WIP: Add demonstrative examples to documentation

[mikeingold]

Preview: https://juliageometry.github.io/MeshIntegrals.jl/previews/PR201/

[github-actions]

Benchmark Results (Julia v1.10)

Time benchmarks

	main	5a5eec9...	main / 5a5eec9...
Differentials/Differential	0.206 ± 0.001 μs	0.204 ± 0.0011 μs	1.01 ± 0.0073
Differentials/Jacobian	0.171 ± 0.001 μs	0.171 ± 0.001 μs	1 ± 0.0083
Integrals/Segment/Scalar GaussKronrod	0.641 ± 0.02 μs	0.622 ± 0.01 μs	1.03 ± 0.036
Integrals/Segment/Scalar GaussLegendre	1.68 ± 0.01 μs	1.66 ± 0.01 μs	1.01 ± 0.0086
Integrals/Segment/Scalar HAdaptiveCubature	0.842 ± 0.02 μs	0.871 ± 0.039 μs	0.967 ± 0.049
Integrals/Segment/Vector GaussKronrod	0.662 ± 0.01 μs	0.731 ± 0.01 μs	0.906 ± 0.018
Integrals/Segment/Vector GaussLegendre	4.71 ± 0.25 μs	4.89 ± 0.29 μs	0.963 ± 0.077
Integrals/Segment/Vector HAdaptiveCubature	0.882 ± 0.029 μs	0.891 ± 0.03 μs	0.99 ± 0.047
Integrals/Sphere/Scalar GaussKronrod	1.14 ± 0.01 μs	1.13 ± 0.01 μs	1.01 ± 0.013
Integrals/Sphere/Scalar GaussLegendre	1.88 ± 0.0036 ms	1.89 ± 0.004 ms	0.995 ± 0.0028
Integrals/Sphere/Scalar HAdaptiveCubature	0.0481 ± 0.00011 ms	0.0483 ± 0.0001 ms	0.996 ± 0.0031
Integrals/Sphere/Vector GaussKronrod	1.17 ± 0.01 μs	1.17 ± 0.01 μs	1 ± 0.012
Integrals/Sphere/Vector GaussLegendre	2.04 ± 0.012 ms	2.05 ± 0.014 ms	0.995 ± 0.0092
Integrals/Sphere/Vector HAdaptiveCubature	0.0494 ± 9.1e-05 ms	0.0496 ± 9.1e-05 ms	0.997 ± 0.0026
Rules/GaussLegendre	21.8 ± 0.6 μs	21.9 ± 0.62 μs	0.998 ± 0.039
Specializations/Scalar GaussLegendre/BezierCurve	0.251 ± 0.0071 ms	0.253 ± 0.0072 ms	0.991 ± 0.04
Specializations/Scalar GaussLegendre/Line	6.95 ± 0.06 μs	7.01 ± 0.079 μs	0.991 ± 0.014
Specializations/Scalar GaussLegendre/Plane	0.786 ± 0.0017 ms	0.786 ± 0.0015 ms	1 ± 0.0028
Specializations/Scalar GaussLegendre/Ray	6 ± 0.051 μs	5.87 ± 0.05 μs	1.02 ± 0.012
Specializations/Scalar GaussLegendre/Rope	0.0513 ± 0.0004 ms	0.0517 ± 0.00018 ms	0.994 ± 0.0085
Specializations/Scalar GaussLegendre/Tetrahedron	0.155 ± 0.00099 s	0.153 ± 0.0007 s	1.01 ± 0.0079
Specializations/Scalar GaussLegendre/Triangle	0.702 ± 0.01 ms	0.613 ± 0.0075 ms	1.15 ± 0.022
time_to_load	1.49 ± 0.0075 s	1.48 ± 0.015 s	1.01 ± 0.011

Memory benchmarks

	main	5a5eec9...	main / 5a5eec9...
Differentials/Differential	3 allocs: 0.0938 kB	3 allocs: 0.0938 kB	1
Differentials/Jacobian	0 allocs: 0 B	0 allocs: 0 B
Integrals/Segment/Scalar GaussKronrod	2 allocs: 0.0469 kB	2 allocs: 0.0469 kB	1
Integrals/Segment/Scalar GaussLegendre	0 allocs: 0 B	0 allocs: 0 B
Integrals/Segment/Scalar HAdaptiveCubature	7 allocs: 0.492 kB	7 allocs: 0.492 kB	1
Integrals/Segment/Vector GaussKronrod	2 allocs: 0.0781 kB	2 allocs: 0.0781 kB	1
Integrals/Segment/Vector GaussLegendre	0.307 k allocs: 12.8 kB	0.307 k allocs: 12.8 kB	1
Integrals/Segment/Vector HAdaptiveCubature	6 allocs: 0.688 kB	6 allocs: 0.688 kB	1
Integrals/Sphere/Scalar GaussKronrod	2 allocs: 0.0469 kB	2 allocs: 0.0469 kB	1
Integrals/Sphere/Scalar GaussLegendre	0 allocs: 0 B	0 allocs: 0 B
Integrals/Sphere/Scalar HAdaptiveCubature	7 allocs: 0.648 kB	7 allocs: 0.648 kB	1
Integrals/Sphere/Vector GaussKronrod	2 allocs: 0.0781 kB	2 allocs: 0.0781 kB	1
Integrals/Sphere/Vector GaussLegendre	30 k allocs: 1.22 MB	30 k allocs: 1.22 MB	1
Integrals/Sphere/Vector HAdaptiveCubature	6 allocs: 0.812 kB	6 allocs: 0.812 kB	1
Rules/GaussLegendre	7 allocs: 0.0325 MB	7 allocs: 0.0325 MB	1
Specializations/Scalar GaussLegendre/BezierCurve	23 allocs: 0.75 kB	23 allocs: 0.75 kB	1
Specializations/Scalar GaussLegendre/Line	21 allocs: 0.938 kB	21 allocs: 0.938 kB	1
Specializations/Scalar GaussLegendre/Plane	22 allocs: 1.03 kB	22 allocs: 1.03 kB	1
Specializations/Scalar GaussLegendre/Ray	21 allocs: 0.938 kB	21 allocs: 0.938 kB	1
Specializations/Scalar GaussLegendre/Rope	0.068 k allocs: 1.62 kB	0.068 k allocs: 1.62 kB	1
Specializations/Scalar GaussLegendre/Tetrahedron	3 M allocs: 0.179 GB	3 M allocs: 0.179 GB	1
Specializations/Scalar GaussLegendre/Triangle	22 allocs: 1.03 kB	22 allocs: 1.03 kB	1
time_to_load	0.153 k allocs: 14.5 kB	0.153 k allocs: 14.5 kB	1

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 100.00%. Comparing base (23d7d25) to head (5a5eec9).
⚠️ Report is 2 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff            @@
##              main      #201   +/-   ##
=========================================
  Coverage   100.00%   100.00%           
=========================================
  Files           19        19           
  Lines          191       191           
=========================================
  Hits           191       191           

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