Showed a spin-frame with anti-ski mapping for comparing with Minkowsk…

…i tetrad.

docs/src/newsreport.md

@@ -75,6 +75,8 @@ Tell us the facts of the story.
 
 ![17](./assets/spinspace/17.PNG)
 
+[A spin-frame](https://github.com/iamazadi/Porta.jl/blob/master/models/newsreport/spacetime/fig117spinframe.jl)
+
 ![18](./assets/spinspace/18.PNG)
 
 ![19](./assets/spinspace/19.PNG)

models/newsreport/spacetime/fig117spinframe.jl

@@ -0,0 +1,195 @@
+using FileIO
+using GLMakie
+import LinearAlgebra
+using Porta
+
+
+figuresize = (4096, 2160)
+segments = 360
+frames_number = 360
+modelname = "fig117spinframe"
+M = Identity(4)
+x̂ = ℝ³([1.0; 0.0; 0.0])
+ŷ = ℝ³([0.0; 1.0; 0.0])
+ẑ = ℝ³([0.0; 0.0; 1.0])
+eyeposition = normalize(ℝ³(1.0, 1.0, 1.0)) * π
+lookat = ℝ³(0.0, 0.0, 0.0)
+up = normalize(ℝ³(0.0, 0.0, 1.0))
+mask = load("data/basemap_mask.png")
+
+makefigure() = Figure(size = figuresize)
+fig = with_theme(makefigure, theme_black())
+pl = PointLight(Point3f(0), RGBf(0.0862, 0.0862, 0.0862))
+al = AmbientLight(RGBf(0.9, 0.9, 0.9))
+lscene = LScene(fig[1, 1], show_axis=false, scenekw = (lights = [pl, al], clear=true, backgroundcolor = :white))
+
+timesign = -1
+ο = SpinVector([Complex(1.0); Complex(0.0)], timesign)
+ι = SpinVector([Complex(0.0); Complex(1.0)], timesign)
+@assert(isapprox(dot(ο, ι), 1.0), "The inner product of spin vectors $ι and $ο is not unity.")
+@assert(isapprox(dot(ι, ο), -1.0), "The inner product of spin vectors $ι and $ο is not unity.")
+
+t = 𝕍( 1.0, 0.0, 0.0, 0.0)
+x = 𝕍( 0.0, 1.0, 0.0, 0.0)
+y = 𝕍( 0.0, 0.0, 1.0, 0.0)
+z = 𝕍( 0.0, 0.0, 0.0, 1.0)
+
+οv = 𝕍( LinearAlgebra.normalize(vec(𝕍(ο))))
+ιv = 𝕍( LinearAlgebra.normalize(vec(𝕍(ι))))
+
+generate() = 2rand() - 1 + im * (2rand() - 1)
+κ = SpinVector(generate(), generate(), timesign)
+@assert(isapprox(dot(κ, ι), vec(κ)[1]), "The first component of the spin vector $κ is not equal to the inner product of $κ and $ι.")
+@assert(isapprox(dot(κ, ο), -vec(κ)[2]), "The second component of the spin vector $κ is not equal to minus the inner product of $κ and $ο.")
+
+οflagpole = (1 / √2) * (t + z)
+ιflagpole = (1 / √2) * (t - z)
+
+@assert(isapprox(-οflagpole, οv), "the ο flagpole representation in Minkowski vector space mut be equal to -(t + z) / √2.")
+@assert(isapprox(-ιflagpole, ιv), "the ι flagpole representation in Minkowski vector space mut be equal to -(t - z) / √2.")
+
+arrowsize = Vec3f(0.06, 0.08, 0.1)
+linewidth = 0.04
+tail = Observable(Point3f(0.0, 0.0, 0.0))
+thead = Observable(Point3f(vec(project(ℍ(vec(t))))...))
+xhead = Observable(Point3f(vec(project(ℍ(vec(x))))...))
+yhead = Observable(Point3f(vec(project(ℍ(vec(y))))...))
+zhead = Observable(Point3f(vec(project(ℍ(vec(z))))...))
+οhead = Observable(Point3f(vec(project(ℍ(vec(οv))))...))
+ιhead = Observable(Point3f(vec(project(ℍ(vec(ιv))))...))
+ps = @lift([$tail, $tail, $tail, $tail, $tail, $tail])
+ns = @lift([$thead, $xhead, $yhead, $zhead, $οhead, $ιhead])
