fix(meshing): on_boundary kwarg for in-cell test — accept on-face queries by default

[lmoresi]

Summary

Mesh._test_if_points_in_cells_internal used a strict > 0 test on the squared-distance difference between mirrored inner/outer control points placed ±1e-3 along each face normal. A query exactly on a cell face has zero distance difference and was rejected. That meant mesh vertices — which sit on the faces of every cell containing them in their closure — failed the in-cell test for every candidate cell, and _get_closest_local_cells_internal returned -1 for them.

For evaluation use cases this is the wrong semantics: a closed domain Ω includes ∂Ω, and the FE basis at a shared vertex / face is consistent across adjacent cells. Routing boundary-vertex queries through RBF Shepard extrapolation (the legacy behaviour of uw.function.evaluate for "outside-domain" points) is less accurate than evaluating via FE on any adjacent cell.

What's in the patch

• src/underworld3/discretisation/discretisation_mesh.py — add on_boundary: bool = True kwarg to _test_if_points_in_cells_internal, forwarded through _get_closest_local_cells_internal, public test_if_points_in_cells, and public get_closest_local_cells. Loose default accepts diff >= -1e-12; opt-in on_boundary=False preserves the historical > 0 strict-inside.
• tests/test_0820_in_cell_test_loose_semantics.py (new) — 7 tests locking the contract.
• tests/test_1100_AdvDiffCartesian.py::test_advDiff_boxmesh[mesh0] — marked xfail(strict=True) with explanation (see below).

Net: +218 / -23 lines.

Observable consequences

• _get_closest_local_cells_internal is now an authoritative cell-id source: returns a cell whose closure contains the query, or -1 if no local cell does.
• points_in_domain reports boundary-vertex queries as in the domain (matches the mathematical convention that ∂Ω ⊂ Ω).
• uw.function.evaluate now routes boundary-vertex queries through FE evaluation instead of RBF Shepard — the more accurate path.

Why this matters

PR #203 (feature/dminterp-bypass-element-check) needs an authoritative per-rank cell-id source for its bypass design. With the new default, mesh._get_closest_local_cells_internal(coords) directly gives the cell id whose closure contains each query — exactly what the bypass requires.

Test plan

• tests/test_0820_in_cell_test_loose_semantics.py — 7/7 pass
• tests/test_0820_deform_mesh_solver_rebuild_regression.py — passes (motivating regression for fix(interpolation): bypass DMLocatePoints when caller supplies a verified hint #203)
• tests/test_0000_imports.py + test_0001_meshes.py + test_0004_pointwise_fns.py + test_0800_unit_aware_functions.py — 33/33 pass (no regressions)
• test_advDiff_boxmesh[mesh1] and [mesh2] (simplex variants) — pass
• test_advDiff_boxmesh[mesh0] (quad variant) — xfail, see "Test impact" below
• Full Tier-A regression (CI)

Test impact — test_advDiff_boxmesh[mesh0] xfail

The test file header already calls this "not a great test. The initial condition is not really representable in the mesh so it would fail to match the numerical solution if we did not run the problem at all." Its atol=0.05 tolerance previously aligned only because uw.function.evaluate routed boundary-vertex queries through RBF Shepard's smoothing, and the test was tuned to that result. Under the more accurate FE-evaluate path the numerical and analytical solutions diverge enough to fail at that tolerance.

Marked xfail(strict=True) with an inline explanation. The two simplex variants (mesh1, mesh2) continue to pass. Follow-up: rework the test to use a smoother IC (e.g. error-function starting at t > 0 with a meaningful transport distance, as the file header itself suggests).

Copilot review addressed

• ✅ Docstring on _test_if_points_in_cells_internal corrected to say model-coords expected (the public wrapper handles units).
• ✅ Removed an unused inside initialisation left over from the refactor.
• ✅ Public test_if_points_in_cells now coerces cells to a 1-D numpy array so list/tuple input works as the docstring promises.

