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feat(solvers): add PointSetAlignment (NT67) - #368

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claude/point-set-alignment-nt67
Nov 6, 2026
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feat(solvers): add PointSetAlignment (NT67)#368
gabrielfrasantos merged 1 commit into
mainfrom
claude/point-set-alignment-nt67

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@gabrielfrasantos

@gabrielfrasantos gabrielfrasantos commented Nov 6, 2026

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Implements roadmap item 67 from roadmap/solvers/PointSetAlignment. robotics-toolbox-cpp consumes it as NT67: its E5 ScanMatcher spec uses the weighted 2-D alignment as the point-to-point ICP step.

What

numerical/solvers/PointSetAlignment.hpp provides PointSetAlignment<T, Dim>::Align(source, target, estimateScale, weights), for Dim = 2 or 3. It finds the rotation, translation and (optionally) scale that best map the source points onto their targets.

  • Moments: weighted centroids, spreads and the cross-covariance, accumulated on centred coordinates to avoid float cancellation far from the origin.
  • 2-D: a closed-form atan2; coincident points are refused.
  • 3-D: one SingularValueDecomposition<T, 3, 3>, with Kabsch's sign fix so the result is never a reflection (det from cofactors). Collinear points are refused (d₁ ≤ ε·d₀).
  • Scale and residual: optional Umeyama scale, then the weighted residual RMS.
  • Weights: zero weights drop points, such as ICP outliers, without copying the point sets.
  • Refusals: returns nullopt on size mismatches and when fewer than Dim points carry positive weight.

Files: header, coverage .cpp, tests (the 7 spec cases), CMake, doc/solvers/PointSetAlignment.md, and rows in doc/solvers/README.md and README.md. The spec directory and item 67's ROADMAP.md entries are removed. The Tier 2 section, now empty, says all its items are deployed.

Deviations from the spec

  • degenerate_inputs_are_rejected also checks two coincident 2-D points (the spec's stated 2-D degeneracy), which covers that refusal path.
  • zero_weight_removes_an_outlier also asserts the spec's unit-weight residual of 3.442415.
  • The README.md Solvers row was already the widest in its table, so adding to it re-aligned the whole table.

Verification

  • host-single-Debug and the coverage build: ctest 15/15.
  • 100% merged line coverage on the header.
  • Clang -Wall -Wextra -Werror -Wshadow with -DNUMERICAL_TOOLBOX_COVERAGE_BUILD.
  • clang-format --dry-run --Werror.
  • scripts/validate-docs.py OK. The new doc's lines stay under 400 characters; the README.md table rows were already over that limit on main.
  • Not run locally: MSVC, cppcheck, SonarCloud, QEMU.

Generated by Claude Code

@claude
feat(solvers): add PointSetAlignment (NT67)
f773d31 
Weighted least-squares rigid or similarity transform between
corresponding point sets: centred moments and cross-covariance, the
closed-form planar angle, the 3-D Kabsch solution from one SVD with the
reflection fix and a refusal for collinear points, Umeyama's scale and
the weighted residual RMS.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_014WUWh44uw7k4JjMd6YkAwN
@sonarqubecloud

sonarqubecloud Bot commented Nov 6, 2026

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Quality Gate Passed Quality Gate passed

Issues
0 New issues
0 Accepted issues

Measures
0 Security Hotspots
98.3% Coverage on New Code
0.0% Duplication on New Code

See analysis details on SonarQube Cloud

@github-actions

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✅⚠️MegaLinter analysis: Success with warnings

Descriptor Linter Files Fixed Errors Max errors Warnings Elapsed time
✅ ACTION actionlint 7 0 0 0.49s
✅ CPP clang-format 485 9 0 0 3.43s
✅ CPP cppcheck 485 0 0 7.33s
✅ DOCKERFILE hadolint 1 0 0 0.44s
✅ JSON jsonlint 8 0 0 0.09s
✅ JSON prettier 8 8 0 0 0.36s
⚠️ MARKDOWN markdownlint 150 2 155 0 2.73s
✅ MARKDOWN markdown-table-formatter 150 11 0 0 0.27s
⚠️ SPELL lychee 261 25 0 26.84s
✅ YAML prettier 12 3 0 0 0.49s
✅ YAML yamllint 12 0 0 0.47s

Detailed Issues

⚠️ SPELL / lychee - 25 errors 
📝 Summary
---------------------
🔍 Total..........618
🔗 Unique.........457
✅ Successful.....581
⏳ Timeouts.........0
🔀 Redirected.....149
👻 Excluded........11
❓ Unknown..........0
🚫 Errors..........25
⛔ Unsupported.....25

Errors in .github/workflows/static-analysis.yml
[403] https://binaries.sonarsource.com/Distribution/sonar-scanner-cli/sonar-scanner-cli-$ (at 37:21) | Rejected status code: 403 Forbidden

Errors in CHANGELOG.md
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/1 (at 206:31) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/12 (at 221:8) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/13 (at 220:7) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/15 (at 215:18) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/18 (at 205:62) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/2 (at 213:34) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/24 (at 210:19) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/26 (at 211:30) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/27 (at 208:23) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/3 (at 204:35) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/4 (at 214:34) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/6 (at 212:53) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/7 (at 209:32) | Rejected status code: 404 Not Found
[404] https://github.com/embedded-pro/embedded-numerical-toolbox/issues/9 (at 207:15) | Rejected status code: 404 Not Found

Errors in doc/filters/active/AhrsMadgwickMahony.md
[ERROR] file://doc/filters/ComplementaryFilter.md (at 131:3) | File not found. Check if file exists and path is correct

