Fix ViewState element type, :rotation interpolation, Pause action, and record frame count

[asinghvi17]

Bug fixes found while driving a 122 s GeoMakie globe animation built from ~750 chained moves. Each commit is one fix and carries a regression test.

• Pause with an action threw UndefVarError (src/pathchange.jl): the method binds pause, but the body said move. The 2-argument Pause(duration, action) constructor the docstring advertised did not exist either, so the line was unreachable from outside.
• ViewState(; ...) hard-coded Float32 (src/viewstate.jl): the element type is now promoted from the arguments, so a path built from Point3d/Float64 values stays in Float64 instead of accumulating segment times in Float32.
• ConstrainedMove(...; constraint = :rotation) was not a slerp (src/pathchange.jl): cospi(f/2)*vold + sinpi(f/2)*vnew preserves norm(eyeposition - lookat) only at 90°; at 0° the camera flies 41% further out and back, and at 180° it passes through the point it is looking at. Now a real rotation of the direction plus a separate interpolation of the length.
• path(t) rejected times at its own segment boundaries (src/path.jl): tend is accumulated separately from t, so t - tend can exceed the change's duration by an ulp and checkt then throws for a time that had just been assigned to that change. The local time is clamped at the call site; checkt still rejects genuinely out-of-range input.
• The plotcamerapath recipe could not be instantiated on Makie 0.24 (ext/FlyThroughPathsMakieExt.jl): Makie.inherit(scene, ...) inside an @recipe ... do scene block throws MethodError: no method matching lookup_default, and arrows! no longer dispatches from within a recipe. Ported to the current @recipe Name (args) begin ... end form and to arrows3d!.

Also adds nframes(path, rate) and a vectorized path(ts) that walks a sorted vector of sample times in one pass (both used by the recipe), and makes LinearAlgebra a dependency.

Decisions worth a look

1. Integer arguments keep the Float32 default. ViewState(eyeposition = [-10, 0, 0], fov = 45) is still ViewState{Float32}, matching the README, the docs, and the existing show round-trip test. Say the word if you would rather have float(promote_type(...)) throughout.
2. The slerp interpolates length geometrically, dold * (dnew/dold)^f, so equal endpoint radii stay exactly constant and a dolly moves at a constant relative rate. A test pins the midpoint of a 10 → 5 move at sqrt(50); linear is a one-line change.
3. The Makie compat bound narrows to 0.24. The recipe rewrite uses @recipe ... begin ... end and arrows3d!, neither of which exists across the whole 0.21–0.24 range the bound previously claimed. Supporting the older versions as well would mean version-conditional code in the extension.
4. The recipe's camera_markersize::Vec3f becomes camera_markerscale::Real, since arrowsize has no equivalent in Arrows3D. It defaults to automatic, scaled from the bounding box of the path — Makie's own automatic sizes the arrow from its own bounding box, which is a single unit-length arrow and comes out invisible. The unused camera_marker attribute is dropped.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 87.50000% with 8 lines in your changes missing coverage. Please review.
✅ Project coverage is 77.72%. Comparing base (9bb201c) to head (5fa8a57).

Files with missing lines	Patch %	Lines
ext/FlyThroughPathsMakieExt.jl	0.00%	8 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             main      #35       +/-   ##
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+ Coverage   65.00%   77.72%   +12.72%     
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  Files           5        5               
  Lines         180      229       +49     
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+ Hits          117      178       +61     
+ Misses         63       51       -12     

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[asinghvi17]

Also fixed the plotcamerapath recipe, which could not be instantiated at all on Makie 0.24 — Makie.inherit(scene, ...) inside an @recipe ... do scene block throws MethodError: no method matching lookup_default(::Observable{Any}, ::Attributes), and arrows! no longer dispatches from within a recipe. It is now on the @recipe Name (args) begin ... end form with @inherit, and on arrows3d! with align = :tail (the old :headstart) and shading = true.

Two consequences worth your judgement, both in the PR body: the Makie compat bound narrows to 0.24, since neither the new @recipe form nor arrows3d! spans the 0.21–0.24 range it previously claimed; and arrowsize has no Arrows3D equivalent, so the recipe's camera_markersize::Vec3f becomes a scalar camera_markerscale defaulting to automatic — sized from the bounding box of the path, because Makie's own automatic scales the arrow by its own bounding box and renders it invisible. The unused camera_marker attribute is dropped.

Verified by rendering the recipe at three times along a path with CairoMakie; the line is coloured by time and the arrow sits at the eye pointing at the lookat.