[michakraus]

Follow-up to the review of #15. That PR merged before these landed on it, so they come as their own change. Seven findings, none of them a bug; two are worth a measurement.

pseudo_cartesian was O(Nθ) per call

It rebuilt the chart coefficients cos.(θ) and sin.(θ) over all Nθ Greville abscissae on every call. They are fixed for the basis, so PolarSplineBasis caches them in the constructor instead. The routine is called once per quadrature point — some 65 000 calls at 64×128 — by both the test suite and the theory page.

Two cold processes, same script, 64×128 cubic:

	before	after
time	1389 ns	63 ns
allocation	3552 B	192 B

For scale, an ordinary evaluate on this basis is 368 B / 125 ns.

A single point written as a vector reached the wrong method

evaluate(B, û, X::AbstractVector) is the vector-of-points method, so evaluate(B, û, [0.3, 1.0]) reached it and failed with a bare BoundsError rather than evaluating at the point (0.3, 1.0). It now dispatches on the element type, AbstractVector{<:Union{Tuple, AbstractVector}}, and a vector point reaches the single-point method.

This was filed in #15 as pre-existing. It is not: TensorProductBasis has four evaluate methods and none of them takes a vector of points, and the one-dimensional form cannot hit it because a one-dimensional point is a scalar. The method is new with the polar space.

The rest

• vec rather than [:] in the two grid comprehensions, which drops a copy of the whole quadrature grid from the per-Newton-iteration path of weighted_matrix.
• The documented signature of PolarSplineQuadrature said quadrature_order.(degree(B)) where the source says map(quadrature_order, degree(B)). Equivalent, but the rendered signature should match.
• A stray second blank line before the 0.2.0 heading in the CHANGELOG.
• Tests for the meshwidth, mesh and domain forwards, for show, and for the new dispatch. Seven assertions, so the polar testset goes 391 → 398.

One finding from the review is not in this diff: scripts/polar_mass_cost.jl has no assertion and no exit, against #15's claim that all four scripts exit non-zero on failure. A timing script needs no threshold, so the description was what was wrong, and #15's body is corrected in place.

Verification

Full suite green on this base: 16 testsets, 0 failures, the polar testset at 398. Aqua passes all eight checks. JuliaFormatter, fatou lint and the NFC check are clean on the three changed files.

One gap worth naming: the local manifest resolved ContinuumArrays 0.20.10, not the 0.21 that main has just admitted, so the 0.21 path is tested here only by CI.

No CHANGELOG entry: the polar space is unreleased, the existing entry describes the end state, and none of its figures move.

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