From 9cdfdab68f6132f5da5a1ece99997dc02c0e16fd Mon Sep 17 00:00:00 2001 From: Mohammad Javad Azadi Date: Sat, 9 Nov 2024 09:20:33 -0800 Subject: [PATCH] Changes omega to minus omega to calculate the correct bilinear map. --- .../fig122spinvectorssumargandplane.jl | 75 ++++++++++++------- .../spacetime/fig123specialframe.jl | 38 ++++------ 2 files changed, 60 insertions(+), 53 deletions(-) diff --git a/models/newsreport/spacetime/fig122spinvectorssumargandplane.jl b/models/newsreport/spacetime/fig122spinvectorssumargandplane.jl index 42370a7..fd63912 100644 --- a/models/newsreport/spacetime/fig122spinvectorssumargandplane.jl +++ b/models/newsreport/spacetime/fig122spinvectorssumargandplane.jl @@ -31,20 +31,13 @@ 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)) generate() = 10rand() - 5 + im * (10rand() - 5) -κ = SpinVector(generate(), generate(), timesign) +scalar = exp(im * rand()) +κ = scalar * SpinVector(generate(), generate(), timesign) ω = SpinVector(generate(), generate(), timesign) -ζ = Complex(κ) -ζ′ = ζ - 1.0 / √2 * ϵ / κ.a[2] -κ = SpinVector(ζ, timesign) -κ′ = SpinVector(ζ′, timesign) -ζ = Complex(ω) -ζ′ = ζ - 1.0 / √2 * ϵ / ω.a[2] -ω = SpinVector(ζ, timesign) -ω′ = SpinVector(ζ′, timesign) -ζ = Complex(κ + ω) -τ = SpinVector(ζ, timesign) -ζ′ = ζ - 1.0 / √2 * ϵ / τ.a[2] -τ′ = SpinVector(ζ′, timesign) +κ′ = SpinVector(Complex(κ) - 1.0 / √2 * ϵ / κ.a[2], timesign) +ω′ = SpinVector(Complex(ω) - 1.0 / √2 * ϵ / ω.a[2], timesign) +τ = κ + ω +τ′ = SpinVector(Complex(τ) - 1.0 / √2 * ϵ / τ.a[2], timesign) w = (Complex(κ + ω) - Complex(κ)) / (Complex(ω) - Complex(κ)) @assert(imag(w) ≤ 0 || isapprox(imag(w), 0.0), "The flagpoles are not collinear: $(Complex(κ)), $(Complex(ω)), $(Complex(κ + ω))") @@ -76,7 +69,7 @@ circlepoints = Observable(Point3f[]) circlecolors = Observable(Int[]) circle = lines!(lscene, circlepoints, color = circlecolors, linewidth = 2linewidth, colorrange = (1, segments), colormap = :rainbow) -titles = ["κ", "ω", "κ+ω", "P", "Q", "R"] +titles = ["κ", "-ω", "κ+ω", "P", "Q", "R"] rotation = gettextrotation(lscene) text!(lscene, @lift(map(x -> Point3f(vec((isnan(x) ? ẑ : x))), [$κhead + $κtail, $ωhead + $ωtail, $τhead + $τtail, $κtail, $ωtail, $τtail])), @@ -93,13 +86,13 @@ sphereobservable = buildsurface(lscene, spherematrix, mask, transparency = true) κflagplanematrix = makeflagplane(κv, κ′v - κv, T, segments = segments) κflagplanecolor = Observable(fill(RGBAf(1.0, 0.0, 0.0, 0.8), segments, segments)) -κflagplaneobservable = buildsurface(lscene, κflagplanematrix, κflagplanecolor, transparency = false) +κflagplaneobservable = buildsurface(lscene, κflagplanematrix, κflagplanecolor, transparency = true) ωflagplanematrix = makeflagplane(ωv, ω′v - ωv, T, segments = segments) ωflagplanecolor = Observable(fill(RGBAf(0.0, 1.0, 0.0, 0.8), segments, segments)) -ωflagplaneobservable = buildsurface(lscene, ωflagplanematrix, ωflagplanecolor, transparency = false) +ωflagplaneobservable = buildsurface(lscene, ωflagplanematrix, ωflagplanecolor, transparency = true) τflagplanematrix = makeflagplane(τv, τ′v - τv, T, segments = segments) τflagplanecolor = Observable(fill(RGBAf(0.0, 0.0, 1.0, 0.8), segments, segments)) -τflagplaneobservable = buildsurface(lscene, τflagplanematrix, τflagplanecolor, transparency = false) +τflagplaneobservable = buildsurface(lscene, τflagplanematrix, τflagplanecolor, transparency = true) meshscatter!