+colorants = [:red, :blue, :green, :orange, :black, :silver]
+arrows!(lscene,
+    ps, ns, fxaa = true, # turn on anti-aliasing
+    color = colorants,
+    linewidth = linewidth, arrowsize = arrowsize,
+    align = :origin
+)
+linewidth = 20
+collection = collect(range(0.0, stop = 1.0, length = segments))
+οlinepoints = []
+ιlinepoints = []
+οlinecolors = []
+ιlinecolors = []
+οlines = []
+ιlines = []
+for (i, scale1) in enumerate(collection)
+    _οlinepoints = Observable(Point3f[])
+    _ιlinepoints = Observable(Point3f[])
+    _οlinecolors = Observable(Int[])
+    _ιlinecolors = Observable(Int[])
+    for (j, scale2) in enumerate(collection)
+        οvector = LinearAlgebra.normalize(vec(scale1 * οv + scale2 * x))
+        ιvector = LinearAlgebra.normalize(vec(scale1 * ιv + scale2 * -x))
+        οpoint = Point3f(vec(project(ℍ(οvector)))...)
+        ιpoint = Point3f(vec(project(ℍ(ιvector)))...)
+        push!(_οlinepoints[], οpoint)
+        push!(_ιlinepoints[], ιpoint)
+        push!(_οlinecolors[], i + j)
+        push!(_ιlinecolors[], 2segments + i + j)
+    end
+    push!(οlinepoints, _οlinepoints)
+    push!(ιlinepoints, _ιlinepoints)
+    push!(οlinecolors, _οlinecolors)
+    push!(ιlinecolors, _ιlinecolors)
+    οline = lines!(lscene, οlinepoints[i], color = οlinecolors[i], linewidth = linewidth, colorrange = (1, 4segments))
+    ιline = lines!(lscene, ιlinepoints[i], color = ιlinecolors[i], linewidth = linewidth, colorrange = (1, 4segments))
+    push!(οlines, οline)
+    push!(ιlines, ιline)
+end
+
+titles = ["t", "x", "y", "z", "ο", "ι"]
+rotation = gettextrotation(lscene)
+text!(lscene,
+    @lift(map(x -> Point3f(vec((isnan(x) ? ẑ : x))), [$thead, $xhead, $yhead, $zhead, $οhead, $ιhead])),
+    text = titles,
+    color = colorants,
+    rotation = rotation,
+    align = (:left, :baseline),
+    fontsize = 0.25,
+    markerspace = :data
+)
+
+spherematrix = makesphere(M, Float64(timesign), compressedprojection = true, segments = segments)
+sphereobservable = buildsurface(lscene, spherematrix, mask, transparency = true)
+
+οflagplanematrix = makeflagplane(οv, x, Float64(timesign), compressedprojection = true, segments = segments)
+οflagplanecolor = Observable(fill(RGBAf(0.5, 0.5, 0.5, 0.8), segments, segments))
+οflagplaneobservable = buildsurface(lscene, οflagplanematrix, οflagplanecolor, transparency = true)
+ιflagplanematrix = makeflagplane(ιv, -x, Float64(timesign), compressedprojection = true, segments = segments)
+ιflagplanecolor = Observable(fill(RGBAf(0.5, 0.5, 0.5, 0.8), segments, segments))
+ιflagplaneobservable = buildsurface(lscene, ιflagplanematrix, ιflagplanecolor, transparency = true)
+
+
+animate(frame::Int) = begin
+    progress = frame / frames_number
+    println("Frame: $frame, Progress: $progress")
+    M = compute_fourscrew(progress, 3) * compute_nullrotation(progress)
+    ϵ = 1e-3
+    t_transformed = M * ℍ(vec(t))
