Reference frame like in CAD software ?

[BambOoxX]

It is common in 3D CAD software to have a reference frame displayed in the picture

e.g. this in CATIA Solidworks

It's fairly obvious that one can reproduce that in GLMakie with arrows, however, it can't figure how to have the arrow origin remain fixed in pixel space. Is there a way to achieve this. I'm guessing something quite equivalent to the :pixe of text would be nice. The arrow should however rotate according to the :data space and the camera angles

[ffreyer]

I think the way to go about this is to create a separate Scene for the indicator and update its view matrix based on the parent plot.

With an LScene (using some 3d camera) this involves reading out eyeposition, lookat and upvector, moving lookat to 0 and adjusting eyeposition to a comfortable zoom level:

# Your plot
fig = Figure()
lscene = LScene(fig[1,1])
p = scatter!(rand(Point3f, 10))
display(fig)

scene = Scene(
    fig.scene, px_area = Rect2f(20, 20, 100, 100), 
    # backgroundcolor = RGBAf(1,1,0), clear = true # to see scene region
);
linesegments!(scene, 
    Point3f[(0,0,0), (1,0,0), (0,0,0), (0,1,0), (0,0,0), (0,0,1)],
    color = [:red, :red, :green, :green, :blue, :blue],
    linewidth = 10
)

cam = cameracontrols(lscene.scene)
scene.camera.projection[] = Makie.perspectiveprojection(45f0, 1f0, 0.01f0, 100f0)
onany(cam.lookat, cam.eyeposition, cam.upvector) do lookat, eyepos, up 
    viewdir = 4f0 * normalize(eyepos - lookat)
    scene.camera.view[] = Makie.lookat(viewdir, Vec3f(0), up)
    return
end

With an Axis3 you need to read out the relevant angles and calculate eyeposition from that:

fig = Figure()
ax = Axis3(fig[1,1])
p = scatter!(ax, rand(Point3f, 10))
display(fig)

scene = Scene(
    fig.scene, px_area = Rect2f(20, 20, 100, 100), 
    backgroundcolor = RGBAf(1,1,0), clear = true # to see scene region
);
linesegments!(scene, 
    Point3f[(0,0,0), (1,0,0), (0,0,0), (0,1,0), (0,0,0), (0,0,1)],
    color = [:red, :red, :green, :green, :blue, :blue],
    linewidth = 10
)

scene.camera.projection[] = Makie.perspectiveprojection(45f0, 1f0, 0.01f0, 100f0)
onany(ax.elevation, ax.azimuth) do theta, phi
    viewdir = 4f0 * Vec3f(cos(theta) * cos(phi), cos(theta) * sin(phi), sin(theta))
    scene.camera.view[] = Makie.lookat(viewdir, Vec3f(0), Vec3f(0,0,1))
    return
end

[BambOoxX]

Thanks @ffreyer ! I will test that ASAP. Quick question, give that you must add a scene with this solution, it's not possible to make a recipe out of it, right? Or is it?

[ffreyer]

It's possible but more cumbersome. Within an LScene you can grab parent_scene(plot).camera_controls and you should be able to pass projection and view as plot attributes within the recipe. Though I'm not sure if this works across all backends and I consider it more of a hack. Alternatively you can apply the matrix transforms manually and use space = :clip. Dealing with an Axis3 from a recipe is harder. I don't think there is a clean way to trace back to it so if you wanted to be general you'd need to extract a rotation matrix from parent_scene(plot).camera.view.

Why not just write a function?

[BambOoxX]

I guess I just thought using a recipe would make it more versatile. Also, I'd like to remain as close as possible to MakieCore but I guess its not possible to avoid Makie on this.

[BambOoxX]

So, I've been able to get this through a bit of fiddling (basically replacing scene by scene.scene) since I'm using an LScene for the sub-scene (woahhh a lot of scenes in this sentence).

