arcgis desktop - Algorithm to determinate neighbor's position (N S E W) of parcels?

After my first publicaation Determinate Parcel Neighbors using PYTHON Where i was looking for a faster way to calculate parcel neighbors and position, and after succeeding that, but the result was not full and reliable at 100%, view of complexity of your shapes, so Mr. Richard Fairhurst proposed me to start a new tread and search for a new algorith more efficient and giving more complete and reliable results !

So me i suggest as algorithm to calculate centroide of each polygon, then make a multiple projections of this point on the intersection between two polygons (target and neighbor polygon)

After calculate a bearing of each line, then associate bearings to the compass points are [45-135] = North, [135-225] = West, [225-315] = South, [315-359.9..., 0-45] = East....

So My Question are :

• what do you think about the algorithm is it strong or can stack...



• Do you have any way or idea how to make a projections explained before ?

for the rest i made it before as you can see on the last publication mentionned before !

I'am using Arcgis 10.1, and Python language.