Add parametric function for Chain

[JoshuaLampert]

This adds a parametric function for Chains, such that a Ring or a Rope can be evaluated at a parameter $t\in [0,1]$. My use case is sampling at the boundary of Ngons and Boxes. I stumbled upon this by trying:

julia> box = Box((0.0, 0.0), (1.0, 1.0))
Box
├─ min: Point(x: 0.0 m, y: 0.0 m)
└─ max: Point(x: 1.0 m, y: 1.0 m)

julia> ring = boundary(box)
Ring
├─ Point(x: 0.0 m, y: 0.0 m)
├─ Point(x: 1.0 m, y: 0.0 m)
├─ Point(x: 1.0 m, y: 1.0 m)
└─ Point(x: 0.0 m, y: 1.0 m)

julia> sampler = RegularSampling(10)
RegularSampling{1}((10,))

julia> collect(sample(ring, sampler))
10-element Vector{Point{𝔼{2}, CoordRefSystems.Cartesian2D{CoordRefSystems.NoDatum, Unitful.Quantity{Float64, 𝐋, Unitful.FreeUnits{(m,), 𝐋, nothing}}}}}:
 Point(x: 0.0 m, y: 0.0 m)
 Point(x: 0.4 m, y: 0.0 m)
 Point(x: 0.8 m, y: 0.0 m)
 Point(x: 1.0 m, y: 0.19999999999999996 m)
 Point(x: 1.0 m, y: 0.6000000000000001 m)
 Point(x: 1.0 m, y: 1.0 m)
 Point(x: 0.6000000000000001 m, y: 1.0 m)
 Point(x: 0.20000000000000018 m, y: 1.0 m)
 Point(x: 0.0 m, y: 0.7999999999999998 m)
 Point(x: 0.0 m, y: 0.3999999999999999 m)

where the last failed before.

cc @mikeingold: We could think of using this to make the specializations for Rope and Ring in MeshIntegrals.jl obsolete.

[codecov]

Codecov Report

Attention: Patch coverage is 90.90909% with 1 line in your changes missing coverage. Please review.

Project coverage is 87.79%. Comparing base (16383a9) to head (e4011bd).
Report is 1 commits behind head on master.

Files with missing lines	Patch %	Lines
src/geometries/polytopes.jl	90.90%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##           master    #1155   +/-   ##
=======================================
  Coverage   87.79%   87.79%           
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  Files         193      193           
  Lines        6046     6057   +11     
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+ Hits         5308     5318   +10     
- Misses        738      739    +1     

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[mikeingold]

cc @mikeingold: We could think of using this to make the specializations for Rope and Ring in MeshIntegrals.jl obsolete.

Without having tried this out to see how well it would work, I’d actually probably lean towards continuing to decompose these into Segments prior to integration. If we treat the entire Chain as a single parametric on a common domain, then differential will usually be discontinuous in value at those segment boundaries, and step changes in integrand values tend to be pretty catastrophic to performance when using adaptive integration rules.

(I’m actually planning to tweak these decomposing methods to make use of reusable buffers that I think will significantly reduce the performance penalty for performing multiple sub-integrals.)

[JoshuaLampert]

Yes, I think you are right @mikeingold. But I think having a parametric function for those geometries can be helpful nevertheless like in the example I gave above.

[mikeingold]

Agreed. I can definitely imagine other uses where having these functions would be useful.

[juliohm]

Thank you @JoshuaLampert. Let's just wait for the tests before merging it.

[JoshuaLampert]

When do you plan to release a new version @juliohm?

[juliohm]

Just waiting for a new fix on the new ValidCoords transform. Will release a patch today or tomorrow at most. Em qui., 19 de dez. de 2024, 10:57, Joshua Lampert ***@***.***> escreveu:

…

When do you plan to release a new version @juliohm <https://github.com/juliohm>? — Reply to this email directly, view it on GitHub <#1155 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAZQW3MRYWJGFL34UTZW4NT2GLGGDAVCNFSM6AAAAABT3EYW72VHI2DSMVQWIX3LMV43OSLTON2WKQ3PNVWWK3TUHMZDKNJUGEZTKNRSGY> . You are receiving this because you were mentioned.Message ID: ***@***.***>

[juliohm]

@JoshuaLampert released a patch to avoid blocking your work: JuliaRegistries/General#121670

Other possible ValidCoords fixes will come in a future patch.

[JoshuaLampert]

Great, thanks!