[GRASS-user] Tessellation of a set of polygons

[Thomas Leduc]

Let's consider a set of input polygons (represented by dark gray polygonal
footprints in the enclosed screenshot [1]). I wonder whether there already
exists a (set of) GRASS instructions to produce the "surrounding
tessellation". I mean, could you please tell me how to compute the set of
multicolor polygons in the enclosed screenshot?

As an example, the blue polygon is the set of points that are:
  - overlayed by the dark gray polygon labeled #1
  - or closer to the dark gray polygon labeled #1 than to any other input
polygon.

Thanks a lot for any help/advice.

Thomas Leduc

PS: I'm aware there already exist in GRASS some functions such as
"v.to.rast, r.grow.distance, and r.contour" which could help in building
map of distances, and isocontours... I'm also aware there already exist
"v.to.rast, r.thin, and r.to.vect feature=line" to build some sort of
medial axis transform or skeleton.

PPS: input data set

create table b(gid int, the_geom GEOMETRY(POLYGON, 2D));
insert into b values (0, GeomFromText('POLYGON ((0 0, 10 0, 10 10, 0 10, 0
0))'));
insert into b values (1, GeomFromText('POLYGON ((30 0, 30 -30, 10 -30, 10
-40, 40 -40, 40 0, 30 0))'));
insert into b values (2, GeomFromText('POLYGON ((20 20, 100 20, 100 40, 60
40, 60 30, 40 30, 40 60, 20 60, 20 20))'));
insert into b values (3, GeomFromText('POLYGON ((60 10, 60 -20, 100 -10,
100 10, 60 10))'));
insert into b values (4, GeomFromText('POLYGON ((-10 -10, -10 -40, -40 -40,
-40 -20, -60 -20, -60 0, -50 0, -50 -10, -10 -10))'));
insert into b values (5, GeomFromText('POLYGON ((-40 20, -40 40, -10 40,
-10 30, -20 20, -40 20))'));

[1] this screenshot of about 11 KB is also downloadable at
https://dl.dropboxusercontent.com/u/8846569/tessellation.png
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://lists.osgeo.org/pipermail/grass-user/attachments/20130829/8d249841/attachment-0001.html>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: tessellation.png
Type: image/png
Size: 10282 bytes
Desc: not available
URL: <http://lists.osgeo.org/pipermail/grass-user/attachments/20130829/8d249841/attachment-0001.png>