Iterating a recursive split of defined depth

Question

I have two vertices (a) and (b) and I want to recursively split them at their midpoints.

The pattern looks like this:

For this specific depth I can write it like this:

       a_b = self.abfn(   a,    b)

      ab_b = self.abfn( a_b,    b)
      a_ab = self.abfn(   a,  a_b)
    
     abb_b = self.abfn(ab_b,    b)
    ab_abb = self.abfn( a_b, ab_b)
     a_aab = self.abfn(   a, a_ab)
    aab_ab = self.abfn(a_ab,  a_b)

However I want to write it such that I can define a depth and repeatedly split to that depth. The one caveat is I do not want to use recursive functions

How can I iterate in this manner?

I'm using python but the language doesn't really matter.

Answer 1

You could use this code:

def midpoint(a, b):
    return ((a[0] + b[0]) / 2, (a[1] + b[1]) / 2)

def abfn(a, b, depth):
    vertices = [a, b]
    for _ in range(depth):
        nextlevel = vertices[:1]
        for a, b in zip(vertices, vertices[1:]):  # all consecutive pairs
            mid = midpoint(a, b)
            nextlevel.extend((mid, b))
        vertices = nextlevel
    return vertices

Example call:

a = (0, 100)
b = (0, 200)
vertices = abfn(a, b, 2)

print(vertices)

Output:

[(0, 100), (0.0, 125.0), (0.0, 150.0), (0.0, 175.0), (0, 200)]