Adjacent elements of a Vertex in Meshes.jl

Specific Domains Visualization
1

How to get the adjacent elements of a vertex in Meshes.jl ?

using Meshes, CoordRefSystems ,GLMakie

r =  Float32[1.6, 1.754088, 1.9230156, 2.1082115, 2.311243, 2.5338273, 2.7778475, 3.0453684, 3.3386526, 3.6601818, 4.012676, 4.3991165, 4.8227735, 5.287231, 5.7964177, 6.354642, 6.9666257, 7.637547, 8.373081]
θ =  Float32[0.0, 0.09817477, 0.19634955, 0.2945243, 0.3926991]
ϕ =  Float32[0.0, 0.3926991, 0.7853982, 1.1780972, 1.5707964, 1.9634954, 2.3561945, 2.7488935, 3.1415927, 3.5342917, 3.9269907, 4.3196898, 4.712389, 5.105088, 5.497787, 5.8904862, 6.2831855]

g = RectilinearGrid{𝔼,typeof(Spherical(0,0,0))}(r, θ, ϕ)
ver = vertex(g,1)

I only need element id numbers.

What does below code represents?

for i in 1:nvertices(g)
    println(Coboundary{0,3}(topology(g))(i))
end
2

Coboundary{0,3} gives you all the elements (Hexahedron’s in this case) that share a given vertex i.

You can confirm this by:

julia> ver = vertex(g,4)
Point with Spherical{NoDatum} coordinates
├─ r: 2.1082115173339844 m
├─ θ: 0.0 rad
└─ ϕ: 0.0 rad

julia> Coboundary{0,3}(topology(g))(4) # returns element id's
(3, 4)

julia> g[3]
Hexahedron
├─ Point(r: 1.9230155944824219 m, θ: 0.0 rad, ϕ: 0.0 rad)
├─ Point(r: 2.1082115173339844 m, θ: 0.0 rad, ϕ: 0.0 rad)  # vertex 4
├─ ...

julia> g[4]
Hexahedron
├─ Point(r: 2.1082115173339844 m, θ: 0.0 rad, ϕ: 0.0 rad) # vertex 4
├─ ...

julia> # do any elements besides 3 and 4 have vertex 4?
julia> any(e -> e ∉ [3,4] && any(v -> v === ver, vertices(g[e])), 1:nelements(g))
false

Coboundary{0,2} will give you the 2d elements that share a given vertex.

2 Likes
3

For my mesh i have a element’s color matrix . This code can be used to create vertex colors when our data don’t have color for vertex. It takes vertex color as average of colors in adjacent elements.

vertex_color = Float64[]
for i in 1:nelements(g)
    el= element(g,i)
    bd = Boundary{3,0}(topology(g))(i)	#Ntuple of vertex ids of i-th element
    for id in bd
		adels= Coboundary{0,3}(topology(g))(id)	#Ntuple of element ids adjacent to this vertex
		clct = collect(Element_color[(elem2cart(topology(g),idx))...] for idx in adels)	#position of i-th element in grid	
		push!(vertex_color, sum(clct)/length(clct))
	end
	@inline viz!(el, color =vertex_color, alpha=0.2)
	#@show clr
end

Can you tell more efficient version of this code? Thanks.