Set-Operations with Overlay

When working with multiple spatial datasets – especially multiple polygon or line datasets – users often wish to create new shapes based on places where those datasets overlap (or don’t overlap). These manipulations are often referred using the language of sets – intersections, unions, and differences. These types of operations are made available in the geopandas library through the overlay function.

The basic idea is demonstrated by the graphic below but keep in mind that overlays operate at the DataFrame level, not on individual geometries, and the properties from both are retained. In effect, for every shape in the first GeoDataFrame, this operation is executed against every other shape in the other GeoDataFrame:

_images/overlay_operations.png

Source: QGIS Documentation

(Note to users familiar with the shapely library: overlay can be thought of as offering versions of the standard shapely set-operations that deal with the complexities of applying set operations to two GeoSeries. The standard shapely set-operations are also available as GeoSeries methods.)

The different Overlay operations

First, we create some example data:

In [1]: from shapely.geometry import Polygon

In [2]: polys1 = gpd.GeoSeries([Polygon([(0,0), (2,0), (2,2), (0,2)]),
   ...:                         Polygon([(2,2), (4,2), (4,4), (2,4)])])
   ...: 

In [3]: polys2 = gpd.GeoSeries([Polygon([(1,1), (3,1), (3,3), (1,3)]),
   ...:                         Polygon([(3,3), (5,3), (5,5), (3,5)])])
   ...: 

In [4]: df1 = gpd.GeoDataFrame({'geometry': polys1, 'df1':[1,2]})

In [5]: df2 = gpd.GeoDataFrame({'geometry': polys2, 'df2':[1,2]})

These two GeoDataFrames have some overlapping areas:

In [6]: ax = df1.plot(color='red');

In [7]: df2.plot(ax=ax, color='green');
_images/overlay_example.png

We illustrate the different overlay modes with the above example. The overlay function will determine the set of all individual geometries from overlaying the two input GeoDataFrames. This result covers the area covered by the two input GeoDataFrames, and also preserves all unique regions defined by the combined boundaries of the two GeoDataFrames.

When using how='union', all those possible geometries are returned:

In [8]: res_union = gpd.overlay(df1, df2, how='union')

In [9]: res_union
Out[9]: 
   df1  df2                                       geometry
0    1  NaN  POLYGON ((2 1, 2 0, 0 0, 0 2, 1 2, 1 1, 2 1))
1    1    1            POLYGON ((2 1, 1 1, 1 2, 2 2, 2 1))
2  NaN    1            POLYGON ((2 1, 2 2, 3 2, 3 1, 2 1))
3  NaN    1            POLYGON ((2 2, 1 2, 1 3, 2 3, 2 2))
4    2  NaN            POLYGON ((3 2, 3 3, 4 3, 4 2, 3 2))
5    2    1            POLYGON ((3 3, 3 2, 2 2, 2 3, 3 3))
6    2  NaN            POLYGON ((3 3, 2 3, 2 4, 3 4, 3 3))
7  NaN    2  POLYGON ((4 3, 4 4, 3 4, 3 5, 5 5, 5 3, 4 3))
8    2    2            POLYGON ((3 4, 4 4, 4 3, 3 3, 3 4))

In [10]: ax = res_union.plot()

In [11]: df1.plot(ax=ax, facecolor='none');

In [12]: df2.plot(ax=ax, facecolor='none');
_images/overlay_example_union.png

The other how operations will return different subsets of those geometries. With how='intersection', it returns only those geometries that are contained by both GeoDataFrames:

In [13]: res_intersection = gpd.overlay(df1, df2, how='intersection')

In [14]: res_intersection
Out[14]: 
   df1  df2                             geometry
0    1    1  POLYGON ((2 1, 1 1, 1 2, 2 2, 2 1))
1    2    1  POLYGON ((3 3, 3 2, 2 2, 2 3, 3 3))
2    2    2  POLYGON ((3 4, 4 4, 4 3, 3 3, 3 4))

In [15]: ax = res_intersection.plot()

In [16]: df1.plot(ax=ax, facecolor='none');

In [17]: df2.plot(ax=ax, facecolor='none');
_images/overlay_example_intersection.png

how='symmetric_difference' is the opposite of 'intersection' and returns the geometries that are only part of one of the GeoDataFrames but not of both:

In [18]: res_symdiff = gpd.overlay(df1, df2, how='symmetric_difference')

In [19]: res_symdiff
Out[19]: 
   df1  df2                                       geometry
0    1  NaN  POLYGON ((2 1, 2 0, 0 0, 0 2, 1 2, 1 1, 2 1))
1  NaN    1            POLYGON ((2 1, 2 2, 3 2, 3 1, 2 1))
2  NaN    1            POLYGON ((2 2, 1 2, 1 3, 2 3, 2 2))
3    2  NaN            POLYGON ((3 2, 3 3, 4 3, 4 2, 3 2))
4    2  NaN            POLYGON ((3 3, 2 3, 2 4, 3 4, 3 3))
5  NaN    2  POLYGON ((4 3, 4 4, 3 4, 3 5, 5 5, 5 3, 4 3))

In [20]: ax = res_symdiff.plot()

In [21]: df1.plot(ax=ax, facecolor='none');

In [22]: df2.plot(ax=ax, facecolor='none');
_images/overlay_example_symdiff.png

To obtain the geometries that are part of df1 but are not contained in df2, you can use how='difference':

In [23]: res_difference = gpd.overlay(df1, df2, how='difference')

