[Axiom-developer] graphing the lattice

[root]

More thought about this subject after closing my eyes for the evening:

You don't need a general 3-space layout. You can do it as a set of
parallel 2-space planes. Consider the following:

create a plane[0]
layout the bootstrap layer along the x axis.
layout the 0th layer above the bootstrap layer.
if a 0th layer item cannot be laid out without crossings
  then create a new plane, say plane[1]
       insert the new item into plane[1] connected with "lines"
              drawn back to plane[0]
layout the 1st layer above the 0th layer
if a 1st layer item cannot be laid out without crossings
  then create a new plane, say plane[2]
       insert the new item into plane[2] connected with "lines"
              drawn back to plane[0]
In general this may require quite a few planes. Only lines that
connect planes need connectors.

An optimization would be to lay out items in a "greedy" manner so 
that you only create plane[2] when a crossing occurs in plane[1].

Tim
address@hidden
address@hidden