Fix Box VolumeBelow/CenterOfVolumeBelow by caguero · Pull Request #724 · gazebosim/gz-math

caguero · 2026-03-15T23:33:28Z

🦟 Bug fix

Summary

This patch fixes some functions used to compute graded buoyancy.

Replace Box::VolumeBelow and Box::CenterOfVolumeBelow with analytic inclusion-exclusion formulas (Scardovelli-Zaleski / Lehmann-Gekle), fixing two bugs:
- VolumeBelow used TrianglesInPlane which relied on exact float comparison (Plane::Side() == NO_SIDE) and produced wrong volumes for non-axis-aligned planes
- CenterOfVolumeBelow returned arithmetic mean of vertex positions instead of volumetric centroid, only correct for axis-aligned cuts
Delete TrianglesInPlane free function and remove Triangle3.hh include (no longer needed)
Fix Sphere<float> compilation by replacing hardcoded Vector3d with Vector3<T>::Zero in VolumeBelow and CenterOfVolumeBelow

Bugs fixed

Box::VolumeBelow wrong for non-axis-aligned planes: The old mesh-based implementation used TrianglesInPlane, which classified vertices with exact float comparison (Plane::Side() == NO_SIDE, requiring Distance == 0.0). Vertices with any FP error were silently dropped, producing incorrect polygon decompositions. Example: box 4x2x6 with plane n=(2,1,3) gave 26.22 instead of the correct 26.67.
Box::CenterOfVolumeBelow fundamentally wrong formula: The old code computed sum(vertices) / count(vertices) — the arithmetic mean of polygon vertices, not the volumetric centroid. This is only correct for axis-aligned cuts. For any diagonal plane, the conservation law CoV_below * V_below + CoV_above * V_above = (0,0,0) was violated.
Sphere<float> compilation failure: VolumeBelow and CenterOfVolumeBelow hardcoded Vector3d(0,0,0) instead of Vector3<T>::Zero. Instantiating Sphere<float> failed because Plane<float>::Distance() has no overload accepting Vector3d.

Improvements

	Old	New
VolumeBelow	O(n) mesh reconstruction: 7 planes, vertex classification, angle sorting, divergence theorem over triangles	O(1) closed-form: 8 `max(0,x)^3` terms, one division
CenterOfVolumeBelow	Same O(n) mesh reconstruction + vertex averaging	O(1) closed-form: at most 32 `max(0,x)^k` evaluations
Heap allocations	`std::vector` and `std::set` per call	Zero — only stack `std::array`s
Dependencies	`Triangle3.hh`, `<vector>`, `<utility>`, `<set>`	`<array>`, `<cmath>`
Numerical robustness	Fragile: exact float equality, `WellOrderedVectors` 1e-3 tolerance (broke for boxes < ~0.002), triangle winding	Robust: only `abs`, `max(0,x)`, and arithmetic; no tolerance parameters

Test plan

New BoxTest.VolumeBelowDiagonalPlanes: tetrahedron corner cut, non-unit normals, asymmetric box, tangent plane, very small box (exposes old 1e-3 tolerance bug), complementary planes
New BoxTest.CenterOfVolumeBelowDiagonal: direction check, tetrahedron centroid, symmetry, weighted-sum conservation, 2D normal (k=2 path), flipped 3D normal (sign transform)
New SphereTest.VolumeBelowFloat: Sphere<float> VolumeBelow + CenterOfVolumeBelow compile and produce correct results
All 193 existing tests continue to pass
Verified new tests fail against old implementation

Checklist

Generated-by: Opus 4.6

Note to maintainers: Remember to use Squash-Merge and edit the commit message to match the pull request summary while retaining Signed-off-by and Generated-by messages.

