Hopf torus with Julia, circle by circle

HopfTorusCbyC.jl

using Meshes
using MeshViz
using GLMakie

function HopfTorus(u, nlobes, A)
  t = [0, pi / 2, pi]
  cos_v = cos.(t)
  sin_v = sin.(t)
  B = pi / 2 - (pi / 2 - A) * cos(u * nlobes)
  C = u + A * sin(2 * u * nlobes)
  y1 = 1 + cos(B)
  y23 = sin(B) .* [cos(C), sin(C)]
  y2 = y23[1]
  y3 = y23[2]
  x1 = y3 .* cos_v + y2 .* sin_v
  x2 = y2 .* cos_v - y3 .* sin_v
  x3 = y1 .* sin_v
  x4 = y1 .* cos_v
  yden = sqrt(2 * y1)
  m = hcat(x1 ./ (yden .- x4), x3 ./ (yden .- x4), x2 ./ (yden .- x4))
  return eachrow(m)
end

function drawHT(alpha1, alpha2)
  sphere = Meshes.discretize(Meshes.Sphere((0, 0, 0), 1))
  fig, ax, plt = MeshViz.viz( # invisible bounding sphere
    sphere; alpha = 0
  )
  ax.show_axis = false
  u_ = LinRange(0, 2 * pi, 210)
  for i = 1:210
    p1, p2, p3 = HopfTorus(u_[i], 3, 0.44)
    torus = Torus(
      Meshes.Point(tuple(p1...)), 
      Meshes.Point(tuple(p2...)), 
      Meshes.Point(tuple(p3...)), 
      0.3
    )
    mesh = discretize(torus)
    MeshViz.viz!(mesh; color = :darkred)
  end
  Makie.scale!(ax.scene, 1.65, 1.65, 1.65)
  Makie.rotate!(fig.scene, Meshes.Vec3f(1, 0, 0), alpha1)
  Makie.rotate!(ax.scene, Meshes.Vec3f(0, 0, 1), alpha2)
  Makie.save("HopfTorus_CbyC.png", fig)
end