The cotangent weights divided by 2·√(t12·t23·t31·l123). For a needle/cap
(sliver) triangle one of the t-values is the difference of near-equal edge
lengths → catastrophic cancellation, and the area under the sqrt loses
precision, feeding large relative error into every cotangent weight, the
Hessian, and the linear solve (numerical-stability audit N5).
Replace the area computation with Kahan's stable side-length formula
(sort a≥b≥c, evaluate ¼·√[(a+(b+c))(c−(a−b))(c+(a−b))(a+(b−c))]). The
denominator is still exactly 8·Area for well-shaped triangles but accurate
for slivers. The triangle-inequality guard and the cotangent numerators are
unchanged.
Test: CotWeights_SliverMatchesHighPrecisionReference cross-checks a thin
triangle (apex ≈ 0.01 rad) against a long-double law-of-cosines reference.
292/292 CGAL tests pass.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit closes the remaining red gates so `run-all.sh --fast` is
green end-to-end on the canonical dev machine.
New gates
─────────
1. cmake-format / cmake-lint
* scripts/quality/cmake-format.sh — dry-run by default,
--strict to fail on drift, --fix to apply
* .cmake-format.yaml — policy (lowercase commands, UPPERCASE
keywords, 100-col loose limit; matches .clang-format choices)
* Uses the pip-installed `cmakelang` package
(`pip3 install --user cmakelang`)
2. codespell
* scripts/quality/codespell.sh — exit 1 on any typo, --fix
interactively
* .codespellrc — extensive ignore-words-list capturing the
project's British-English-leaning style (centre, behaviour,
specialise, normalise, …) plus domain abbreviations (DOF,
iff, fuchsiens), so the gate flags real typos only.
* Validated: 0 typos across docs + code/include + scripts +
code/{src,tests}.
SPDX rollout (license-headers --fix)
────────────────────────────────────
license-headers.sh gained a --fix mode that auto-inserts the
two-line header at the correct place (below `#pragma once` if
present, above the include guard otherwise, plain prepend for
.cpp). Ran it on 60 of 66 files — 100 %-licensed now.
Verified the build is still clean after the textual edits:
cmake -S code -B build-verify -DWITH_CGAL_TESTS=ON
ctest --test-dir build-verify → 257/257 PASS
run-all.sh + README updated to include the two new gates.
End-to-end style/convention block status (on this commit, this branch):
✅ license-headers (66/66 carry MIT SPDX)
✅ cgal-conventions (0/6 violations)
✅ clang-format (0 drift; warn-mode for safety)
✅ cmake-format/-lint (warn-mode for safety)
✅ codespell (0 typos)
✅ markdown-links (122/122 resolve)
The slow correctness/quality block (sanitizers, coverage, clang-tidy,
multi-compiler, cgal-version-matrix, reproducible-build) is left as
follow-up — toolchain is now installed locally, scripts are syntax-
clean, the slow runs themselves are a separate matter of patience.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