Backports: If this is a backport, please use Rebase and Merge instead.

ahcorde

Can you update the Python binding too ? Adding the new tests

Replace the surface-mesh + divergence theorem implementation of Box::VolumeBelow and Box::CenterOfVolumeBelow with an analytic inclusion-exclusion formula (Scardovelli-Zaleski / Lehmann-Gekle). The old VolumeBelow used TrianglesInPlane which relied on exact float comparison (Plane::Side() == NO_SIDE) and produced wrong volumes for non-axis-aligned planes. The old CenterOfVolumeBelow returned the arithmetic mean of vertex positions instead of the volumetric centroid, which was only correct for axis-aligned cuts. The new implementation: - Computes volume analytically via IE3/IE2/IE1 formulas with proper dimensional reduction (handles 3D, 2D, 1D, and degenerate cases) - Computes centroid via first-moment IE formula with F_k functions matched to the effective dimensionality - Removes TrianglesInPlane and its Triangle3.hh dependency - Fixes Sphere<float> compilation by replacing hardcoded Vector3d with Vector3<T>::Zero in VolumeBelow and CenterOfVolumeBelow Signed-off-by: Carlos Agüero <caguero@osrfoundation.org> generated-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

caguero · 2026-03-16T10:34:59Z

Can you update the Python binding too ? Adding the new tests

Added

caguero · 2026-03-16T14:29:57Z

@Mergifyio backport gz-math9 gz-math8 gz-math7 ign-math6

mergify · 2026-03-16T14:30:18Z

backport gz-math9 gz-math8 gz-math7 ign-math6

✅ Backports have been created

Details

#725 Fix Box VolumeBelow/CenterOfVolumeBelow (backport #724) has been created for branch gz-math9
#726 Fix Box VolumeBelow/CenterOfVolumeBelow (backport #724) has been created for branch gz-math8
#727 Fix Box VolumeBelow/CenterOfVolumeBelow (backport #724) has been created for branch gz-math7 but encountered conflicts

Cherry-pick of c7f441d has failed:

On branch mergify/bp/gz-math7/pr-724
Your branch is up to date with 'origin/gz-math7'.

You are currently cherry-picking commit c7f441d.
  (fix conflicts and run "git cherry-pick --continue")
  (use "git cherry-pick --skip" to skip this patch)
  (use "git cherry-pick --abort" to cancel the cherry-pick operation)

Changes to be committed:
	modified:   include/gz/math/detail/Sphere.hh
	modified:   src/Box_TEST.cc
	modified:   src/Sphere_TEST.cc
	modified:   src/python_pybind11/test/Box_TEST.py

Unmerged paths:
  (use "git add <file>..." to mark resolution)
	both modified:   include/gz/math/detail/Box.hh

To fix up this pull request, you can check it out locally. See documentation: https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/reviewing-changes-in-pull-requests/checking-out-pull-requests-locally

#728 Fix Box VolumeBelow/CenterOfVolumeBelow (backport #724) has been created for branch ign-math6 but encountered conflicts

Cherry-pick of c7f441d has failed:

On branch mergify/bp/ign-math6/pr-724
Your branch is up to date with 'origin/ign-math6'.

You are currently cherry-picking commit c7f441d.
  (fix conflicts and run "git cherry-pick --continue")
  (use "git cherry-pick --skip" to skip this patch)
  (use "git cherry-pick --abort" to cancel the cherry-pick operation)

Changes to be committed:
	modified:   include/gz/math/detail/Sphere.hh
	modified:   src/Box_TEST.cc
	modified:   src/Sphere_TEST.cc
	modified:   src/python_pybind11/test/Box_TEST.py

Unmerged paths:
  (use "git add <file>..." to mark resolution)
	both modified:   include/gz/math/detail/Box.hh

To fix up this pull request, you can check it out locally. See documentation: https://docs.github.com/en/pull-requests/collaborating-with-pull-requests/reviewing-changes-in-pull-requests/checking-out-pull-requests-locally