Now it's not directly related, but how is the 3D text rotation handled, I couldn't find an example on that... I tried to see how an LScene is initialized but I did not understand how the axis labels were handled.

[ffreyer]

I think you can specify a Vector of Vec3f as a rotation (per string/position). If not a Vector of (Makie) Quaternionf's should work (Makie.qrotation(axis, angle) for example)

[ffreyer]

I put something interactive together. You can click on the mesh to switch to different views.

using GLMakie
using GeometryBasics, Statistics, LinearAlgebra

function gen_mesh()
    o = 1 / (1 + sqrt(2))
    ps = Point3f[
        (-o, -o, -1), (-o, o, -1), (o, o, -1), (o, -o, -1),
        (-1, o, -o), (-o, 1, -o), (o, 1, -o), (1, o, -o), 
            (1, -o, -o), (o, -1, -o), (-o, -1, -o), (-1, -o, -o),
        (-1, o, o), (-o, 1, o), (o, 1, o), (1, o, o), 
            (1, -o, o), (o, -1, o), (-o, -1, o), (-1, -o, o),
        (-o, -o, 1), (-o, o, 1), (o, o, 1), (o, -o, 1),
    ]
    QF = QuadFace
    TF = TriangleFace
    faces = [
        # bottom quad
        QF(1, 2, 3, 4), 

        # bottom triangles
        TF(2, 5, 6), TF(3, 7, 8), TF(4, 9, 10), TF(1, 11, 12),

        # bottom diag quads
        QF(3, 2, 6, 7), QF(4, 3, 8, 9), QF(1, 4, 10, 11), QF(2, 1, 12, 5), 

        # quad ring
        QF(13, 14, 6, 5), QF(14, 15, 7, 6), QF(15, 16, 8, 7), QF(16, 17, 9, 8),
        QF(17, 18, 10, 9), QF(18, 19, 11, 10), QF(19, 20, 12, 11), QF(20, 13, 5, 12),

        # top diag quads
        QF(22, 23, 15, 14), QF(21, 22, 13, 20), QF(24, 21, 19, 18), QF(23, 24, 17, 16), 

        # top triangles
        TF(21, 20, 19), TF(24, 18, 17), TF(23, 16, 15), TF(22, 14, 13),

        # top
        QF(21, 24, 23, 22)
    ]

    remapped_ps = Point3f[]
    remapped_fs = AbstractFace[]
    remapped_cs = RGBf[]
    remapped_index = Int[]
    for (idx, f) in enumerate(faces)
        i = length(remapped_ps)
        append!(remapped_ps, ps[f])
        push!(remapped_fs, length(f) == 3 ? TF(i+1, i+2, i+3) : QF(i+1, i+2, i+3, i+4))
        c = RGBf(abs.(mean(ps[f]))...)
        append!(remapped_cs, (c for _ in f))
        append!(remapped_index, [idx for _ in f])
    end

    _faces = decompose(GLTriangleFace, remapped_fs)
    return GeometryBasics.Mesh(
        meta(
            remapped_ps; 
            normals = normals(remapped_ps, _faces), 
            color = remapped_cs,
            index = remapped_index
        ), 
        _faces
    )
end

function connect_camera!(ax::Axis3, scene::Scene)
    scene.camera.projection[] = Makie.perspectiveprojection(45f0, 1f0, 0.01f0, 100f0)
    onany(ax.elevation, ax.azimuth) do theta, phi
        viewdir = 3f0 * Vec3f(cos(theta) * cos(phi), cos(theta) * sin(phi), sin(theta))
        scene.lights[1].position[] = viewdir
        scene.camera.view[] = Makie.lookat(viewdir, Vec3f(0), Vec3f(0,0,1))
        return
    end
    notify(ax.elevation)
    return
end

