In the context of generating random test data using QGIS (in a shapefile):
I can generate random, continuous (adjacent) polygons by first creating n random points using ftools and then generating a Voronoi diagram from those. Using this technique I get n convex polygons within some extent. Additionally, I know that all the polygons are contiguous and it is possible to build an adjacency matrix.
Is it possible to generate random convex and concave polygons that are (1) bounded by some defined extent and (2) continuous?
My initial thought is to generate n x 3 polygons and then begin randomly merging them (using a Python script) until only n remain. This should generate at least a few convex polygons.
Does QGIS (or GRASS) offer a means to do this? How about an external package?
Edited for @whuber's comment:
It is possible to trace a path from any polygon to any other polygon without exiting a polygon in the set, e.g. the contiguous U.S. Adding the Hawaii multipolygon would fail the contiguity test because one has to exit California (for example), enter unbounded planar space, and then re-enter the polygon set.
The probability distribution of the random points is not important, in that, the density of polygons generated from the randomly distributed points does not matter. The goal is simply to vary the number of neighbors each polygon has - the distribution of the neighbor cardinality is not important, but it should not be equal across all polygons as with a regular lattice.
This is a test of regionalization algorithms using randomly generated data These tests have used lattices and Voronoi diagrams. I want to explore a particular algorithm on test data using convex and concave polygons. The generation of convex polygons that meet my constraints is handled using the technique I describe above.