Standardize view and projection matrices

[ffreyer]

Description

This prepares some things for #3226:

• move translations from projection to view matrices
• track eyeposition in Axis and PolarAxis
• rework Axis3 to use perspectiveprojection and lookat without modification (though I split up lookat into two steps)
• add inv(::Quaternion)

And some random minor cleanup of Axis3 docs (indention, wrong render order in W/GLMakie, double-plotting of Label) + camera controller (name change).

Axis3 comparsion

Axis3 has more extensive changes so things could be different. Here are some new vs old comparisons with docs:

Aspect

Viewing angles

Tick placement seems to be slightly different (e.g. bottom left z is cut off more, top left z's overlap more(?))

Slightly less space to the title here as well

Perspectiveness

viewmodes

Also checked this with perspectiveness = 0.6, no visible changes.

Tight frustum testing/debugging

This will show you the generated frustum (i.e. what area of the scene will be rendered) with th view space bounding box (+ bounding sphere for :fit) of the Axis3.

using GeometryBasics

function camera_debug(gridpos, ax::Axis3)
    function frustum_snapshot(cam)
        r = Rect3f(Point3f(-1, -1, -1), Vec3f(2, 2, 2))
        rect_ps = coordinates(r) .|> Point3f
        insert!(rect_ps, 13, Point3f(1, -1, 1)) # fix bad line

        inv_pv = inv(cam.projectionview[])
        return map(rect_ps) do p
            p = inv_pv * to_ndim(Point4f, p, 1)
            return p[Vec(1,2,3)] / p[4]
        end
    end

    scene = ax.scene
    cam = scene.camera
    frustum = map(pv -> frustum_snapshot(cam), cam.projectionview)

    scene2 = LScene(gridpos, show_axis = false)

    _cc = Makie.Camera3D(
        scene2.scene, projectiontype = Makie.Orthographic,
        near = 0.001f0, far = 1000.0f0, clipping_mode = :static
    )
    lines!(scene2, frustum, color = :blue, linestyle = :dot)

    # bbox is Axis3 specific
    bbox = ax.finallimits
    model = ax.scene.transformation.model
    bb = map(model, bbox) do model, bb
        ps = [(model * to_ndim(Point4f, p, 1))[Vec(1,2,3)] for p in Makie.corners(bb)]
        Rect3f(ps)
    end
    r = map(bb -> maximum(norm.(Makie.corners(bb))), bb)

    linesegments!(scene2, bb, color = :black)
    wireframe!(scene2, map(r -> Sphere(Point3f(0), r), r), color = (:black, 0.2), transparency = true)
    # scatter!(scene2, scene.camera.eyeposition, color = :red)
    scatter!(scene2, Point3f(0), color = :blue)

    r = map(frustum) do frustum
        ps = vcat(frustum[1:12], frustum[14:end])
        normal_mesh(ps, faces(Rect3f()))
    end
    mesh!(scene2, r, color = (:red, 0.3), fxaa = false, transparency = true)
    notify(frustum)

    return scene2
end

begin
    fig = Figure()

    # show the extent of each cell using a box
    b = Box(fig[1, 1], strokewidth = 0, color = :gray95)
    translate!(b.blockscene, Vec3f(0, 0, -10_000))

    ax = Axis3(
        fig[1, 1]; viewmode = :stretch, protrusions = 0,
        aspect = (1,2,3), perspectiveness = 0.5
    )
    hidedecorations!(ax)
    camera_debug(fig[1, 2], ax)
    fig
end

Type of change

• internal adjustments

Checklist

• Added an entry in NEWS.md (for new features and breaking changes)
• Added or changed relevant sections in the documentation
• Added unit tests for new algorithms, conversion methods, etc.
• Added reference image tests for new plotting functions, recipes, visual options, etc.