function connect_camera!(lscene::LScene, scene::Scene)
    cam = cameracontrols(lscene.scene)
    scene.camera.projection[] = Makie.perspectiveprojection(45f0, 1f0, 0.01f0, 100f0)
    onany(cam.lookat, cam.eyeposition, cam.upvector) do lookat, eyepos, up 
        viewdir = 3f0 * normalize(eyepos - lookat)
        scene.lights[1].position[] = viewdir
        scene.camera.view[] = Makie.lookat(viewdir, Vec3(0.0), up)
        return
    end
    notify(cam.lookat)
    return
end

function update_camera!(ax::Axis3, phi, theta)
    ax.azimuth[] = phi
    ax.elevation[] = theta
    return
end

function update_camera!(lscene::LScene, phi, theta)
    cam = cameracontrols(lscene.scene)
    dir = Vec3f(cos(theta) * cos(phi), cos(theta) * sin(phi), sin(theta))
    cam.eyeposition[] = cam.lookat[] + norm(cam.eyeposition[] - cam.lookat[]) * dir
    return
end

function reference_frame(parent, bbox = Rect2f(20, 20, 100, 100))
    scene = Scene(
        Makie.rootparent(parent.blockscene), px_area = bbox, 
        backgroundcolor = RGBAf(1,1,1,1), clear = true
    )

    m = gen_mesh()
    mp = mesh!(scene, m, transparency = false)
    tp = text!(scene,
        1.05 .* Point3f[(-1, 0, 0), (1, 0, 0), (0, -1, 0), (0, 1, 0), (0, 0, -1), (0, 0, 1)],
        text = ["-X", "X", "-Y", "Y", "-Z", "Z"],
        align = (:center, :center),
        rotation = [
            Makie.qrotation(Vec3f(1, 0, 0), pi/2) * Makie.qrotation(Vec3f(0, 1, 0), -pi/2),
            Makie.qrotation(Vec3f(1, 0, 0), -pi/2) * Makie.qrotation(Vec3f(0, 1, 0), pi/2),
            Makie.qrotation(Vec3f(0, 1, 0), 0) * Makie.qrotation(Vec3f(1, 0, 0), -3pi/2),
            Makie.qrotation(Vec3f(1, 0, 0), pi/2),
            Makie.qrotation(Vec3f(1, 0, 0), pi),
            Makie.qrotation(Vec3f(1, 0, 0), 0),
        ],
        markerspace = :data, fontsize = 0.4, color = :white,
        strokewidth = 0.1, strokecolor = :black, transparency = false
    )

    connect_camera!(parent, scene)

    on(events(scene).mousebutton, priority = 20) do event
        if event.button == Mouse.left && event.action == Mouse.press
            p, idx = Makie.pick(scene)
            if p === tp.plots[1]
                phi, theta = [
                    (pi, 0), (pi, 0), (0, 0), (-pi/2, 0), (-pi/2, 0), 
                    (pi/2, 0), (0, -pi/2), (0, -pi/2), (0, pi/2)
                ][idx]
                update_camera!(parent, phi, theta)
            elseif p === mp
                face_idx = m.index[idx]
                phi, theta = [
                    (-pi/2, -pi/2),
                    (3pi/4, -pi/4), (1pi/4, -pi/4), (7pi/4, -pi/4), (5pi/4, -pi/4),
                    (pi/2, -pi/4), (0, -pi/4), (-pi/2, -pi/4), (-pi, -pi/4),
                    (3pi/4, 0), (2pi/4, 0), (pi/4, 0), (0, 0), 
                    (7pi/4, 0), (6pi/4, 0), (5pi/4, 0), (pi, 0),
                    (pi/2, pi/4), (pi, pi/4), (3pi/2, pi/4), (0, pi/4),
                    (5pi/4, pi/4), (7pi/4, pi/4), (pi/4, pi/4), (3pi/4, pi/4),
                    (-pi/2, pi/2)
                ][face_idx]
                update_camera!(parent, phi, theta)
            end
        end
    end

    return scene 
end

This can be used with either Axis3 or LScene:

fig = Figure()
ax = Axis3(fig[1,1])
p = scatter!(ax, rand(Point3f, 10))
display(fig)
scene = reference_frame(ax);

fig = Figure()
lscene = LScene(fig[1,1])
p = scatter!(rand(Point3f, 10))
display(fig)
scene = reference_frame(lscene);

[BambOoxX]

This is awesome ! I think I'm gonna slightly alter the style but it's really nice ! Thanks for your help.