+    x_transformed = M * ℍ(vec(x))
+    y_transformed = M * ℍ(vec(y))
+    z_transformed = M * ℍ(vec(z))
+    οv_transformed = M * ℍ(vec(οv))
+    ιv_transformed = M * ℍ(vec(ιv))
+    ο′v_transformed = M * ℍ(vec(οv + ϵ * x))
+    ι′v_transformed = M * ℍ(vec(ιv - ϵ * x))
+
+    thead[] = Point3f(vec(project(t_transformed))...)
+    xhead[] = Point3f(vec(project(x_transformed))...)
+    yhead[] = Point3f(vec(project(y_transformed))...)
+    zhead[] = Point3f(vec(project(z_transformed))...)
+    οhead[] = Point3f(vec(project(οv_transformed))...)
+    ιhead[] = Point3f(vec(project(ιv_transformed))...)
+
+    οv_transformed = 𝕍( vec( οv_transformed))
+    ιv_transformed = 𝕍( vec( ιv_transformed))
+    ο′v_transformed = 𝕍( vec( ο′v_transformed))
+    ι′v_transformed = 𝕍( vec( ι′v_transformed))
+
+    for (i, scale1) in enumerate(collection)
+        _οlinepoints = Point3f[]
+        _ιlinepoints = Point3f[]
+        _οlinecolors = Int[]
+        _ιlinecolors = Int[]
+        for (j, scale2) in enumerate(collection)
+            οvector = normalize(ℍ(vec(scale1 * οv_transformed + scale2 * 𝕍(LinearAlgebra.normalize(vec(οv_transformed - ο′v_transformed))))))
+            ιvector = normalize(ℍ(vec(scale1 * ιv_transformed + scale2 * 𝕍(LinearAlgebra.normalize(vec(ιv_transformed - ι′v_transformed))))))
+            οpoint = Point3f(vec(project(οvector))...)
+            ιpoint = Point3f(vec(project(ιvector))...)
+            push!(_οlinepoints, οpoint)
+            push!(_ιlinepoints, ιpoint)
+            push!(_οlinecolors, i + j)
+            push!(_ιlinecolors, 2segments + i + j)
+        end
+        οlinepoints[i][] = _οlinepoints
+        ιlinepoints[i][] = _ιlinepoints
+        οlinecolors[i][] = _οlinecolors
+        ιlinecolors[i][] = _ιlinecolors
+        notify(οlinepoints[i])
+        notify(ιlinepoints[i])
+        notify(οlinecolors[i])
+        notify(ιlinecolors[i])
+    end
+
+    spherematrix = makesphere(M, Float64(timesign))
+    updatesurface!(spherematrix, sphereobservable)
+
+    οflagplanematrix = makeflagplane(οv_transformed, 𝕍(LinearAlgebra.normalize(vec(ο′v_transformed - οv_transformed))), Float64(timesign), compressedprojection = true, segments = segments)
+    ιflagplanematrix = makeflagplane(ιv_transformed, 𝕍(LinearAlgebra.normalize(vec(ι′v_transformed - ιv_transformed))), Float64(timesign), compressedprojection = true, segments = segments)
+    updatesurface!(οflagplanematrix, οflagplaneobservable)
+    updatesurface!(ιflagplanematrix, ιflagplaneobservable)
+    οflagplanecolor[] = fill(RGBAf(convert_hsvtorgb([progress * 360.0; 1.0; 1.0])..., 0.8), segments, segments)
+    ιflagplanecolor[] = fill(RGBAf(convert_hsvtorgb([360.0 - (progress * 360.0); 1.0; 1.0])..., 0.8), segments, segments)
+
+    updatecamera!(lscene, eyeposition, lookat, up)
+end
+
+
+animate(1)
+
+
+record(fig, joinpath("gallery", "$modelname.mp4"), 1:frames_number) do frame
+    animate(frame)
+end