alain Baeckeroot wrote:
Le vendredi 23 février 2007 01:19, Matt Gokey a écrit :
Here is a thought experiment to test: define the board only logically
using a graph (nodes and neighbor nodes). No topological shape and no
mesh layout over any shape is needed. If all nodes have exactly four
neighbors, there is no method or algorithm that you can run to find an
edge. All nodes will look equivalent.
I was partly wrong, but i maintain this board is anisotropic :
It contains squares and triangles, not equally spaced, all triangles
are on the borders.
Here is a simple algorithm to define the borders:
Starting from one node and moving to the next, you can go to the
Left, Front, Right or Back.
- Insides nodes : if you go always to the Right, in 4 steps you are back
to the initial position.
- Near border nodes: there is one starting direction where you need only
3 steps to go back if you always turn to the Right
- Border nodes: 9 steps.
QED number of neighbors is not enought to define the topology, (i suspect
this is well known ;-)
Yes.
So i maintain it is a cylinder, with 2 borders which correspond to our
visual feeling.
I think you are right.
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