Quick note : There is a Vec3 instead of a Vec3f in the connect_camera! for LScene.

[SimonDanisch]

Ha nice! I implemented something like this for the predecessor of GLMakie, which was still called GLVisualize: https://vimeo.com/184020541 I don't us it in the video, but it was working pretty similar to 3Ds max back then ;)

[BambOoxX]

You did a lot already (and even more so) but here are some questions about this solution

• I tried to reduce the size of the chamfered edges in the mesh with o = 1 / (1 + 0.15) but it makes the cube overflow the bounding box ? zoom! doesn't seem to work in this case...
• How would you constrain the camera update so that whenever one clicks on a face of the mesh, the up vector is along the Z direction (or another one for that matter) so that one can keep things in order

[ffreyer]

If you want to make the visualization larger or smaller you can change the 3f0 in connect_camera!. The o in the mesh generation comes from the constraint that each square should have the same side length. (If you consider an octagon in a -1 .. 1 square, o is the offeset from 0 that the corners have. I.e. (o, 1), (-1, -o), etc.)

For an LScene you can probably just set cam.upvector. Axis3 is keeping the up direction steady on its own.

[BambOoxX]

You mean modifying the interaction as

up0 = Vec3f(0,0,1) #0, 0, 1 for z direction up vector
onany(cam.lookat, cam.eyeposition, cam.upvector) do lookat, eyepos, up 
    viewdir = 3f0 * normalize(eyepos - lookat)
    scene.lights[1].position[] = viewdir
    scene.camera.view[] = Makie.lookat(viewdir, Vec3(0.0), up0) #? So that the sun scene follows the z direction
    cam.upvector[] =up0#? So that the main scene follows the z direction
    return 
end

I have tried something close to that but got a stackoverflow ^^

[ffreyer]

I was thinking here

function update_camera!(lscene::LScene, phi, theta)
    cam = cameracontrols(lscene.scene)
    dir = Vec3f(cos(theta) * cos(phi), cos(theta) * sin(phi), sin(theta))
    cam.eyeposition[] = cam.lookat[] + norm(cam.eyeposition[] - cam.lookat[]) * dir
    return
end

That would trigger only when you click on a face.

[BambOoxX]

Just for information, I wanted to put the "cube" in the top right corner so I used the px_area of the rootparent and added an event with the following signature

widths=Vec2(200, 200)
root = Makie.rootparent(parent.blockscene)
on(events(root).window_area, priority=20) do event
        scene.scene.px_area = Rect2i(event.widths - widths, widths)
    end

so that when the window is resized, the cube remains at the same position in the top right corner.

Also while trying to lock the vertical axis I had to detect when theta would be close to the vertical otherwise when clicking on the +/- Z faces I'd get a blank screen.

function update_camera!(lscene::LScene, phi, theta)
    cam = cameracontrols(lscene.scene)
    dir = Vec3f(cos(theta) * cos(phi), cos(theta) * sin(phi), sin(theta))
    cam.eyeposition[] = cam.lookat[] + norm(cam.eyeposition[] - cam.lookat[]) * dir

    if theta≈ π / 2 || theta≈ -π / 2
        cam.upvector[] = Vec3f(1, 0, 0)
    else
        cam.upvector[] = Vec3f(0, 0, 1)
    end
    return
end

There are still some glitches though, as I get some BoundsError sometimes while updating the camera. Not sure why yet...

[BambOoxX]

@ffreyer Thanks again for all the help ! I will close this now, but maybe this could be added to some documentation or beautiful Makie fort instance. What do you think ?