Re: [zzdev] Re: [zzdev] Fully general cell references

[Antti-Juhani Kaijanaho <gaia@xxxxxx>]

On 20000816T101717+0300, Antti-Juhani Kaijanaho wrote:
> On 20000816T101000+0300, Antti-Juhani Kaijanaho wrote:
> > I have not been able to design such a structure using any bounded number
> > of dimensions.  
> 
> Actually, I just had an idea.  I'll post details when I've convinced
> myself that it works.

Ok, here goes:

   We need three dimensions, call them for now d.start-reference,
   d.continue-reference and d.finish-reference.  In the following
   diagrams, negative-to-positive d.start-reference is lower-left to
   upper-right, negative-to-positive d.continue-reference is left to
   right and negative-to-positive d.finish-reference is bottom to up. In
   the diagrams, a star denotes a helper cell (each star a different cell)

   A cell A refers to a cell B which is not referred to by anyone else:
  
                  B
		  |
		  *
                 /
		A

   Now, add a cell C that also refers to B.

                  B
                  |
	    *-----*
	   /     / 
          C     A

   Call one of the stars D and add a cell E that refers to it.
   
                  B
		  |
	    *-----D
	   /	 /|
	  C	A *
                 /               
                E

   Thus we can define that a cell A refers to a cell B if and only
   if there is a cell C that is a positive neighbour of A along
   d.start-reference and there is a cell D that is the endcell of the
   rank along d.continue-reference on which C lies and B is the positive
   neighbour of D along d.finish-reference.

I believe this works and is reasonably efficient.  Comments?
-- 
%%% Antti-Juhani Kaijanaho % gaia@xxxxxx % http://www.iki.fi/gaia/ %%%