de9im: DE-9IM utilities

As part of my continuing education about the theory and methods underlying Shapely, GEOS, JTS, and the OGC's Simple Features specs, I've written a small package of utilities for working with DE-9IM [1] matrices and patterns: Shapely provides the standard predicates (these are probably my favorite OGC standards) as geometry class methods,

>>> from shapely.wkt import loads
>>> p = loads('POLYGON ((1.0 0.0, 0.0 -1.0, -1.0 0.0, 0.0 1.0, 1.0 0.0))')
>>> q = loads('POLYGON ((3.0 0.0, 2.0 -1.0, 1.0 0.0, 2.0 1.0, 3.0 0.0))')
>>> p.disjoint(q)
>>> p.intersects(q)
>>> p.touches(q)

but what if you wanted to test whether the features touched at exactly one point only? A "side hug", you might say. Instead of computing the intersection and checking its geometry type, you can use the de9im package to define a DE-9IM matrix pattern and test it against the relation matrix for the two features. The 0 in the pattern below requires that the intersection of the boundaries of the features be a 0-dimensional figure. In other words: a point.

>>> from de9im import pattern
>>> side_hug = pattern('FF*F0****')
>>> im = p.relate(q)
>>> print im
>>> side_hug.matches(im)

The de9im package is 100% tested, which gives me a good starting point for experimenting with more optimal implementations.

There seems to be almost enough standardization between GeoDjango, Shapely, and SQLAlchemy that I could make these patterns callable, and call the relate method on a pair of objects:

class Pattern(object):
    def __call__(self, a, b):
        return self.matches(a.relate(b))

to use like so:

>>> side_hug(p, q)
[1] C. Strobl, “Dimensionally Extended Nine-Intersection Model (DE-9IM),” Encyclopedia of GIS, S. Shekhar and H. Xiong, Eds., Springer, 2008, pp. 240-245. [PDF]


reading list

Author: Jonathan Hartley

Hey Sean,

Recently I think you published a small reading list of geometric papers and the like on topics such as this, and now I can't find it again. Did I imagine this? Can you point me to it? Thanks.


Re: de9im: DE-9IM utilities

Author: Sean

It's If you're interested in adding references, let me know.

Re: de9im: DE-9IM utilities

Author: Jonathan Hartley

Thanks! That link once again, without the terminating period included: