ADR 0029: Certified finite traces become split faces plus embedded curves

• Status: Accepted
• Date: 2026-08-31
• Depends on: ADR 0024, ADR 0028

Context

ADR 0028 provides bounded traces for transverse single-span affine NURBS patches. Each endpoint carries native parameter boxes for both patches and a conservative residual bound. A trace is not by itself a valid trimmed B-rep.

A straight chord partitions a rectangular face only when both endpoints are on that face's boundary. If both endpoints are interior to another rectangular face, placing the chord in a loop on that face would create an open or doubled wire; it would not partition a disk. Extending it to the boundary would invent geometry outside the certified bounded intersection.

The strict ExactBRep contract also requires explicit analytic 3D supports, pcurves, and native parameter intervals. It must not infer pcurves by inversion.

Decision

axiolid-construct owns the L2 topology integration function split_surface_pair_certified.

The first supported arrangement requires exactly one complete affine trace:

1. Both endpoint boxes are fixed on two distinct native boundary sides of one patch, and their side coordinates are strictly interior to those sides.
2. Both endpoint representatives are strictly interior to the other patch's native rectangle.
3. The trace's conservative residual upper bound is finite and no larger than the caller's explicit max_surface_residual.

The boundary-owned patch becomes two closed trimmed faces. Its rectangle boundary is split at the two certified endpoints. One shared intersection edge closes both loops, once forward and once reversed, with a separate pcurve for each traversal.

The containing patch remains one closed rectangular face. The same edge is attached through EmbeddedFaceCurve, which stores the face, edge, pcurve, and native pcurve interval explicitly. This relation records an interior arrangement feature without pretending it is a closed trim.

The result retains the original TransverseSurfaceSurfaceTrace3, deterministic face/edge identities, and a global carrier-to-surface residual bound. For affine supports, the carrier and pcurve images are affine in the same unit parameter; the norm of their difference over the segment is bounded by the maximum endpoint certificate.

Resource and failure policy

Topology size is fixed for this slice: ten vertices, eleven edges, three loops, three faces, eleven 3D line supports, thirteen pcurves, and two surfaces. Generic topology arenas and strict B-rep catalogs expose fallible capacity reservation. Surface control nets, knot vectors, multiplicities, and optional weights are copied with fallible reservation. Loop and face vectors are also reserved fallibly.

The operation returns Unresolved and preserves the original intersection evidence for:

• incomplete or multiple traces;
• mixed, same-side, corner, or dual-boundary ownership;
• boundary-touching endpoints on the embedded face;
• non-finite, degenerate, or residual-policy-exceeding representatives;
• all unsupported cases inherited from ADR 0028.

Allocation failure and an internal strict B-rep contract violation remain structured GeomError failures. A disjointness certificate returns Empty without constructing a B-rep.

Consequences

• The result is a topology-aware open arrangement, not a solid or Boolean.
• The split patch has valid closed trim loops and explicit analytic supports.
• The unsplit patch retains the finite intersection as an explicit embedded feature available to later arrangement/Boolean algorithms.
• No endpoint box is widened, no pcurve is inferred, and no artificial seam is extended beyond the certified trace.
• Aligned traces owned by both patch boundaries remain unresolved until the intersection layer proves boundary-root ownership and deduplication.
• Curved traces, periodic seams, closed intersection loops, tangency, coincidence, overlap, multi-span stitching, and solid classification remain future work.