Add support for integrating over PolyArea and Domain types

[mikeingold]

Changes

• Adds integral methods for Meshes.PolyArea and subtypes of Meshes.Domain with explicit tests for
  • CartesianGrid
  • PolyArea
  • RegularGrid
  • SimpleMesh
• Generalizes the alias functions (e.g. lineintegral) to also accept Domains.
• Update docstrings to improve clarity and consistency.

Closes:

• Integral on SimpleMesh not yet implemented #27
• Integral on PolyArea not yet implemented #169

[github-actions]

Benchmark Results

	main	4e7c1cd...	main / 4e7c1cd...
Differentials/Differential	0.203 ± 0.001 μs	0.205 ± 0.002 μs	0.99 ± 0.011
Differentials/Jacobian	0.17 ± 0.0011 μs	0.169 ± 0.001 μs	1.01 ± 0.0088
Integrals/Segment/Scalar GaussKronrod	0.552 ± 0.0083 μs	0.585 ± 0.0092 μs	0.944 ± 0.02
Integrals/Segment/Scalar GaussLegendre	1.61 ± 0.008 μs	1.68 ± 0.0079 μs	0.962 ± 0.0066
Integrals/Segment/Scalar HAdaptiveCubature	0.714 ± 0.021 μs	0.727 ± 0.018 μs	0.983 ± 0.038
Integrals/Segment/Vector GaussKronrod	2.78 ± 0.11 μs	2.8 ± 0.11 μs	0.994 ± 0.055
Integrals/Segment/Vector GaussLegendre	18.4 ± 1.2 μs	18 ± 1 μs	1.03 ± 0.09
Integrals/Segment/Vector HAdaptiveCubature	3.8 ± 0.15 μs	3.63 ± 0.19 μs	1.05 ± 0.069
Integrals/Sphere/Scalar GaussKronrod	0.0693 ± 0.0019 ms	0.069 ± 0.0019 ms	1 ± 0.039
Integrals/Sphere/Scalar GaussLegendre	1.87 ± 0.01 ms	1.87 ± 0.0054 ms	0.999 ± 0.0063
Integrals/Sphere/Scalar HAdaptiveCubature	0.0476 ± 0.00011 ms	0.0477 ± 0.00012 ms	0.999 ± 0.0034
Integrals/Sphere/Vector GaussKronrod	0.104 ± 0.002 ms	0.105 ± 0.0041 ms	0.997 ± 0.044
Integrals/Sphere/Vector GaussLegendre	3.36 ± 0.1 ms	3.32 ± 0.15 ms	1.01 ± 0.056
Integrals/Sphere/Vector HAdaptiveCubature	0.102 ± 0.0023 ms	0.1 ± 0.0025 ms	1.01 ± 0.034
Rules/GaussLegendre	22.2 ± 1.6 μs	22.7 ± 0.95 μs	0.978 ± 0.081
Specializations/Scalar GaussLegendre/BezierCurve	0.253 ± 0.0071 ms	0.253 ± 0.0072 ms	1 ± 0.04
Specializations/Scalar GaussLegendre/Line	6.94 ± 0.068 μs	7.23 ± 0.13 μs	0.959 ± 0.02
Specializations/Scalar GaussLegendre/Plane	0.745 ± 0.0024 ms	0.746 ± 0.0021 ms	0.999 ± 0.0043
Specializations/Scalar GaussLegendre/Ray	5.85 ± 0.065 μs	5.9 ± 0.058 μs	0.99 ± 0.015
Specializations/Scalar GaussLegendre/Rope	0.0515 ± 0.00023 ms	0.0527 ± 0.0002 ms	0.979 ± 0.0057
Specializations/Scalar GaussLegendre/Tetrahedron	0.157 ± 0.0024 s	0.158 ± 0.0033 s	0.995 ± 0.026
Specializations/Scalar GaussLegendre/Triangle	0.602 ± 0.0075 ms	0.609 ± 0.0075 ms	0.989 ± 0.017
time_to_load	1.43 ± 0.013 s	1.45 ± 0.014 s	0.987 ± 0.013

Benchmark Plots

A plot of the benchmark results have been uploaded as an artifact to the workflow run for this PR.
Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).

[mikeingold]

Interesting. The remaining errors with the SimpleMesh tests are invalid barycentric coords errors from integrating Triangles.

[mikeingold]

Still debugging. One of the remaining issues (UndefVarError: geometry not defined) has a stack trace that appeared at first to be throwiing directly from combinations.jl:138's use of geometry, but I've done some debugging and it appears to be coming from some other function further along the stack.

Edit: got it. There was a holdover in the default rule selection for the integral(::Domain) method.

[mikeingold]

I've run some tests locally to figure out why the Meshes.CartesianGrid test set takes so long, and I've run across some odd results.

• The test set initially took about 80 minutes to run on my computer.
• I ran some tests in a separate REPL and couldn't find any obvious slow integration. Then I tried adding some Logging.@debug lines to give me a quick trace on where the tests are spending all of their time, and suddenly it would repeatably run in about 15 seconds.
• I manually reverted my local repo state to the current commit to make sure there wasn't some unnoticed change and then I rebooted VS Code. Re-running the test set, the first run took about 12 minutes, but then successive runs took 10-15 seconds.

[mikeingold]

Based on a little more debugging, even in the longer CartesianGrid runs the actual runtests function only requires 10-15 seconds, so I suspect that TestItems is also measuring compilation time and that must be dominating the first runtime in this case. Odd that it only seems to be an issue here and not also for RegularGrid. Maybe some kind of type instability/inference issue?

[mikeingold]

I had a vague suspicion that turned out to be true. The really extreme CI times were nearly 100% compilation time. The output of elements(discretize(geometry)) is a generator, so I wondered if additionally collecting this array before integration would simplify things for the compiler at the cost of a single small additional allocation. Based on the new CI times this seems to have worked.

[mikeingold]

@juliohm Should Meshes.GeometryOrDomain be exported? This PR currently triggers a CI fail (ExplicitImports.jl) over importing it as a non-public/exported reference. I can always just define it locally if it wasn't intended for stable external use.

[juliohm]

It is an internal type for dispatch purposes. Not something intended for end users. Em sáb., 19 de jul. de 2025, 14:12, Michael Ingold ***@***.***> escreveu:

…

*mikeingold* left a comment (JuliaGeometry/MeshIntegrals.jl#182) <#182 (comment)> @juliohm <https://github.com/juliohm> Should Meshes.GeometryOrDomain be exported? This PR currently triggers a CI fail (ExplicitImports.jl) over importing it as a non-public/exported reference. I can always just define it locally if it wasn't intended for stable external use. — Reply to this email directly, view it on GitHub <#182 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAZQW3IDUQQEG23ZVAWASFD3JJ37HAVCNFSM6AAAAAB76YG6B6VHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZTAOJSGQ3DCNJQGI> . You are receiving this because you were mentioned.Message ID: ***@***.***>

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 100.00%. Comparing base (5c7a06e) to head (4e7c1cd).
Report is 1 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##              main      #182   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
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  Files           18        19    +1     
  Lines          181       190    +9     
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+ Hits           181       190    +9     

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[JoshuaLampert]

Really nice! I only have some minor comments.

[mikeingold]

I accepted the suggestions but had to reformat the _default_rule definition to avoid exceeding our max line length formatting rule.

[JoshuaLampert]

Thanks!