[MakieBot]

Compile Times benchmark

Note, that these numbers may fluctuate on the CI servers, so take them with a grain of salt. All benchmark results are based on the mean time and negative percent mean faster than the base branch. Note, that GLMakie + WGLMakie run on an emulated GPU, so the runtime benchmark is much slower. Results are from running:

using_time = @ctime using Backend
# Compile time
create_time = @ctime fig = scatter(1:4; color=1:4, colormap=:turbo, markersize=20, visible=true)
display_time = @ctime Makie.colorbuffer(display(fig))
# Runtime
create_time = @benchmark fig = scatter(1:4; color=1:4, colormap=:turbo, markersize=20, visible=true)
display_time = @benchmark Makie.colorbuffer(fig)

	using	create	display	create	display
GLMakie	3.44s (3.33, 3.61) 0.11+-	394.91ms (377.80, 418.02) 15.32+-	480.01ms (463.39, 500.48) 14.17+-	7.37ms (7.13, 7.74) 0.22+-	25.54ms (25.26, 25.94) 0.29+-
master	3.43s (3.34, 3.49) 0.05+-	404.26ms (391.81, 420.29) 10.08+-	481.27ms (464.89, 534.73) 24.04+-	7.39ms (7.08, 7.79) 0.24+-	25.62ms (25.31, 25.92) 0.22+-
evaluation	1.00x invariant, 0.01s (0.11d, 0.85p, 0.08std)	1.02x invariant, -9.35ms (-0.72d, 0.21p, 12.70std)	1.00x invariant, -1.25ms (-0.06d, 0.91p, 19.10std)	1.00x invariant, -0.01ms (-0.06d, 0.91p, 0.23std)	1.00x invariant, -0.08ms (-0.31d, 0.57p, 0.25std)
CairoMakie	3.07s (3.04, 3.12) 0.03+-	323.74ms (318.14, 330.18) 4.19+-	143.89ms (142.22, 145.87) 1.47+-	7.68ms (7.50, 8.08) 0.20+-	616.61μs (609.81, 624.18) 5.49+-
master	3.09s (3.03, 3.12) 0.03+-	327.71ms (320.60, 334.00) 4.46+-	147.24ms (140.97, 156.87) 5.55+-	7.55ms (7.45, 7.69) 0.08+-	610.42μs (605.64, 616.98) 4.00+-
evaluation	1.00x invariant, -0.01s (-0.42d, 0.45p, 0.03std)	1.01x invariant, -3.98ms (-0.92d, 0.11p, 4.32std)	1.02x invariant, -3.35ms (-0.83d, 0.17p, 3.51std)	0.98x invariant, 0.13ms (0.87d, 0.15p, 0.14std)	0.99x slower X, 6.18μs (1.29d, 0.03p, 4.74std)
WGLMakie	3.82s (3.78, 3.88) 0.04+-	339.80ms (330.17, 359.16) 10.11+-	9.32s (9.22, 9.41) 0.07+-	9.97ms (9.65, 11.24) 0.57+-	71.30ms (68.95, 77.77) 2.98+-
master	3.85s (3.80, 3.92) 0.04+-	348.01ms (329.97, 394.06) 21.64+-	9.46s (9.25, 9.63) 0.15+-	9.84ms (9.51, 10.36) 0.33+-	71.30ms (68.13, 77.48) 3.21+-
evaluation	1.01x invariant, -0.03s (-0.73d, 0.20p, 0.04std)	1.02x invariant, -8.21ms (-0.49d, 0.39p, 15.88std)	1.02x faster ✓, -0.14s (-1.21d, 0.05p, 0.11std)	0.99x invariant, 0.13ms (0.27d, 0.62p, 0.45std)	1.00x invariant, -0.01ms (-0.00d, 1.00p, 3.10std)

[ffreyer]

space 3D failing is expected because the near and far planes are now tight to the finallimits in Axis3. This should also change OIT there, but I don't think we explicitly test that.

Failures in CairoMakie are one-pixel offsets of tick labels in Axis3. GLMakie and WGLMakie are the expected space 3D