Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule and Cone by caguero · Pull Request #730 · gazebosim/gz-math

caguero · 2026-03-16T20:35:29Z

🎉 New feature

Summary

Continuing with #724 , this patch extends the volume API (VolumeBelow and CenterOfVolumeBelow) — previously available only on Sphere and Box — to Ellipsoid, Cylinder, Capsule, and Cone.

Each shape computes the volume and centroid of the region below an arbitrary cutting plane, which is the key primitive needed for buoyancy force and torque calculations in simulation.

Algorithms

Shape	Complexity	Technique	Notes
Ellipsoid	O(1)	Affine map to unit sphere + spherical cap formula	1 `sqrt`, 0 trig, 0 heap allocs
Cylinder	O(1)	Closed-form circular segment antiderivatives (Cavalieri's principle)	2-5 trig calls, 0 heap allocs. Shared helpers in `WetVolume.hh`
Capsule	O(1)	Decomposes into Cylinder + 2 Sphere hemispheres	Stability guard for tiny hemisphere slices avoids catastrophic cancellation
Cone	O(1)	10-point Gauss-Legendre quadrature over smooth sub-intervals	<= 90 integrand evals. Varying radius prevents closed-form. Kink-point subdivision ensures smoothness

All implementations are header-only, zero-allocation, and suitable for real-time stepping.

Changes

detail/WetVolume.hh (new) — shared circular-segment and GL10 quadrature helpers, eliminating duplication between Cylinder and Cone.
detail/{Ellipsoid,Cylinder,Capsule,Cone}.hh — VolumeBelow and CenterOfVolumeBelow implementations.
Public headers — method declarations added.
C++ tests — per-shape tests (horizontal, vertical, oblique, tilted planes; complement symmetry; rotational offset) + VolumeBelowFloat tests for all four shapes.
Python pybind11 — volume_below / center_of_volume_below bindings and tests for all four shapes.
Ruby SWIG — VolumeBelow / CenterOfVolumeBelow added to Cylinder.i, Cone.i. New Ellipsoid.i, Capsule.i created (preparatory; not in active build).

Test plan

All 193 existing + new C++ tests pass (ctest --output-on-failure)
New Python binding tests pass for all four shapes
Float instantiation tests compile and pass for all four shapes
CI passes on all platforms

Checklist

Generated-by: Claude

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.

… Cone - Extract shared circular-segment and GL10 quadrature helpers into detail/WetVolume.hh, replacing duplicate code in Cylinder and Cone - Improve Capsule CenterOfVolumeBelow numerical stability by guarding against catastrophic cancellation when hemisphere slice volume is tiny - Add float instantiation tests for all four shapes - Add Python pybind11 bindings and tests for volume_below and center_of_volume_below on all four shapes - Add Ruby SWIG bindings for VolumeBelow/CenterOfVolumeBelow on Cylinder, Cone, and new Ellipsoid/Capsule .i files - Fix MSVC C4305 truncation warning in Ellipsoid::Volume Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

ahcorde

it's being a while since we didn't update the Ruby files. Not sure if we have any policy about this.

caguero · 2026-03-19T12:53:35Z

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

mergify · 2026-03-19T12:53:51Z

backport gz-math9 gz-math8 gz-math7

✅ Backports have been created

Details

#732 Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule and Cone (backport #730) has been created for branch gz-math9
#733 Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule and Cone (backport #730) has been created for branch gz-math8 but encountered conflicts

Cherry-pick of 2860804 has failed:

On branch mergify/bp/gz-math8/pr-730
Your branch is up to date with 'origin/gz-math8'.

You are currently cherry-picking commit 2860804.
  (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/Capsule.hh
	modified:   include/gz/math/Cone.hh
	modified:   include/gz/math/Cylinder.hh
	modified:   include/gz/math/Ellipsoid.hh
	modified:   include/gz/math/detail/Capsule.hh
	modified:   include/gz/math/detail/Cone.hh
	modified:   include/gz/math/detail/Cylinder.hh
	modified:   include/gz/math/detail/Ellipsoid.hh
	new file:   include/gz/math/detail/WetVolume.hh
	modified:   src/Capsule_TEST.cc
	modified:   src/Cone_TEST.cc
	modified:   src/Cylinder_TEST.cc
	modified:   src/Ellipsoid_TEST.cc
	modified:   src/python_pybind11/src/Capsule.hh
	modified:   src/python_pybind11/src/Cone.hh
	modified:   src/python_pybind11/src/Cylinder.hh
	modified:   src/python_pybind11/src/Ellipsoid.hh
	new file:   src/ruby/Capsule.i
	modified:   src/ruby/Cone.i
	modified:   src/ruby/Cylinder.i
	new file:   src/ruby/Ellipsoid.i

