# 2D Structured Mesh Generator

This is more of a programming question than a Julia question… I am trying to create a 2D structured mesh generator for an arbitrary domain shape of square elements. There are probably packages available to accomplish this task but I would like to learn how to do it from foundations… it seems like an achievable project.

I want to provide a function with a node step size(1 for now) and an array of n 2D tuples inputs and output an array of node tuples and an array, that I can later enumerate, with m rows(=elements) by 4 columns(=nodes associated to square elements).

I’m brainstorming ways to accomplish this and I feel like there are two directions I can go with it. I could trace the domain unit by unit guided by logic statements or there might be a way to exploit some of set theory functions offered by Julia.

Any recommendations?

This is where I am at least… It feels inefficient and I’d prefer to use immutable variables.

I believe I can define the valid nodes by some set operation between the boundary and an outer mesh. Followed by another trace process for element association… It feels like I’m doubling the operations by not defining elements concurrently with node generation.

``````A = [(0, 0), (4, 0), (4, 3), (9, 3), (9, 6), (4, 7), (0, 7), (4, 6)]

function testmesh(size::Int64, A::Array{Tuple{Int64,Int64},1})
#Input validation
#even number of coordinates per dimension

#Outer Mesh
xmax = 0
xmin = 0
ymax = 0
ymin = 0
for pt in A
if pt > xmax
xmax = pt
end
if pt > ymax
ymax = pt
end
end
mesh = [(x,y) for y in ymin:ymax for x in xmin:xmax];

#Border Trace
surf = Array{Tuple{Int64,Int64},1}(undef, 1)
B = sort(A, by=x->x)
p = popfirst!(B)
B = push!(B, p)
surf = p
for count in 1:length(B)
xsgn = B - p
ysgn = B - p

if sign(xsgn) != 0
for i in 1:abs(xsgn)
surf = push!(surf, (p+sign(xsgn)*i, B))
end
end
if sign(ysgn) != 0
for i in 1:abs(ysgn)
surf = push!(surf, (B, p+sign(ysgn)*i))
end
end
p = popfirst!(B)
end
pop!(surf)

return surf
end
``````