[WIP] non-SDF Meshing

[sjkelly]

This removes the requirement of a SignedDistanceField from the meshing process and allows direct sampling of a function over a specified bound. See below:

torus_fn(v) = (sqrt(v[1]^2+v[2]^2)-0.5)^2 + v[3]^2 - 0.25 # torus
marching_cubes(torus_fn, HyperRectangle(Vec(-2,-2,-2.),Vec(4,4,4.)), (80,80,80))

I noticed that the current approach is bottlenecked by cache-misses when constructing the voxels. I originally was attempting a caching approach, but suspected this would be faster.

Benchmarking Meshing.jl...https://github.com/JuliaGeometry/Meshing.jl/issues/24
  242.589 ms (3188657 allocations: 68.93 MiB) # sdf generation time (precompiled)

function MC
BenchmarkTools.Trial: 
  memory estimate:  1.17 MiB
  allocs estimate:  37
  --------------
  minimum time:     10.651 ms (0.00% GC)
  median time:      11.157 ms (0.00% GC)
  mean time:        11.921 ms (1.30% GC)
  maximum time:     272.196 ms (4.89% GC)
  --------------
  samples:          417
  evals/sample:     1

sdf MarchingCubes{Float64}
BenchmarkTools.Trial: 
  memory estimate:  3.75 MiB
  allocs estimate:  59
  --------------
  minimum time:     8.653 ms (0.00% GC)
  median time:      9.392 ms (0.00% GC)
  mean time:        9.974 ms (1.76% GC)
  maximum time:     220.567 ms (0.00% GC)
  --------------
  samples:          501
  evals/sample:     1

If we include the construction of the SDF in the timings, the non-SDF approach is ~25x faster and allocates orders of magnitude less memory.

This is currently just implemented for Marching Cubes, but I will take a similar approach to the other algorithms as well. Once I clean up the API this should allow me to bring in my Dual Contours examples from Descartes since it requires the function to determine the normals.

TODO:

• MarchingCubes
• NaiveSurfaceNets
• MarchingTetrahedra
• Finalize API

[sjkelly]

I forgot to add that as consequence of having the function available we can find the true iso-level of the surface, albeit with a performance penalty. This is important for my solid modeling applications since the mesh needs to be accurate. For visualization the standard interpolation approach should be acceptable.