Volume below a plane

[arjo129]

🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸🔸

🎉 New feature

Adds a VolumeBelow(Plane<T> &_plane) function to some of the shapes. This is useful for simulating surface behavior when the vehicle is buoyant. It also introduces a CenterOfVolumeBelow(const Planed &_plane) which is useful for calculating the center of buoyancy. This is to support gazebosim/gz-sim#818.

Summary

Currently the following shapes have a VolumeBelow:

• Box
• Sphere

The sphere calculation is relatively simple formula can be found here.
The box calculation is relatively difficult. However the essence of it is we find out the points at which the plane intersects with the plane itself. We then reconstruct a triangle mesh using the resulting vertices. Subsequently we use the generic triangle mesh volume formula.

TODO:

• Cylinders
  Cylinder slices are relatively simple to calculate using Cylinder wedges. [To Be done in a Separate PR]

Checklist

• Signed all commits for DCO
• Added tests
• Added example and/or tutorial
• Updated documentation (as needed)
• Updated migration guide (as needed)
• codecheck passed (See contributing)
• All tests passed (See test coverage)
• While waiting for a review on your PR, please help review another open pull request to support the maintainers

Note to maintainers: Remember to use Squash-Merge

[codecov]

Codecov Report

Merging #219 (b4f9ddc) into ign-math6 (4af8a25) will increase coverage by 0.01%.
The diff coverage is 100.00%.

@@              Coverage Diff              @@
##           ign-math6     #219      +/-   ##
=============================================
+ Coverage      99.40%   99.41%   +0.01%     
=============================================
  Files             66       67       +1     
  Lines           6185     6347     +162     
=============================================
+ Hits            6148     6310     +162     
  Misses            37       37              

Impacted Files	Coverage Δ
include/ignition/math/Box.hh	100.00% <ø> (ø)
include/ignition/math/Sphere.hh	100.00% <ø> (ø)
include/ignition/math/Vector3.hh	98.84% <ø> (ø)
include/ignition/math/Line3.hh	100.00% <100.00%> (ø)
include/ignition/math/Plane.hh	100.00% <100.00%> (ø)
include/ignition/math/detail/Box.hh	100.00% <100.00%> (ø)
include/ignition/math/detail/Sphere.hh	100.00% <100.00%> (ø)
include/ignition/math/detail/WellOrderedVector.hh	100.00% <100.00%> (ø)

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[arjo129]

@scpeters I've addressed your feedback and removed the controversial function.

[scpeters]

thanks for your patience with my review! the API looks good to me. I haven't gone over the test cases, but I think it is good for merging once CI is happy