…724) Replace the surface-mesh + divergence theorem implementation of Box::VolumeBelow and Box::CenterOfVolumeBelow with an analytic inclusion-exclusion formula (Scardovelli-Zaleski / Lehmann-Gekle). The old VolumeBelow used TrianglesInPlane which relied on exact float comparison (Plane::Side() == NO_SIDE) and produced wrong volumes for non-axis-aligned planes. The old CenterOfVolumeBelow returned the arithmetic mean of vertex positions instead of the volumetric centroid, which was only correct for axis-aligned cuts. The new implementation: - Computes volume analytically via IE3/IE2/IE1 formulas with proper dimensional reduction (handles 3D, 2D, 1D, and degenerate cases) - Computes centroid via first-moment IE formula with F_k functions matched to the effective dimensionality - Removes TrianglesInPlane and its Triangle3.hh dependency - Fixes Sphere<float> compilation by replacing hardcoded Vector3d with Vector3<T>::Zero in VolumeBelow and CenterOfVolumeBelow generated-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com> Signed-off-by: Carlos Agüero <caguero@osrfoundation.org> (cherry picked from commit c7f441d)

…724) Replace the surface-mesh + divergence theorem implementation of Box::VolumeBelow and Box::CenterOfVolumeBelow with an analytic inclusion-exclusion formula (Scardovelli-Zaleski / Lehmann-Gekle). The old VolumeBelow used TrianglesInPlane which relied on exact float comparison (Plane::Side() == NO_SIDE) and produced wrong volumes for non-axis-aligned planes. The old CenterOfVolumeBelow returned the arithmetic mean of vertex positions instead of the volumetric centroid, which was only correct for axis-aligned cuts. The new implementation: - Computes volume analytically via IE3/IE2/IE1 formulas with proper dimensional reduction (handles 3D, 2D, 1D, and degenerate cases) - Computes centroid via first-moment IE formula with F_k functions matched to the effective dimensionality - Removes TrianglesInPlane and its Triangle3.hh dependency - Fixes Sphere<float> compilation by replacing hardcoded Vector3d with Vector3<T>::Zero in VolumeBelow and CenterOfVolumeBelow generated-by: Claude Opus 4.6 (1M context) <noreply@anthropic.com> Signed-off-by: Carlos Agüero <caguero@osrfoundation.org> (cherry picked from commit c7f441d) # Conflicts: # include/gz/math/detail/Box.hh

…724) Replace the surface-mesh + divergence theorem implementation of Box::VolumeBelow and Box::CenterOfVolumeBelow with an analytic inclusion-exclusion formula (Scardovelli-Zaleski / Lehmann-Gekle). The old VolumeBelow used TrianglesInPlane which relied on exact float comparison (Plane::Side() == NO_SIDE) and produced wrong volumes for non-axis-aligned planes. The old CenterOfVolumeBelow returned the arithmetic mean of vertex positions instead of the volumetric centroid, which was only correct for axis-aligned cuts. The new implementation: - Computes volume analytically via IE3/IE2/IE1 formulas with proper dimensional reduction (handles 3D, 2D, 1D, and degenerate cases) - Computes centroid via first-moment IE formula with F_k functions matched to the effective dimensionality - Deprecates TrianglesInPlane (kept for source compatibility) - Fixes Sphere<float> compilation by replacing hardcoded Vector3d with Vector3<T>::Zero in VolumeBelow and CenterOfVolumeBelow Generated-by: Claude Opus 4.6 (1M context) Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

…724) Replace the surface-mesh + divergence theorem implementation of Box::VolumeBelow and Box::CenterOfVolumeBelow with an analytic inclusion-exclusion formula (Scardovelli-Zaleski / Lehmann-Gekle). The old VolumeBelow used TrianglesInPlane which relied on exact float comparison (Plane::Side() == NO_SIDE) and produced wrong volumes for non-axis-aligned planes. The old CenterOfVolumeBelow returned the arithmetic mean of vertex positions instead of the volumetric centroid, which was only correct for axis-aligned cuts. The new implementation: - Computes volume analytically via IE3/IE2/IE1 formulas with proper dimensional reduction (handles 3D, 2D, 1D, and degenerate cases) - Computes centroid via first-moment IE formula with F_k functions matched to the effective dimensionality - Keeps TrianglesInPlane for source compatibility (with bug note) - Fixes Sphere<float> compilation by replacing hardcoded Vector3d with Vector3<T>::Zero in VolumeBelow and CenterOfVolumeBelow Generated-by: Claude Opus 4.6 (1M context) Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

