Showed a cross-section of a fiber bundle.

docs/src/newsreport.md

@@ -281,10 +281,12 @@ This is related to the fact that the weak interaction in the Standard Model is n
 
 ![29](./assets/newsreport/29.PNG)
 
-[How to glue two copies of the Riemann sphere (closed complex plane) together for clutching construction.](https://github.com/iamazadi/Porta.jl/blob/master/models/newsreport/gaugeconnections/fig155gluingspheres.jl)
+[How to glue two copies of the Riemann sphere for constructing a vector bundle.](https://github.com/iamazadi/Porta.jl/blob/master/models/newsreport/gaugeconnections/fig155gluingspheres.jl)
 
 ![30](./assets/newsreport/30.PNG)
 
+[A cross-section of a fiber bundle](https://github.com/iamazadi/Porta.jl/blob/master/models/newsreport/gaugeconnections/fig156crosssection.jl)
+
 ![31](./assets/newsreport/31.PNG)
 
 ![32](./assets/newsreport/32.PNG)

models/newsreport/gaugeconnections/fig155gluingspheres.jl

@@ -1,6 +1,5 @@
 using FileIO
 using GLMakie
-import LinearAlgebra
 using Porta
 
 
@@ -16,12 +15,6 @@ eyeposition = normalize(ℝ³(1.0, 0.0, 1.0)) * float(π)
 lookat = ℝ³(0.0, 0.0, 0.0)
 up = normalize(ℝ³(0.0, 0.0, 1.0))
 sphereradius = 1.0
-attributespath = "data/naturalearth/geometry-attributes.csv"
-nodespath = "data/naturalearth/geometry-nodes.csv"
-boundary_names = Set{String}()
-boundary_nodes = Vector{Vector{ℝ³}}()
-indices = Dict{String,Int}()
-reference = load("data/basemap_color.png")
 mask = load("data/basemap_mask.png")
 
 makefigure() = Figure(size = figuresize)
@@ -30,21 +23,6 @@ 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))
 
-## Load the Natural Earth data
-countries = loadcountries(attributespath, nodespath)
-while length(boundary_names) < 10
-    push!(boundary_names, rand(countries["name"]))
-end
-for i in eachindex(countries["name"])
-    for name in boundary_names
-        if countries["name"][i] == name
-            push!(boundary_nodes, countries["nodes"][i])
-            println(name)
-            indices[name] = length(boundary_nodes)
-        end
-    end
-end
-
 lspace1 = range(-π, stop = float(π), length = segments)
 lspace2 = range(-π / 2, stop = π / 2, length = segments)
 plane1 = [ℝ³([θ; ϕ; -1.0]) for θ in lspace2, ϕ in lspace1]

