Makie extension

Makie can be used to visualize level set functions in both 2 and 3 dimensions. After loading one of the Makie backends (we recommend GLMakie for 3D), you can simply call plot on the level set function to visualize it. For example:

using LevelSetMethods, GLMakie
grid = CartesianGrid((-2, -2), (2, 2), (100, 100))
ϕ = LevelSetMethods.star(grid)
plot(ϕ)

By default, only the zero level set is plotted as a contour line. For more control, simply call the contour (or contourf) function from Makie directly. For example:

contour(ϕ; levels = [-0.5, 0, 0.5], labels = true)

Although you can manually customize the Axis attributes for the plot, LevelSetMethods provides a Theme with some reasonable defaults for plotting level set functions:

theme = LevelSetMethods.makie_theme()
with_theme(theme) do
  plot(ϕ)
end

In 3D, the plot function will plot the zero level set as an isosurface. For example:

using LevelSetMethods, GLMakie, LinearAlgebra
grid = CartesianGrid((-1.5, -1.5, -1.5), (1.5, 1.5, 1.5), (50, 50, 50))
P1, P2 = (-1, 0, 0), (1, 0, 0)
b = 1.05
ϕ = LevelSet(grid) do x
  norm(x .- P1)*norm(x .- P2) - b^2
end
theme = LevelSetMethods.makie_theme()
with_theme(theme) do
  plot(ϕ)
end

Once again, you can manually customize the options by calling the volume function from Makie directly:

with_theme(theme) do
  volume(ϕ; algorithm = :iso, isovalue = 0.5)
end