0091 — Mesh sections report in-plane faces as regions and cut curves as chains

• Status: Accepted
• Date: 2026-10-28
• Deciders: Friedrich Schrödter
• Supersedes: —
• Amends: 0033
• Amended by: 0092, 0093

Context

Issue #359 (consumer: rheonda/cad). A floor plan is a section at, say, 1.0 m. A railing, a slab or a wall top that lies exactly in that plane is a face in the cutting plane. ADR 0033's MeshPlaneSection::section refuses such a mesh as degenerate, because a two-dimensional overlap is not a curve, and it refuses an open mesh as not manifold. The consumer needs both answered: what is in the plane, and on which side its material lies, kept apart from the curves where the surface crosses the plane. The consumer's decision, taken there: a face in the plane comes back as a region tagged with a side, no cut loop is invented for it, and the kernel never decides "just below".

SectionOutcome, SectionEvidence, SectionLimits and the conformance types are public structs with public fields and no #[non_exhaustive], so adding to them is a breaking change.

Decision

The existing method keeps its behaviour and messages. A new opt-in method, MeshPlaneSection::section_request, takes a SectionRequest and returns a PlaneSection. It is a provided method whose default refuses with Unsupported, so every existing provider still compiles and a registry falls back past one that does not implement it. All new types are #[non_exhaustive]; every change is additive.

• Regions. Faces lying in the plane come back as InPlaneRegions: an outer ring, hole rings, and an InPlaneSide. Below means the face normal agrees with the frame's +z, so the material lies on the -z side; Above is the opposite; Both is reserved for coincident faces of both facings.
• Chains. SectionChains are transversal crossings only. A mesh edge in the plane yields a cut segment only when both of its triangles are off the plane and their third vertices lie on opposite sides. An edge next to an in-plane triangle is a region boundary, and an edge whose neighbours all lie on one side only touches the plane: nothing is emitted and the touching edge is counted in the evidence. A chain may therefore be open, ending on a region (ChainEnd::InPlaneRegion); its end points and the region vertices are projected by one function and are bit-identical.
• Exactness. Every decision is an exact orient3d or orient2d on the original binary64 coordinates with one axis dropped, never on projected or interpolated values. Regions come from topology, without a planar boolean: same-facing in-plane triangles sharing an edge form a component, boundary edges are linked into rings by fan order at each vertex, and the outer ring is told from a hole by the exact turn at its lexicographically smallest vertex. A ring that visits that vertex twice (a footprint or hole touching the outer boundary at a corner) is decided at the next lexicographic extreme; such a region has one weakly simple outer ring and no hole.
• Exact chains. A closed chain is made counter-clockwise from the exact vertex signs of its triangles: the cut leaves a triangle where the winding goes from above the plane to below it. A node is dropped only when its two cut segments are exactly collinear: a vertex node between two vertex nodes with a zero orient2d, or an edge node whose two triangles are exactly coplanar (orient3d of their four vertices). The nodes of in-plane triangles and the ends of an open chain are never dropped. No tolerance and no rounded coordinate takes part in a decision.
• Refusals by name. Overlapping in-plane faces of one side, in-plane faces of opposite sides that overlap, and a saddle vertex (more than two cut segments at one vertex) are UnsupportedInput with the constants REFUSED_OVERLAPPING_IN_PLANE_FACES, REFUSED_IN_PLANE_FACES_ON_BOTH_SIDES and REFUSED_SADDLE_VERTEX. A face that collapses under projection is Degenerate. Budgets get their own names: in-plane regions, region vertices and in-plane pairs.
• Registry. MeshPlaneSectionRegistry::section_request validates the source as before, then checks the answer against the documented output invariants: frame, cardinalities, finiteness, adjacent duplicates, canonical ring starts and orders, budgets and evidence counts. It does not check ring orientation, since a floating-point area sign is unreliable far from the origin (#274); the conformance suite checks orientation on fixtures. register_request_conformant registers a provider after both suites and rejects a claimed failure; a provider that does not claim the method passes on the base suite.
• Conformance. RegionConformanceSuite runs hand-derived fixtures: a cube through its top and bottom, a square frame with a hole, a parapet with a post rising out of it (the railing case), edge and point contact, and the two overlap cases, where a provider may refuse by name or merge. A provider whose first case returns Unsupported does not claim the method and passes.

