Benjamin Ducke wrote:
Dear all,
in an attempt to better understand the GRASS vector and topology
model, I imported a set of 3 polygons from an ESRI Shapefile (see
attachment). The polygon in the upper left has 4 holes (called
islands for some reason by GRASS), the lower one consists of 3
parts (QGIS calls this a polygon with islands -- good to know we
understand each other in the GIS world!).
Yes, maybe the way the term islands is used in GRASS is a bit
misleading. According to simple feature specifications, GRASS islands
are (more or less, not sure if 100%) equivalent to holes.
The third is a simple,
convex shape.
Displaying the imported map shows all geometries exactly as it
should. So far so good.
Now, when I run v.info on the imported map, I get:
Number of lines: 0
Number of boundaries: 9
Number of centroids: 5
Number of areas: 9
Number of islands: 9
This completely baffles me!
The GRASS documentation consistently states that an area
is a boundary + a centroid + any number of "islands".
That's an error in the documentation. An area is a closed ring of
boundaries (can be only one boundary) + any number of "islands" (holes)
within + *optionally* an attached centroid. An area without centroid can
not have a category but as far as topology is concerned, it's a valid area.
Now, assuming that the lines around the four "islands" count
as boundaries, I understand why there are 9 boundaries
altogether. 5 centroids also check out, given that there
is no 1:1 equivalent for a shapefile multipart polygon in GRASS.
But how in the (GRASS) world can there be 9 areas if there
are only 5 centroids?
See above, an area in GRASS topology does not need to have a centroid
attached.
And why 9 islands?
Every area is also an island if no boundary is shared with another area.
If a boundary is shared with another area, these two areas together form
one island. In your example, the area in the upper left with the four
islands: the four islands are also areas, but without centroid attached.
When attaching islands during topology building, the internal IDs of all
islands falling inside the outer area are added to the topology
information of that outer area. If one of these four islands would share
a separate boundary with two other islands each, and only one islands
would be completely isolated, that thing in the upper left would still
consist of five areas (four inside, one outer), but of only three
islands, one consisting of three connected areas, one for the remaining
isolated inside area, one for the outer area.
When building topology, areas and islands are constructed first, islands
are not yet attached to areas. Only in the next step are islands
attached to areas, areas get holes. In the last step, centroids are
attached to areas, or more precisely: for each area a not yet attached
centroid is searched for, if found attached, if already attached, it's a
duplicate centroid. There may also be several centroids falling inside
the current area and only inside this area, these will also become
duplicate centroids.
AFAICT, GRASS vector topology is very much based on simple feature
specifications, but not strictly, it deviates here and there in the
usage of terms and in the methods to build topology. The methods are not
a problem, they are consistent even though not 100% following simple
feature specifications, but the usage of terms can be confusing,
particularly with misleading documentation and sometimes different
meanings in closely related applications (QGIS).
Markus M
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