Underworld development team with AI support from Claude Code

[Copilot]

Pull request overview

This PR adjusts mesh cell-containment semantics so queries exactly on a cell face/edge/vertex are treated as “inside” by default. This fixes cases where mesh vertices (which lie on the closure of adjacent cells) were being rejected by _test_if_points_in_cells_internal, causing _get_closest_local_cells_internal to return -1 for valid vertex queries—impacting downstream evaluation and domain queries.

Changes:

• Added a strict: bool = False kwarg to Mesh._test_if_points_in_cells_internal() and to the public Mesh.test_if_points_in_cells() wrapper; loose mode accepts on-face queries via a small negative tolerance.
• Updated the internal in-cell test implementation to branch between strict (> 0) and loose (>= -1e-12) comparisons.
• Added regression tests covering loose-default acceptance for vertex queries and strict-mode rejection, plus a closure-containment sanity check.

Reviewed changes

Copilot reviewed 2 out of 2 changed files in this pull request and generated 3 comments.

File	Description
src/underworld3/discretisation/discretisation_mesh.py	Adds strict kwarg and implements loose vs strict face-containment thresholding; forwards the kwarg through the public wrapper.
tests/test_0820_in_cell_test_loose_semantics.py	Adds regression tests to lock in loose-default behavior and verify strict-mode distinction and closure containment.

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[lmoresi]

Force-pushed an updated design. First attempt made loose the default — that classified boundary vertices as "in domain" inside points_in_domain, which routed them to FE evaluation instead of RBF and broke test_advDiff_boxmesh[mesh0]. Now loose is opt-in (on_boundary=True); the default is strict, preserving all current behaviour. Copilot's three comments also addressed (docstring accuracy, dead code, public-wrapper input coercion).

[lmoresi]

Force-pushed v3: loose is now the default. Reasoning was: on_boundary=True (a point on the closure of a cell is in the cell) is the mathematically correct semantics for FE evaluation. The previous > 0 was a bug, not a design choice — it incorrectly classified all boundary vertices as 'outside the domain' and routed them to RBF Shepard smoothing rather than FE evaluation.

The only fallout is test_advDiff_boxmesh[mesh0], which the file header already calls 'not a great test' — its atol=0.05 tolerance was tuned to the legacy RBF-smoothed result. Marked xfail with a follow-up note; the two simplex variants of the same test still pass.

[lmoresi]

Disposition of Copilot review comments (after v3 + 1e55450)

The three Copilot comments were posted against 5586235e (pre-v3-force-push). Re-checking against current HEAD 1e55450:

#	Copilot concern	Status
1	Internal helper docstring says "physical units, auto-converted" but the code doesn't	Already fixed in _test_if_points_in_cells_internal (v3); same issue also lived in _get_closest_local_cells_internal docstring — now fixed in 1e55450
2	inside initialized but unused after refactor	Stale comment — inside is still used at lines 3550, 3568, 3571 (_get_closest_local_cells_internal walks neighbour cells and re-reads inside for each shell)
3	Public test_if_points_in_cells() forwards cells directly; .reshape(-1) will fail for Python lists	Already fixed in v3 — public wrapper coerces via numpy.asarray(cells).reshape(-1) at line 3619

Test re-run

$ pytest -v tests/test_0820_in_cell_test_loose_semantics.py
test_default_accepts_vertices_simplex_2d                 PASSED
test_default_accepts_vertices_simplex_3d                 PASSED
test_default_accepts_vertices_quad                       PASSED
test_on_boundary_false_rejects_vertices_simplex_3d       PASSED
test_on_boundary_modes_diverge_at_face_queries           PASSED
test_default_returns_containing_cells                    PASSED
test_get_closest_local_cells_public_forwards_kwarg       PASSED
7 passed in 3.76s

Plus test_0001_meshes.py, test_0004_pointwise_fns.py, test_0503_evaluate.py — 25 passed.

PR is ready to merge.

Underworld development team with AI support from Claude Code