In [24]: res_difference
Out[24]: 
   df1   df2                                       geometry
0    1  None  POLYGON ((2 1, 2 0, 0 0, 0 2, 1 2, 1 1, 2 1))
1    2  None            POLYGON ((3 2, 3 3, 4 3, 4 2, 3 2))
2    2  None            POLYGON ((3 3, 2 3, 2 4, 3 4, 3 3))

In [25]: ax = res_difference.plot()

In [26]: df1.plot(ax=ax, facecolor='none');

In [27]: df2.plot(ax=ax, facecolor='none');
_images/overlay_example_difference.png

Finally, with how='identity', the result consists of the surface of df1, but with the geometries obtained from overlaying df1 with df2:

In [28]: res_identity = gpd.overlay(df1, df2, how='identity')

In [29]: res_identity
Out[29]: 
   df1  df2                                       geometry
0    1  NaN  POLYGON ((2 1, 2 0, 0 0, 0 2, 1 2, 1 1, 2 1))
1    1    1            POLYGON ((2 1, 1 1, 1 2, 2 2, 2 1))
2    2  NaN            POLYGON ((3 2, 3 3, 4 3, 4 2, 3 2))
3    2    1            POLYGON ((3 3, 3 2, 2 2, 2 3, 3 3))
4    2  NaN            POLYGON ((3 3, 2 3, 2 4, 3 4, 3 3))
5    2    2            POLYGON ((3 4, 4 4, 4 3, 3 3, 3 4))

In [30]: ax = res_identity.plot()

In [31]: df1.plot(ax=ax, facecolor='none');

In [32]: df2.plot(ax=ax, facecolor='none');
_images/overlay_example_identity.png

Overlay Countries Example

First, we load the countries and cities example datasets and select :

In [33]: world = gpd.read_file(gpd.datasets.get_path('naturalearth_lowres'))

In [34]: capitals = gpd.read_file(gpd.datasets.get_path('naturalearth_cities'))

# Select South Amarica and some columns
In [35]: countries = world[world['continent'] == "South America"]

In [36]: countries = countries[['geometry', 'name']]

# Project to crs that uses meters as distance measure
In [37]: countries = countries.to_crs('+init=epsg:3395')

In [38]: capitals = capitals.to_crs('+init=epsg:3395')

To illustrate the overlay function, consider the following case in which one wishes to identify the “core” portion of each country – defined as areas within 500km of a capital – using a GeoDataFrame of countries and a GeoDataFrame of capitals.

# Look at countries:
In [39]: countries.plot();

# Now buffer cities to find area within 500km.
# Check CRS -- World Mercator, units of meters.
In [40]: capitals.crs
Out[40]: '+init=epsg:3395'

# make 500km buffer
In [41]: capitals['geometry']= capitals.buffer(500000)

In [42]: capitals.plot();
_images/world_basic.png _images/capital_buffers.png

To select only the portion of countries within 500km of a capital, we specify the how option to be “intersect”, which creates a new set of polygons where these two layers overlap:

In [43]: country_cores = gpd.overlay(countries, capitals, how='intersection')
---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
<ipython-input-43-0142b1627c7c> in <module>()
----> 1 country_cores = gpd.overlay(countries, capitals, how='intersection')

//anaconda/envs/py35/lib/python3.5/site-packages/geopandas-0.2-py3.5.egg/geopandas/tools/overlay.py in overlay(df1, df2, how, use_sindex)
    113     # determine spatial relationship
    114     collection = []
--> 115     for fid, newpoly in enumerate(newpolys):
    116         cent = newpoly.representative_point()
    117 

//anaconda/envs/py35/lib/python3.5/site-packages/shapely/ops.py in polygonize(self, lines)
     49         product = lgeos.GEOSPolygonize(byref(geom_array), len(obs))
     50         collection = geom_factory(product)
---> 51         for g in collection.geoms:
     52             clone = lgeos.GEOSGeom_clone(g._geom)
     53             g = geom_factory(clone)

//anaconda/envs/py35/lib/python3.5/site-packages/shapely/geometry/base.py in __iter__(self)
    835         self._update()
    836         for i in range(self.__len__()):
--> 837             yield self._get_geom_item(i)
    838 
    839     def __len__(self):

KeyboardInterrupt: 

In [44]: country_cores.plot();
_images/country_cores.png

Changing the “how” option allows for different types of overlay operations. For example, if we were interested in the portions of countries far from capitals (the peripheries), we would compute the difference of the two.

In [45]: country_peripheries = gpd.overlay(countries, capitals, how='difference')
---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
<ipython-input-45-c647a7c2552d> in <module>()
----> 1 country_peripheries = gpd.overlay(countries, capitals, how='difference')

//anaconda/envs/py35/lib/python3.5/site-packages/geopandas-0.2-py3.5.egg/geopandas/tools/overlay.py in overlay(df1, df2, how, use_sindex)
    127         if use_sindex and df2.sindex is not None:
    128             candidates2 = [x.object for x in
--> 129                            df2.sindex.intersection(newpoly.bounds, objects=True)]
    130         else:
    131             candidates2 = [i for i, x in df2.iterrows()]

//anaconda/envs/py35/lib/python3.5/site-packages/shapely/geometry/base.py in bounds(self)
    446             return ()
    447         else:
--> 448             return self.impl['bounds'](self)
    449 
    450     @property

//anaconda/envs/py35/lib/python3.5/site-packages/shapely/coords.py in __call__(self, this)
    197         temp = c_double()
    198         for i in range(cs_len.value):
--> 199             lgeos.GEOSCoordSeq_getX(cs, i, byref(temp))
    200             x = temp.value
    201             if x < minx: minx = x

KeyboardInterrupt: 

In [46]: country_peripheries.plot();
_images/country_peripheries.png

More Examples

A larger set of examples of the use of overlay can be found here