models/newsreport/gaugeconnections/fig156crosssection.jl

@@ -0,0 +1,143 @@
+using FileIO
+using GLMakie
+using Porta
+
+
+figuresize = (4096, 2160)
+segments = 90
+frames_number = 360
+modelname = "fig156crosssection"
+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)) * float(π)
+lookat = ℝ³(0.0, 0.0, 0.0)
+up = normalize(ℝ³(0.0, 0.0, 1.0))
+sphereradius = 1.0
+mask = load("data/basemap_mask.png")
+reference = load("data/basemap_color.png")
+attributespath = "data/naturalearth/geometry-attributes.csv"
+nodespath = "data/naturalearth/geometry-nodes.csv"
+boundary_names = Set()
+boundary_nodes = Vector{Vector{ℝ³}}()
+points = Vector{Vector{ℍ}}()
+indices = Dict()
+T, X, Y, Z = vec(normalize(ℝ⁴(1.0, 0.0, 1.0, 0.0)))
+u = 𝕍(T, X, Y, Z)
+q = ℍ(T, X, Y, Z)
+tolerance = 1e-3
+@assert(isnull(u, atol = tolerance), "u in not a null vector, $u.")
+@assert(isapprox(norm(q), 1, atol = tolerance), "q in not a unit quaternion, $(norm(q)).")
+gauge1 = 0.0
+gauge2 = π / 2
+gauge3 = float(π)
+gauge4 = 3π / 2
+gauge5 = 2π
+latitudescale = 1 / 2
+longitudescale = 1 / 4
+chart = (-π * latitudescale / 2, π * latitudescale / 2, -π * longitudescale, π * longitudescale)
+M = Identity(4)
+
+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))
+lscene1 = LScene(fig[1, 2], show_axis=true, scenekw = (lights = [pl, al], clear=true, backgroundcolor = :white))
+lscene2 = LScene(fig[1, 1], show_axis=false, scenekw = (lights = [pl, al], clear=true, backgroundcolor = :white))
+
+## Load the Natural Earth data
+countries = loadcountries(attributespath, nodespath)
+while length(boundary_names) < 10
+    push!(boundary_names, rand(countries["name"]))
+end
+for i in eachindex(countries["name"])
+    for name in boundary_names
+        if countries["name"][i] == name
+            push!(boundary_nodes, countries["nodes"][i])
+            println(name)
+            indices[name] = length(boundary_nodes)
+        end
+    end
+end
+for i in eachindex(boundary_nodes)
+    _points = Vector{ℍ}()
+    for node in boundary_nodes[i]
+        r, θ, ϕ = convert_to_geographic(node)
+        push!(_points, q * ℍ(exp(ϕ * longitudescale * K(1) + θ * latitudescale * K(2))))
+    end
+    push!(points, _points)
+end
+basemap1 = Basemap(lscene2, q, gauge1, M, chart, segments, mask, transparency = true)
+basemap2 = Basemap(lscene2, q, gauge2, M, chart, segments, mask, transparency = true)
+basemap3 = Basemap(lscene2, q, gauge3, M, chart, segments, mask, transparency = true)
+basemap4 = Basemap(lscene2, q, gauge4, M, chart, segments, mask, transparency = true)
+
+whirls1 = []
+whirls2 = []
+whirls3 = []
+whirls4 = []
+for i in eachindex(boundary_nodes)
+    color1 = getcolor(boundary_nodes[i], reference, 0.2)
+    color2 = getcolor(boundary_nodes[i], reference, 0.4)
+    color3 = getcolor(boundary_nodes[i], reference, 0.6)
+    color4 = getcolor(boundary_nodes[i], reference, 0.8)
+    whirl1 = Whirl(lscene2, points[i], gauge1, gauge2, M, segments, color1, transparency = true)
+    whirl2 = Whirl(lscene2, points[i], gauge2, gauge3, M, segments, color2, transparency = true)
+    whirl3 = Whirl(lscene2, points[i], gauge3, gauge4, M, segments, color3, transparency = true)
+    whirl4 = Whirl(lscene2, points[i], gauge4, gauge5, M, segments, color4, transparency = true)
+    push!(whirls1, whirl1)
+    push!(whirls2, whirl2)
+    push!(whirls3, whirl3)
+    push!(whirls4, whirl4)
+end
+
+lspace1 = range(-π, stop = float(π), length = segments)
+lspace2 = range(-π / 2, stop = π / 2, length = segments)
+plane = [ℝ³([-θ; ϕ; 0.0]) * (1 / float(π)) for θ in lspace2, ϕ in lspace1]
+sectionobservable = buildsurface(lscene1, plane, mask, transparency = true)
+fibersobservable = Tuple{Observable{Matrix{Float64}}, Observable{Matrix{Float64}}, Observable{Matrix{Float64}}}[]
+lspace = range(float(-π), stop = float(π), length = segments)
+for index in 1:length(boundary_names)
+    boundary = convert_to_geographic.(boundary_nodes[index])
+    fiber = [ℝ³(vec(boundary[i])[2:3]..., height) * (1 / float(π)) for i in eachindex(boundary), height in lspace]
+    color = fill(getcolor(boundary_nodes[index], reference, 0.8), length(boundary), segments)
+    push!(fibersobservable, buildsurface(lscene1, fiber, color, transparency = true))
+end
+
+
+animate(frame::Int) = begin
+    progress = Float64(frame / frames_number)
+    println("Frame: $frame, Progress: $progress")
+    ψ = sin(progress * 2π) * π
+    plane = [ℝ³([-θ; ϕ; ψ]) * (1 / float(π)) for θ in lspace2, ϕ in lspace1]
+    updatesurface!(plane, sectionobservable)
+    update!(basemap1, q, gauge1 + ψ, M)
+    update!(basemap2, q, gauge2 + ψ, M)
+    update!(basemap3, q, gauge3 + ψ, M)
+    update!(basemap4, q, gauge4 + ψ, M)
+    points = Vector{Vector{ℍ}}()
+    for i in eachindex(boundary_nodes)
+        _points = Vector{ℍ}()
+        for node in boundary_nodes[i]
+            r, θ, ϕ = convert_to_geographic(node)
+            push!(_points, q * ℍ(exp(ϕ * longitudescale * K(1) + θ * latitudescale * K(2))))
+        end
+        push!(points, _points)
+    end
+    for i in eachindex(whirls1)
+        update!(whirls1[i], points[i], gauge1 + ψ, gauge2 + ψ, M)
+        update!(whirls2[i], points[i], gauge2 + ψ, gauge3 + ψ, M)
+        update!(whirls3[i], points[i], gauge3 + ψ, gauge4 + ψ, M)
+        update!(whirls4[i], points[i], gauge4 + ψ, gauge5 + ψ, M)
+    end
+
+    updatecamera!(lscene1, eyeposition, sum(plane) * (1 / segments^2), up)
+    updatecamera!(lscene2, eyeposition, lookat, up)
+end
+
+
+animate(1)
+
+record(fig, joinpath("gallery", "$modelname.mp4"), 1:frames_number) do frame
+    animate(frame)
+end