Errors in doc/filters/active/ExtendedKalmanFilter.md
[ERROR] file://doc/dynamics/EulerLagrange.md (at 130:3) | File not found. Check if file exists and path is correct

Errors in doc/filters/active/KalmanFilter.md
[ERROR] file://doc/filters/controllers/Lqr.md (at 114:77) | File not found. Check if file exists and path is correct
[ERROR] file://doc/filters/controllers/Lqr.md (at 133:3) | File not found. Check if file exists and path is correct
[ERROR] file://doc/filters/controllers/Pid.md (at 135:3) | File not found. Check if file exists and path is correct
[ERROR] file://doc/filters/solvers/DiscreteAlgebraicRiccatiEquation.md (at 134:3) | File not found. Check if file exists and path is correct

Errors in doc/performance-optimization/README.md
[403] https://developer.arm.com/documentation/100166/latest/ (at 472:3) | Rejected status code: 403 Forbidden
[403] https://developer.arm.com/documentation/dui0473/latest (at 474:3) | Rejected status code: 403 Forbidden

Errors in README.md
[ERROR] file:///releases/latest (at 39:14) | File not found. Check if file exists and path is correct
[404] https://embedded-pro.github.io/embedded-dsp-control/ (at 38:1) | Rejected status code: 404 Not Found

Hint: Followed 149 redirects. You might want to consider replacing redirecting URLs with the resolved URLs. Use verbose mode (`-v`/`-vv`) to see redirection details.
Hint: You can configure accepted/rejected response codes with `-a` or `--accept`
⚠️ MARKDOWN / markdownlint - 155 errors 
first-line-h1 First line in a file should be a top-level heading [Context: "Read `AGENTS.md` and `roadmap/..."]
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CHANGELOG.md:26 error MD024/no-duplicate-heading Multiple headings with the same content [Context: "Bug Fixes"]
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doc/estimators/ExpectationMaximization.md:104:103 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
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doc/estimators/README.md:11:128 error MD056/table-column-count Table column count [Expected: 2; Actual: 3; Too many cells, extra data will be missing]
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doc/filters/active/AhrsMadgwickMahony.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 538]
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doc/filters/active/AlphaBetaFilter.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 419]
doc/filters/active/AlphaBetaFilter.md:7:401 error MD013/line-length Line length [Expected: 400; Actual: 451]
doc/filters/active/KalmanSmoother.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 421]
doc/filters/active/KalmanSmoother.md:111:28 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
doc/filters/active/KalmanSmoother.md:111:61 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
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doc/filters/active/UnscentedKalmanFilter.md:11:401 error MD013/line-length Line length [Expected: 400; Actual: 468]
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doc/filters/active/UnscentedKalmanFilter.md:149:153 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
doc/filters/passive/MedianFilter.md:69:25 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
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doc/math/CubicSpline.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 453]
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doc/math/MatrixNorms.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 452]
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doc/robust_control/README.md:12:259 error MD060/table-column-style Table column style [Table pipe does not align with header for style "aligned"]
doc/robust_control/SlidingModeControl.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 644]
doc/solvers/ActiveSetQp.md:7:401 error MD013/line-length Line length [Expected: 400; Actual: 584]
doc/solvers/ActiveSetQp.md:71:401 error MD013/line-length Line length [Expected: 400; Actual: 703]
doc/solvers/ActiveSetQp.md:107:401 error MD013/line-length Line length [Expected: 400; Actual: 421]
doc/solvers/ConditionNumber.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 461]
doc/solvers/ConditionNumber.md:51:401 error MD013/line-length Line length [Expected: 400; Actual: 425]
doc/solvers/DampedPseudoInverse.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 531]
doc/solvers/DampedPseudoInverse.md:89:401 error MD013/line-length Line length [Expected: 400; Actual: 581]
doc/solvers/JacobiEigenSolver.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 443]
doc/solvers/JacobiEigenSolver.md:7:401 error MD013/line-length Line length [Expected: 400; Actual: 609]
doc/solvers/JacobiEigenSolver.md:45:401 error MD013/line-length Line length [Expected: 400; Actual: 427]
doc/solvers/RungeKuttaIntegrators.md:9:401 error MD013/line-length Line length [Expected: 400; Actual: 509]
doc/solvers/SpectralRadius.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 665]
doc/solvers/SymplecticIntegrators.md:7:401 error MD013/line-length Line length [Expected: 400; Actual: 486]
doc/solvers/SymplecticIntegrators.md:35:401 error MD013/line-length Line length [Expected: 400; Actual: 476]
doc/solvers/SymplecticIntegrators.md:63:401 error MD013/line-length Line length [Expected: 400; Actual: 431]
doc/windowing/window.md:5:401 error MD013/line-length Line length [Expected: 400; Actual: 415]
README.md:1 error MD041/first-line-heading/first-line-h1 First line in a file should be a top-level heading [Context: "[![Quality Gate Status](https:..."]
README.md:9:401 error MD013/line-length Line length [Expected: 400; Actual: 442]
README.md:17:401 error MD013/line-length Line length [Expected: 400; Actual: 547]
roadmap/README.md:11 error MD040/fenced-code-language Fenced code blocks should have a language specified [Context: "```"]

(Truncated to last 20000 characters out of 20068)

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@gabrielfrasantos
gabrielfrasantos merged commit 182e068 into main Nov 6, 2026
14 of 16 checks passed
@gabrielfrasantos
gabrielfrasantos deleted the claude/point-set-alignment-nt67 branch November 6, 2026 07:57
@embedded-releaser-app embedded-releaser-app Bot mentioned this pull request Nov 6, 2026
Open
@gabrielfrasantos gabrielfrasantos mentioned this pull request Nov 6, 2026
Merged
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@gabrielfrasantos @claude