(lscene, κtail, markersize = markersize, color = colorants[1]) meshscatter!(lscene, ωtail, markersize = markersize, color = colorants[2]) @@ -110,48 +103,74 @@ animate(frame::Int) = begin progress = Float64(frame / frames_number) println("Frame: $frame, Progress: $progress") z₁ = Complex(κ) - z₂ = Complex(ω) + z₂ = Complex(-ω) z₃ = Complex(κ + ω) - w₁ = progress * exp(im * 0.0) + (1 - progress) * z₁ - w₂ = progress * exp(im * 2π / 3.0) + (1 - progress) * z₂ - w₃ = progress * exp(im * 4π / 3.0) + (1 - progress) * z₃ + if progress ≤ 0.5 + α = min(2progress, 1.0) + w₁ = α * exp(im * 0.0) + (1 - α) * z₁ + w₂ = α * exp(im * 2π / 3.0) + (1 - α) * z₂ + w₃ = α * exp(im * 4π / 3.0) + (1 - α) * z₃ + else + α = 2(progress - 0.5) * 2π + w₁ = exp(im * α) + w₂ = exp(im * (2π / 3.0 + α)) + w₃ = exp(im * (4π / 3.0 + α)) + end f = calculatetransformation(z₁, z₂, z₃, w₁, w₂, w₃) - _κ = SpinVector(f(Complex(κ)), timesign) + + _κ = scalar * SpinVector(f(Complex(κ)), timesign) + + _κ′ = SpinVector(Complex(_κ) - 1.0 / √2 * ϵ / _κ.a[2], timesign) + _ω = SpinVector(f(Complex(-ω)), timesign) - _κ′ = SpinVector(f(Complex(κ′)), timesign) - _ω′ = SpinVector(f(Complex(ω′)), timesign) + + _ω′ = SpinVector(Complex(_ω) - 1.0 / √2 * ϵ / _ω.a[2], timesign) + _κv = 𝕍( normalize(ℝ⁴(𝕍( _κ)))) _κ′v = 𝕍( normalize(ℝ⁴(𝕍( _κ′)))) _ωv = 𝕍( normalize(ℝ⁴(𝕍( _ω)))) _ω′v = 𝕍( normalize(ℝ⁴(𝕍( _ω′)))) + _κv = 𝕍( _κ) + _κ′v = 𝕍( _κ′) + _ωv = 𝕍( _ω) + _ω′v = 𝕍( _ω′) + _τ = _κ + _ω + _τ′ = SpinVector(Complex(_τ) - 1.0 / √2 * ϵ / _τ.a[2], timesign) + _τv = 𝕍( normalize( ℝ⁴( 𝕍( _τ)))) + _τ′v = 𝕍( normalize( ℝ⁴( 𝕍( _τ′)))) + + κflagplane1 = _κv κflagplane2 = 𝕍( normalize( ℝ⁴( _κ′v - _κv))) ωflagplane1 = _ωv ωflagplane2 = 𝕍( normalize( ℝ⁴( _ω′v - _ωv))) τflagplane1 = _τv τflagplane2 = 𝕍( normalize( ℝ⁴( _τ′v - _τv))) + updatesurface!(makesphere(f, T, compressedprojection = true, segments = segments), sphereobservable) updatesurface!(makeflagplane(κflagplane1, κflagplane2, T, segments = segments), κflagplaneobservable) updatesurface!(makeflagplane(ωflagplane1, ωflagplane2, T, segments = segments), ωflagplaneobservable) updatesurface!(makeflagplane(τflagplane1, τflagplane2, T, segments = segments), τflagplaneobservable) - κtail[] = Point3f(project(ℝ⁴(_κv))) - ωtail[] = Point3f(project(ℝ⁴(_ωv))) - τtail[] = Point3f(project(ℝ⁴(_τv))) + + κtail[] = Point3f(project(normalize(ℝ⁴(_κv)))) + ωtail[] = Point3f(project(normalize(ℝ⁴(_ωv)))) + τtail[] = Point3f(project(normalize(ℝ⁴(_τv)))) κhead[] = Point3f(project(normalize(ℝ⁴(_κ′v - _κv)))) ωhead[] = Point3f(project(normalize(ℝ⁴(_ω′v - _ωv)))) τhead[] = Point3f(project(normalize(ℝ⁴(_τ′v - _τv)))) + _circlepoints = Point3f[] _circlecolors = Int[] for (i, ϕ) in enumerate(collect(range(-4π, stop = 4π, length = segments))) κζ = Complex(_κ) ωζ = Complex(_ω) ζ = κζ - ωζ - circlevector = normalize(ℝ⁴(𝕍( SpinVector(κζ + ϕ * ζ, timesign)))) + circlevector = normalize(ℝ⁴(𝕍( SpinVector(ωζ + ϕ * ζ, timesign)))) circlepoint = Point3f(project(circlevector)) push!(_circlepoints, circlepoint) push!