That's the idea. See, right now, you are creating a list. That's one n. Then, you are sorting that list using an n^2 method. After that, you effectively sort the resulting ID list as you parse through it, presumably with a "Go until you find the right one" approach, which , when sent through the list n times for n vertexes, is sum(1,n).

Altogether this comes to n+n^2+sum(1,n). For a 6-member list this is 6+36+21=53. n^2 is 36.

Then don't create any ID list, but directly sort the distance list instead. So you'll come up with a single sorted list.

I'll try to implement the sorting method I used with AxeJh3D.

I see what I think is an optimisation, I'll just make an Axe-like algorithm out of it :

Lbl GSortID
...
GDB1ZFACE is a nbFaces*2 large free area
GDB1FACE contains the face definition in the form of Data(0,4,2,...)
GDB1ZVERT contains the 2-bytes Z coordinate of each vertex
GDB1SORT is a nbFaces large free area
...

.Z-average value for each face
For(r₂,0,nbFaces)
  0→{r₂*2+GDB1ZFACE→r₃}^r
  For(r₁,0,nbVerticesForThisFace)
    {{r₂*nbVerticesForThisFace+GDB1FACE}*2+GDB1ZVERT}^r+{r₃}^r→{r₃}^r
  End
  {r₃}^r//nbVerticesForThisFace→{r₃}^r
End

.Sort
While 1
  0→F
  For(r₁,0,nbFaces-1)
    If {{r₁+GDB1SORT}*2+GDB1ZFACE}^r<<{{r₁+GDB1SORT+1}*2+GDB1ZFACE}^r
      1→F
      Exch(r₁+GDB1SORT,r₁+GDB1SORT+1,1)
    End
  End
End!If F
Return

With that you have your list in GDB1SORT. I can't really test it since I'm really not familiar with GLib's environment, so I let you test. Ask if you don't understand something.

Matrefeytontias you're code work perfectly, I just need to do speed test.

If we implement the in-place sort, the ID list becomes unnecessary, as it's implied that it goes {0 1 2 3 .. highest ID}

I really don't know how to do in-place sort...

I test one place sort,and... forget it. The speed is just horrible 

But you will be happy to know that I work on this, and a update will come soon, with some  new commands.... who are just awesome 
I will upload it when I can.

(ohh, and Matrefeytontias can you send me the data you use for the omnimaga logo (test program of your axiom) ?    )

Bump,

There you go, all the 20 vertices :

:ΔList(-40^r,40^r,5^r)→GDB1IN
:ΔList(-40^r,-40^r,5^r)
:ΔList(40^r,-40^r,5^r)
:ΔList(40^r,30^r,5^r)
:ΔList(60^r,30^r,5^r)
:ΔList(60^r,40^r,5^r)
:ΔList(-30^r,30^r,5^r)
:ΔList(-30^r,-30^r,5^r)
:ΔList(30^r,-30^r,5^r)
:ΔList(30^r,30^r,5^r)
:ΔList(-40^r,40^r,-5^r)
:ΔList(-40^r,-40^r,-5^r)
:ΔList(40^r,-40^r,-5^r)
:ΔList(40^r,30^r,-5^r)
:ΔList(60^r,30^r,-5^r)
:ΔList(60^r,40^r,-5^r)
:ΔList(-30^r,30^r,-5^r)
:ΔList(-30^r,-30^r,-5^r)
:ΔList(30^r,-30^r,-5^r)
:ΔList(30^r,30^r,-5^r)

no don't worry, it's not dead at all       I currently work actively on it....
It's just I prepare you a super mega update of the death 

Anyway, here is the last progress :