Unmerged paths:
  (use "git add <file>..." to mark resolution)
	both modified:   src/python_pybind11/test/Capsule_TEST.py
	both modified:   src/python_pybind11/test/Cone_TEST.py
	both modified:   src/python_pybind11/test/Cylinder_TEST.py
	both modified:   src/python_pybind11/test/Ellipsoid_TEST.py

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

#734 Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule and Cone (backport #730) has been created for branch gz-math7 but encountered conflicts

Cherry-pick of 2860804 has failed:

On branch mergify/bp/gz-math7/pr-730
Your branch is up to date with 'origin/gz-math7'.

You are currently cherry-picking commit 2860804.
  (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/Capsule.hh
	modified:   include/gz/math/Cone.hh
	modified:   include/gz/math/Cylinder.hh
	modified:   include/gz/math/Ellipsoid.hh
	modified:   include/gz/math/detail/Ellipsoid.hh
	new file:   include/gz/math/detail/WetVolume.hh
	modified:   src/Capsule_TEST.cc
	modified:   src/Cone_TEST.cc
	modified:   src/Cylinder_TEST.cc
	modified:   src/Ellipsoid_TEST.cc
	modified:   src/python_pybind11/src/Capsule.hh
	modified:   src/python_pybind11/src/Cone.hh
	modified:   src/python_pybind11/src/Cylinder.hh
	modified:   src/python_pybind11/src/Ellipsoid.hh
	new file:   src/ruby/Capsule.i
	modified:   src/ruby/Cone.i
	modified:   src/ruby/Cylinder.i
	new file:   src/ruby/Ellipsoid.i

Unmerged paths:
  (use "git add <file>..." to mark resolution)
	both modified:   include/gz/math/detail/Capsule.hh
	both modified:   include/gz/math/detail/Cone.hh
	both modified:   include/gz/math/detail/Cylinder.hh
	both modified:   src/python_pybind11/test/Capsule_TEST.py
	both modified:   src/python_pybind11/test/Cone_TEST.py
	both modified:   src/python_pybind11/test/Cylinder_TEST.py
	both modified:   src/python_pybind11/test/Ellipsoid_TEST.py

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

… Cone (#730) - Extract shared circular-segment and GL10 quadrature helpers into detail/WetVolume.hh, replacing duplicate code in Cylinder and Cone - Improve Capsule CenterOfVolumeBelow numerical stability by guarding against catastrophic cancellation when hemisphere slice volume is tiny - Add float instantiation tests for all four shapes - Add Python pybind11 bindings and tests for volume_below and center_of_volume_below on all four shapes - Add Ruby SWIG bindings for VolumeBelow/CenterOfVolumeBelow on Cylinder, Cone, and new Ellipsoid/Capsule .i files - Fix MSVC C4305 truncation warning in Ellipsoid::Volume Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org> (cherry picked from commit 2860804)

… Cone (#730) - Extract shared circular-segment and GL10 quadrature helpers into detail/WetVolume.hh, replacing duplicate code in Cylinder and Cone - Improve Capsule CenterOfVolumeBelow numerical stability by guarding against catastrophic cancellation when hemisphere slice volume is tiny - Add float instantiation tests for all four shapes - Add Python pybind11 bindings and tests for volume_below and center_of_volume_below on all four shapes - Add Ruby SWIG bindings for VolumeBelow/CenterOfVolumeBelow on Cylinder, Cone, and new Ellipsoid/Capsule .i files - Fix MSVC C4305 truncation warning in Ellipsoid::Volume Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org> (cherry picked from commit 2860804) # Conflicts: # src/python_pybind11/test/Capsule_TEST.py # src/python_pybind11/test/Cone_TEST.py # src/python_pybind11/test/Cylinder_TEST.py # src/python_pybind11/test/Ellipsoid_TEST.py

