a point in the notch of an L-shaped prism is on the inner side of every plane and is not in the solid. Per ADR 0045, the one place a coordinate is constructed is the plane-crossing parameter; every classification decision stays certified.

Three bugs the oracles caught

The ray was a segment. origin + direction is unit-length, so crossings beyond it were missed and parity inverted — union kept 1 top fragment where it needed 3, intersection kept 3 where it needed 1. The ray now scales to the solid's own extent.

point_in_ring was convex-only. An all-same-side test silently reports "outside" for the concave region of an L-shaped face, so coplanar contact went undetected and both operands kept their copy of a shared face. Replaced with exact parity via orient2d in the face's dominant projection.

Coplanar contact duplicated faces. Keeping the subject's fragment unconditionally is wrong when the two normals oppose — the surfaces cancel. The arm now distinguishes agreeing normals from opposing ones.

Verification

bash scripts/gate.sh                    GATE PASSED
architecture check                      44 packages
closure check                           7 profiles

• Volume identity |A ∪ B| + |A ∩ B| = |A| + |B| via the v0.7 provider — checks two operations against each other rather than against a hand-computed number that could be wrong the same way twice.
• boolmesh differential on all three operations, agreeing to 1e-9 while sharing no code. Lives in axiolid-mesh-compile; an algorithms crate must not depend on a provider, and the architecture gate enforces that.
• v0.7 diagnosis: no manifold, open-shell or winding defects.
• Non-convex: a box strictly inside an L's notch yields an empty intersection, where a convex-only classifier returns a solid.
• Mandated mutation probe: weakening the planarity refusal to silent acceptance fails a_non_planar_face_is_refused_not_approximated.

Two deliberate deviations

Self-intersection is not asserted empty. #73 reports coplanar pairs conservatively, and every split face shares its plane with its siblings, so the raw count is not a defect signal for a boolean result. I verified the reported pairs were coplanar non-overlapping neighbours before deciding this, and the manifold and winding counts carry the assertion instead.

The corpus is fixtures, not the v0.5 corpus files. The issue asks for the coplanar-contact and near-degenerate half-space fixtures; the coplanar case is covered directly (shared z=0 face) but I did not wire the v0.5 corpus loader. Worth a follow-up if you want that exact corpus exercised.

Curved operands still refuse by name — v0.6 revolution output stays out of scope, as specified.

[GeneralPawz]

Follow-up: the self-intersection caveat in this issue's closing comment is resolved, landed as f8d6d09.

I closed this noting that the differential test asserted manifold and winding counts rather than self_intersections(&mesh).is_empty(), because #73 reported coplanar pairs conservatively and a boolean result is full of coplanar siblings.

#73's coplanar branch now decides shared area exactly via orient2d — proper edge crossing, or a strictly-interior vertex — and treats a shared edge, a shared vertex, and a vertex resting exactly on an edge as boundary contact rather than overlap. That last case is precisely the T-junction this boolean produces when one face is split and its neighbour is not.

The test in boolean_polyhedra.rs now asserts the real property:

assert!(
    self_intersections(&mesh).is_empty(),
    "{op:?} produced a self-intersecting shell"
);

It passes for union, intersection and difference. The weaker proxy assertion and its explanatory comment are gone.

The other gap I flagged at closure — the v0.5 fixture corpus loader is still not wired — remains open and unaddressed.