[R-sig-Geo] The length of common boundaries

[Barry Rowlingson]

Michael Sumner wrote:

> Hello, could you expand on what you mean by "topology" in this context?
> I assume it means that any area/polygon object in a given set is a
> subdivision of the plane - i.e. no "overlaps"?  Since, if that were true
> of the dataset then "common shared boundaries" is something that can be
> assumed reliably.  

  Each polygon in an sp Polygon object is just a set of (x,y) coordinate 
pairs that make up the ring that is the polygon. There's no data that 
describes polygon adjacency, and boundary lines between polygons are 
stored twice, once for each polygon. This is sometimes known as 
'doubly-digitised polygons'. The polygons are the fundamental unit.

  Another way of storing GIS data is to use Arc-Node topology. You have 
a table of Nodes (which are where arcs meet), and a table of Arcs. Each 
Arc has a set of (x,y) coordinate pairs. You then have a table of 
Polygons, which is a set of Arcs. To draw polygon X, you find its Arcs, 
then you look up the coordinates in the Arc table. Each line is only 
stored once, but referenced twice - by the polygons on either side.

  The advantage of this is that you can easily figure out adjacency 
matrices by looking at the Polygon-Arc relationship.

  It's possible to reconstruct Arc-Node topology from doubly-digitised 
polygons, but its a very complex operation to do right, and best left to 
GIS programs such as Arc/Info.

  Hope this helps!

Baz