… Cone (#730) - Extract shared circular-segment and GL10 quadrature helpers into detail/WetVolume.hh, replacing duplicate code in Cylinder and Cone - Improve Capsule CenterOfVolumeBelow numerical stability by guarding against catastrophic cancellation when hemisphere slice volume is tiny - Add float instantiation tests for all four shapes - Add Python pybind11 bindings and tests for volume_below and center_of_volume_below on all four shapes - Add Ruby SWIG bindings for VolumeBelow/CenterOfVolumeBelow on Cylinder, Cone, and new Ellipsoid/Capsule .i files - Fix MSVC C4305 truncation warning in Ellipsoid::Volume Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org> (cherry picked from commit 2860804) # Conflicts: # include/gz/math/detail/Capsule.hh # include/gz/math/detail/Cone.hh # include/gz/math/detail/Cylinder.hh # src/python_pybind11/test/Capsule_TEST.py # src/python_pybind11/test/Cone_TEST.py # src/python_pybind11/test/Cylinder_TEST.py # src/python_pybind11/test/Ellipsoid_TEST.py

… Cone (#730) Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

… Cone (#730) - Extract shared circular-segment and GL10 quadrature helpers into detail/WetVolume.hh, replacing duplicate code in Cylinder and Cone - Improve Capsule CenterOfVolumeBelow numerical stability by guarding against catastrophic cancellation when hemisphere slice volume is tiny - Add float instantiation tests for all four shapes - Add Python pybind11 bindings and tests for volume_below and center_of_volume_below on all four shapes - Add Ruby SWIG bindings for VolumeBelow/CenterOfVolumeBelow on Cylinder, Cone, and new Ellipsoid/Capsule .i files - Fix MSVC C4305 truncation warning in Ellipsoid::Volume Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org> (cherry picked from commit 2860804)

… Cone (#730) Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

…730) Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

caguero requested review from adityapande-1995 and scpeters as code owners March 16, 2026 20:35

github-actions bot added the 🏯 kura label Mar 16, 2026

azeey added this to Core development Mar 16, 2026

github-project-automation bot moved this to Inbox in Core development Mar 16, 2026

caguero force-pushed the buoyancy-new-shapes branch 4 times, most recently from 13df206 to d377d08 Compare March 16, 2026 21:47

caguero force-pushed the buoyancy-new-shapes branch from d377d08 to 3b0a8b0 Compare March 16, 2026 22:21

Merge branch 'main' into buoyancy-new-shapes

a70743e

caguero requested review from ahcorde and arjo129 March 17, 2026 12:16

ahcorde approved these changes Mar 19, 2026

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github-project-automation bot moved this from Inbox to In review in Core development Mar 19, 2026

caguero merged commit 2860804 into main Mar 19, 2026
12 checks passed

caguero deleted the buoyancy-new-shapes branch March 19, 2026 12:43

github-project-automation bot moved this from In review to Done in Core development Mar 19, 2026

mergify bot mentioned this pull request Mar 19, 2026

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule and Cone (backport #730) #732

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mergify bot mentioned this pull request Mar 19, 2026

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule and Cone (backport #730) #733

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mergify bot mentioned this pull request Mar 19, 2026

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule and Cone (backport #730) #734

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caguero added a commit that referenced this pull request Mar 19, 2026

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule,…

dd81d5f

… Cone (#730) Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

caguero added a commit that referenced this pull request Mar 19, 2026

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule,…

3b2056b

… Cone (#730) Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

caguero added a commit that referenced this pull request Mar 19, 2026

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule,…

05af857

… Cone (#730) Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

caguero added a commit that referenced this pull request Mar 19, 2026

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule,…

b380186

… Cone (#730) Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

caguero added a commit that referenced this pull request Mar 19, 2026

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule (#…

699ba31

…730) Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

caguero mentioned this pull request Mar 19, 2026

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

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caguero added a commit that referenced this pull request Mar 19, 2026

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule (#…

dedda12

…730) Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

caguero added a commit that referenced this pull request Mar 23, 2026

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule (#…

ec41999

…730) Generated-by: Claude Signed-off-by: Carlos Agüero <caguero@osrfoundation.org>

caguero mentioned this pull request Mar 24, 2026

Add cylinder, capsule, ellipsoid and cone support to graded buoyancy gazebosim/gz-sim#3423

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scpeters mentioned this pull request Mar 26, 2026

Prepare for 9.1.0 release #738

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

Add VolumeBelow/CenterOfVolumeBelow for Ellipsoid, Cylinder, Capsule and Cone#730
caguero merged 2 commits intomainfrom
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caguero commented Mar 16, 2026 • edited Loading Uh oh! There was an error while loading. Please reload this page.

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🎉 New feature

Summary

Algorithms

Changes

Test plan

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caguero commented Mar 19, 2026

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✅ Backports have been created

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caguero commented Mar 16, 2026 •

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