Barth sextic with Julia

BarthSextic.jl

using MarchingCubes
import Meshes
using MeshViz
using GLMakie
using Makie
using Printf

# isosurface function f=0
phi = (1 + sqrt(5)) / 2
function f(x, y, z)
  if x*x + y*y + z*z > 3 # clip the mesh to the ball of radius sqrt(3)
    return 1000.0
  end
  - 4 * (phi^2*x^2 - y^2) * (phi^2*y^2 - z^2) * (phi^2*z^2 - x^2) + 
    (1 + 2*phi) * (x^2 + y^2 + z^2 - 1)^2
end

# make the isosurface
n = 200
voxel = zeros(Float32, n, n, n)
rg = LinRange{Float32,Int32}(-1.8, 1.8, n)
coords = convert(Vector{Float32}, collect(rg))
for k in 1:n, j in 1:n, i in 1:n
  voxel[i, j, k] = f(rg[i], rg[j], rg[k])
end
mc = MC(voxel, Int32; x = coords, y = coords, z = coords)
march(mc, Float32(0))
mesh = MarchingCubes.makemesh(Meshes, mc) 

println("marching cubes done")


function drawBS()
  alpha_ = LinRange(0, 2*pi, 181)[1:180]
  for i in 1:180
    sphere = Meshes.discretize(Meshes.Sphere((0, 0, 0), 1.8))
    fig, ax, plt = MeshViz.viz(
      sphere; alpha = 0 # invisible bounding sphere
    )
    ax.show_axis = false
    MeshViz.viz!(mesh; color = :purple)
    Makie.scale!(ax.scene, 1.8, 1.8, 1.8)
    Makie.rotate!(ax.scene, Meshes.Vec3f(0, 0, 1), alpha_[i])
    png = @sprintf "zzpic%03d.png" i
    Makie.save(png, fig)
  end
end