MMG extension

This extension provides functions to generate meshes of level-set functions using MMG. It defines two methods: export_volume_mesh and export_surface_mesh. For both of them, it is possible to control the size of the generated mesh using the following optional parameters:

  • hgrad control the growth ratio between two adjacent edges.
  • hmin and hmax control the edge sizes to be (respectively) greater than the hmin parameter and lower than the hmax one.
  • hausd control the maximal distance between the piecewise linear representation of the boundary and the reconstructed ideal boundary.

Generation of 2D and 3D mesh from a level-set

For 2 and 3-dimensional Cartesian level set, one can use the export_volume_mesh function to generate meshes. This method relies on the mmg2d_O3 and mmg3d_O3 utilities. Example in 2D:

using LevelSetMethods, MMG_jll
grid = CartesianGrid((-2, -2), (2, 2), (50, 50))
ϕ = LevelSetMethods.star(grid)
volume_mesh2d = LevelSetMethods.export_volume_mesh(ϕ, joinpath(@__DIR__, "volume2D.mesh"))
"/home/runner/work/LevelSetMethods.jl/LevelSetMethods.jl/docs/build/volume2D.mesh"

You can then use e.g. Gmsh to visualize the mesh:

using Gmsh
try
  gmsh.initialize()
  gmsh.option.setNumber("General.Verbosity", 0)
  gmsh.open(volume_mesh2d)
  gmsh.fltk.initialize()
  gmsh.write(joinpath(@__DIR__, "volume2d.png"))
  gmsh.fltk.finalize()
finally
  gmsh.finalize()
end
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Volume2D

And similarly in 3D:

using LevelSetMethods, MMG_jll
grid = CartesianGrid((-1, -1, -1), (+1, +1, +1), (20, 20, 20))
ϕ = LevelSetMethods.sphere(grid; radius = 0.5)
volume_mesh3d = LevelSetMethods.export_volume_mesh(ϕ, joinpath(@__DIR__, "volume3d.mesh"))
"/home/runner/work/LevelSetMethods.jl/LevelSetMethods.jl/docs/build/volume3d.mesh"

Volume3D

Generation of 3D surface mesh with MarchingCubes.jl

Using the mmgs_O3 utility, the MarchingCubes.jl library and the export_surface_mesh function it is possible to obtain a mesh of the levelset contour.

using LevelSetMethods, MMG_jll, MarchingCubes
grid = CartesianGrid((-2, -1, -1), (+2, +1, +1), (40, 20, 20))
ϕ₁ = LevelSetMethods.sphere(grid; radius = 0.5, center = (-1, 0, 0))
ϕ₂ = LevelSetMethods.sphere(grid; radius = 0.5, center = (+1, 0, 0))
ϕ₃ = LevelSetMethods.rectangle(grid; center = (0, 0, 0), width = (2, 0.25, 0.25))
ϕ  = ϕ₁ ∪ ϕ₂ ∪ ϕ₃
surf_mesh3d = LevelSetMethods.export_surface_mesh(ϕ, joinpath(@__DIR__,"surface3D.mesh"); hausd = 1.2, hmax = 1.0)
"/home/runner/work/LevelSetMethods.jl/LevelSetMethods.jl/docs/build/surface3D.mesh"

Again, to visualize it we can use Gmsh:

using Gmsh
try
  gmsh.initialize()
  gmsh.option.setNumber("General.Verbosity", 0)
  gmsh.open(surf_mesh3d)
  gmsh.fltk.initialize()
  gmsh.write(joinpath(@__DIR__, "surface3d.png"))
  gmsh.fltk.finalize()
finally
  gmsh.finalize()
end
XRequest.18: BadValue 0x0

Surface3D