Sheets (open meshes)

SectionRequest::role (with_role, default SectionRole::Solid, today's semantics) says what the mesh is, so an open mesh (a terrain, a surface body) is sectioned too. All additions are non-breaking.

• Registry. A Solid is validated as before. A Sheet follows hidden_lines.rs::validate_topology: boundary edges are allowed, while a degenerate triangle (Degenerate), a non-manifold edge or an inconsistent winding (NotManifold) is refused before dispatch. The answer's evidence repeats the role and boundary_edges, which must equal the audit's count, and a Solid answer with a ChainEnd::MeshBoundary is a contract violation.
• Chain ends. A chain of a sheet can end on the mesh boundary (ChainEnd::MeshBoundary): at a crossed edge that is a boundary edge, or at a vertex on the boundary that no in-plane triangle touches. A vertex of an in-plane triangle is still InPlaneRegion. Any other degree-one node is an internal error. The ends travel with the points when a chain is turned to start at its smaller end.
• Edges in the plane. A boundary edge lying in the plane is a region boundary when its one triangle is in the plane, and a touching edge when that triangle is off the plane. A Solid still refuses an edge in the plane with one triangle.
• Regions. A sheet in the plane is a region exactly like a face of a solid: Below when its normal agrees with the frame's +z, whatever the mesh boundary around it. A sheet folded flat onto itself, two triangles of opposite facing sharing an edge on the same side of it, is not skipped by the overlap test and is refused as faces of both sides.
• Closed chains. A sheet has no inside, so the segment directions say only which side its faces point to. A closed chain of a sheet is made counter-clockwise by the exact sign of the signed area of the polygon it returns (the cross products summed in expansion arithmetic), and a chain with zero area is Degenerate.
• Conformance. A provider may support solids only: when its first sheet case returns Unsupported, the sheet cases are skipped and the report says sheets_claimed == false; it still passes. The suite adds the terrain cut by a vertical plane and through vertices, a sheet in the plane in both windings, an annulus sheet and a saddle, all with hand-derived values.

Alternatives considered

Option	Why not
Change SectionOutcome to carry regions	Breaking: the type has public fields and no #[non_exhaustive].
Add axiolid-overlay to axiolid-reference to merge overlapping faces and name Both	Contradicts the dependency rationale of ADR 0090 and ADR 0036 and needs a maintainer decision (also on overlay tolerance snapping, #222). The overlaps are refused by name instead.
A new capability id	The operation is the same; a provider without the method refuses with Unsupported.
Let the kernel decide "just below" for an in-plane face	The consumer owns that decision; the kernel reports the side the material lies on.
Emit a closed cut loop around an in-plane face	Invents a curve that is not a crossing, and the loop would hide the region.

Consequences

Positive

• A floor plan at a level that coincides with a slab or railing top gets the filled region and the crossing curves, instead of a refusal.
• Output is deterministic and every decision is exact.

Negative / costs

• Elements that are soups of overlapping bodies with flush tops are refused by name until faces can be merged.
• A boundary edge of a sheet lying in the plane next to an off-plane triangle is only counted as touching; PlaneSection has no field for it yet.
• The reference implementation is quadratic in the worst case in the overlap sweep and in ring simplification; it is an oracle, not a performance tier.

Follow-ups / risks to watch

• Landing 3 (maintainer decision): Both and the merge of overlapping same-side faces, through axiolid-overlay or a focused provider. Done differently in 0093: an exact arrangement in the reference module, no axiolid-overlay.
• Landing 4: pair cut segments at a saddle vertex by fan order.

Relation to existing code

• crates/contracts/operations/mesh-section/src/request.rs: the request, result, evidence and refusal names; fixtures.rs and region_conformance.rs: the suite.
• crates/execution/dispatch/src/section.rs and section_request.rs: the registry method, the topology check per role and the outcome checks.
• crates/algorithms/reference/src/section/: request.rs (orchestration), regions.rs (in-plane regions), chains.rs (chains); the legacy path is unchanged.
• crates/facade/axiolid/src/application.rs: Application::section_mesh_request.
• scripts/probe_section_regions_mutants.py: the mutation probe.