normal_mesh based visualisation not valid.

[Kevin-Mattheus-Moerman]

The example in the README contains something like:

mesh!(ax1,normal_mesh(result),color=:blue, transparency=false, overdraw=false,shading = FastShading)

Where use is made of normal_mesh. However this function does not correctly obtain the triangles.

Below is my first attempt at fixing this, i.e. to get the tetrahedra and then to create a face based mesh representation to correctly visualise the tetrahedral mesh.

function tetgen2facemesh(result)
    E = faces(result) # Called "faces" but these are tetrahedral elements really 
    V = coordinates(result)

    F = Vector{TriangleFace{Int64}}(undef,length(E)*4)
    for q = eachindex(E)
        e = E[q]
        qf = 1 + (q-1)*4
        F[qf] = TriangleFace{Int64}(e[1],e[2],e[3])
        F[qf+1] = TriangleFace{Int64}(e[1],e[2],e[4])
        F[qf+2] = TriangleFace{Int64}(e[2],e[3],e[4])
        F[qf+3] = TriangleFace{Int64}(e[3],e[1],e[4])
    end

    return GeometryBasics.Mesh(V,F)
end

M = tetgen2facemesh(result)

# N,VN=meshnormal(M)

#Visualize mesh
GLMakie.activate!(inline=false) # To avoid plotting in plotpane as per: https://github.com/MakieOrg/Makie.jl/issues/2956
fig = Figure()

ax1=Axis3(fig[1, 1], aspect = :data, xlabel = "X", ylabel = "Y", zlabel = "Z", title = "Using normal_mesh")
mesh!(ax1,normal_mesh(result),color=:blue, transparency=false, overdraw=false,shading = FastShading)
wireframe!(result, linewidth=5,  color=:black)

ax2=Axis3(fig[1, 2], aspect = :data, xlabel = "X", ylabel = "Y", zlabel = "Z", title = "Proper conversion to faces")
poly!(ax2,M,strokewidth=5, color=:blue, transparency=false, overdraw=false,shading = FastShading)
# arrows!(ax2,VN,N)

fig

My guess is that normal_mesh does not create all 4 tetrahedron triangles. The below shows the issue, i.e. several "holes" exist in the mesh (sorry hard to see as shading for these is a mess too... not sure how to fix that @SimonDanisch) and the bottom corner for instance clearly misses triangles. The visualisation on the right is for my "fixed" visualisation using the above.