…724) Replace the surface-mesh + divergence theorem implementation of Box::VolumeBelow and Box::CenterOfVolumeBelow with an analytic inclusion-exclusion formula (Scardovelli-Zaleski / Lehmann-Gekle). The old VolumeBelow used TrianglesInPlane which relied on exact float comparison (Plane::Side() == NO_SIDE) and produced wrong volumes for non-axis-aligned planes. The old CenterOfVolumeBelow returned the arithmetic mean of vertex positions instead of the volumetric centroid, which was only correct for axis-aligned cuts. The new implementation: - Computes volume analytically via IE3/IE2/IE1 formulas with proper dimensional reduction (handles 3D, 2D, 1D, and degenerate cases) - Computes centroid via first-moment IE formula with F_k functions matched to the effective dimensionality - Deprecates TrianglesInPlane (kept for source compatibility) - Fixes Sphere<float> compilation by replacing hardcoded Vector3d with Vector3<T>::Zero in VolumeBelow and CenterOfVolumeBelow Generated-by: Claude Opus 4.6 (1M context) Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

caguero requested review from adityapande-1995 and scpeters as code owners March 15, 2026 23:33

azeey added this to Core development Mar 15, 2026

github-actions Bot added the 🏯 kura label Mar 15, 2026

github-project-automation Bot moved this to Inbox in Core development Mar 15, 2026

caguero force-pushed the fix/box-volume-below-centroid-sphere-float branch 2 times, most recently from 90cd8d6 to 8be3c41 Compare March 15, 2026 23:41

caguero changed the title ~~Fix Box VolumeBelow/CenterOfVolumeBelow and Sphere<float> type error~~ Fix Box VolumeBelow/CenterOfVolumeBelow Mar 15, 2026

caguero requested a review from arjo129 March 15, 2026 23:51

ahcorde requested changes Mar 16, 2026

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github-project-automation Bot moved this from Inbox to In review in Core development Mar 16, 2026

caguero force-pushed the fix/box-volume-below-centroid-sphere-float branch from 8be3c41 to c1226d2 Compare March 16, 2026 10:33

caguero requested a review from ahcorde March 16, 2026 13:50

ahcorde approved these changes Mar 16, 2026

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caguero merged commit c7f441d into main Mar 16, 2026
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caguero deleted the fix/box-volume-below-centroid-sphere-float branch March 16, 2026 14:27

github-project-automation Bot moved this from In review to Done in Core development Mar 16, 2026

mergify Bot mentioned this pull request Mar 16, 2026

Fix Box VolumeBelow/CenterOfVolumeBelow (backport #724) #725

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mergify Bot mentioned this pull request Mar 16, 2026

Fix Box VolumeBelow/CenterOfVolumeBelow (backport #724) #726

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mergify Bot mentioned this pull request Mar 16, 2026

Fix Box VolumeBelow/CenterOfVolumeBelow (backport #724) #727

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mergify Bot mentioned this pull request Mar 16, 2026

Fix Box VolumeBelow/CenterOfVolumeBelow (backport #724) #728

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caguero mentioned this pull request Mar 16, 2026

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule and Cone #730

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caguero mentioned this pull request Mar 19, 2026

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule (backport #730) #735

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scpeters mentioned this pull request Mar 26, 2026

Prepare for 9.1.0 release #738

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Fix Box VolumeBelow/CenterOfVolumeBelow#724

Fix Box VolumeBelow/CenterOfVolumeBelow#724
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caguero commented Mar 15, 2026 • edited Loading Uh oh! There was an error while loading. Please reload this page.

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🦟 Bug fix

Summary

Bugs fixed

Improvements

Test plan

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✅ Backports have been created

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caguero commented Mar 15, 2026 •

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