(_circlecolors, i) diff --git a/models/newsreport/spacetime/fig123specialframe.jl b/models/newsreport/spacetime/fig123specialframe.jl index c7e1bdd..abb60d3 100644 --- a/models/newsreport/spacetime/fig123specialframe.jl +++ b/models/newsreport/spacetime/fig123specialframe.jl @@ -32,26 +32,14 @@ lscene = LScene(fig[1, 1], show_axis=false, scenekw = (lights = [pl, al], clear= generate() = 10rand() - 5 + im * (10rand() - 5) scalar = exp(im * rand()) -κ = SpinVector(generate(), generate(), timesign) +κ = scalar * SpinVector(generate(), generate(), timesign) ω = SpinVector(generate(), generate(), timesign) -ζ = Complex(κ) -ζ′ = ζ - 1.0 / √2 * ϵ / κ.a[2] -κ = scalar * SpinVector(ζ, timesign) -κ′ = scalar * SpinVector(ζ′, timesign) -ζ = Complex(ω) -ζ′ = ζ - 1.0 / √2 * ϵ / ω.a[2] -ω = SpinVector(ζ, timesign) -ω′ = SpinVector(ζ′, timesign) +κ′ = SpinVector(Complex(κ) - 1.0 / √2 * ϵ / κ.a[2], timesign) +ω′ = SpinVector(Complex(ω) - 1.0 / √2 * ϵ / ω.a[2], timesign) τ = κ + ω -ζ = Complex(τ) -ζ′ = ζ - 1.0 / √2 * ϵ / τ.a[2] -τ = SpinVector(ζ, timesign) -τ′ = SpinVector(ζ′, timesign) +τ′ = SpinVector(Complex(τ) - 1.0 / √2 * ϵ / τ.a[2], timesign) ψ = κ + -ω -ζ = Complex(ψ) -ψ = SpinVector(ζ, timesign) -ζ′ = ζ - 1.0 / √2 * ϵ / ψ.a[2] -ψ′ = SpinVector(ζ′, timesign) +ψ′ = SpinVector(Complex(ψ) - 1.0 / √2 * ϵ / ψ.a[2], timesign) w = (Complex(κ + ω) - Complex(κ)) / (Complex(ω) - Complex(κ)) @assert(imag(w) ≤ 0 || isapprox(imag(w), 0.0), "The flagpoles are not collinear: $(Complex(κ)), $(Complex(ω)), $(Complex(κ + ω))") @@ -141,16 +129,16 @@ animate(frame::Int) = begin f = calculatetransformation(z₁, z₂, z₃, w₁, w₂, w₃) _κ = scalar * SpinVector(f(Complex(κ)), timesign) - _κ′ = scalar * SpinVector(Complex(_κ) - 1.0 / √2 * ϵ / _κ.a[2], timesign) + _κ′ = SpinVector(Complex(_κ) - 1.0 / √2 * ϵ / _κ.a[2], timesign) _ω = SpinVector(f(Complex(ω)), timesign) - _ω′ = scalar * SpinVector(Complex(_ω) - 1.0 / √2 * ϵ / _ω.a[2], timesign) + _ω′ = SpinVector(Complex(_ω) - 1.0 / √2 * ϵ / _ω.a[2], timesign) _κv = 𝕍( normalize(ℝ⁴(𝕍( _κ)))) _κ′v = 𝕍( normalize(ℝ⁴(𝕍( _κ′)))) _ωv = 𝕍( normalize(ℝ⁴(𝕍( _ω)))) _ω′v = 𝕍( normalize(ℝ⁴(𝕍( _ω′)))) - _τ = _κ + _ω + _τ = (1 / √2) * (_κ + _ω) _τ′ = SpinVector(Complex(_τ) - 1.0 / √2 * ϵ / _τ.a[2], timesign) @@ -158,7 +146,7 @@ animate(frame::Int) = begin _τ′v = 𝕍( normalize( ℝ⁴( 𝕍( _τ′)))) - _ψ = _κ + -_ω + _ψ = (1 / √2) * (_κ + -_ω) _ψ′ = SpinVector(Complex(_ψ) - 1.0 / √2 * ϵ / _ψ.a[2], timesign) @@ -181,10 +169,10 @@ animate(frame::Int) = begin updatesurface!(makeflagplane(τflagplane1, τflagplane2, T, segments = segments), τflagplaneobservable) updatesurface!(makeflagplane(ψflagplane1, ψflagplane2, T, segments = segments), ψflagplaneobservable) - κtail[] = Point3f(project(ℝ⁴(_κv))) - ωtail[] = Point3f(project(ℝ⁴(_ωv))) - τtail[] = Point3f(project(ℝ⁴(_τv))) - ψtail[] = Point3f(project(ℝ⁴(_ψv))) + κtail[] = Point3f(project(normalize(ℝ⁴(_κv)))) + ωtail[] = Point3f(project(normalize(ℝ⁴(_ωv)))) + τtail[] = Point3f(project(normalize(ℝ⁴(_τv)))) + ψtail[] = Point3f(project(normalize(ℝ⁴(_ψv)))) κhead[] = Point3f(project(normalize(ℝ⁴(_κ′v - _κv)))) ωhead[] = Point3f(project(normalize(ℝ⁴(_ω′v - _ωv)))) τhead[] = Point3f(project(normalize(ℝ⁴(_τ′v - _τv))))