# Geometric operations¶

## Overlay analysis¶

In this tutorial, the aim is to make an overlay analysis where we create a new layer based on geometries from a dataset that `intersect`

with geometries of another layer. As our test case, we will select Polygon grid cells from `TravelTimes_to_5975375_RailwayStation_Helsinki.shp`

that intersects with municipality borders of Helsinki found in `Helsinki_borders.shp`

.

Typical overlay operations are (source: QGIS docs):

## Download data¶

For this lesson, you should download a data package that includes 3 files:

- Helsinki_borders.shp
- Travel_times_to_5975375_RailwayStation.shp
- Amazon_river.shp

```
$ cd /home/jovyan/notebooks/L4
$ wget https://github.com/AutoGIS/data/raw/master/L4_data.zip
$ unzip L4_data.zip
```

Let’s first read the data and see how they look like.

- Import required packages and read in the input data:

```
[1]:
```

```
import geopandas as gpd
import matplotlib.pyplot as plt
import shapely.speedups
%matplotlib inline
# File paths
border_fp = "data/Helsinki_borders.shp"
grid_fp = "data/TravelTimes_to_5975375_RailwayStation.shp"
# Read files
grid = gpd.read_file(grid_fp)
hel = gpd.read_file(border_fp)
```

- Visualize the layers:

```
[2]:
```

```
# Plot the layers
ax = grid.plot(facecolor='gray')
hel.plot(ax=ax, facecolor='None', edgecolor='blue')
```

```
[2]:
```

```
<matplotlib.axes._subplots.AxesSubplot at 0x2552bc671d0>
```

Here the grey area is the Travel Time Matrix grid (13231 grid squares) that covers the Helsinki region, and the blue area represents the municipality of Helsinki. Our goal is to conduct an overlay analysis and select the geometries from the grid polygon layer that intersect with the Helsinki municipality polygon.

When conducting overlay analysis, it is important to check that the CRS of the layers match!

- Check if Helsinki polygon and the grid polygon are in the same crs:

```
[3]:
```

```
# Ensure that the CRS matches, if not raise an AssertionError
assert hel.crs == grid.crs, "CRS differs between layers!"
```

Indeed, they do. Hence, the pre-requisite to conduct spatial operations between the layers is fullfilled (also the map we plotted indicated this).

- Let’s do an overlay analysis and create a new layer from polygons of the grid that
`intersect`

with our Helsinki layer. We can use a function called`overlay()`

to conduct the overlay analysis that takes as an input 1) the GeoDataFrame where the selection is taken, 2) the GeoDataFrame used for making the selection, and 3) parameter`how`

that can be used to control how the overlay analysis is conducted (possible values are`'intersection'`

,`'union'`

,`'symmetric_difference'`

,`'difference'`

, and`'identity'`

):

```
[4]:
```

```
intersection = gpd.overlay(grid, hel, how='intersection')
```

- Let’s plot our data and see what we have:

```
[5]:
```

```
intersection.plot(color="b")
```

```
[5]:
```

```
<matplotlib.axes._subplots.AxesSubplot at 0x2552bd9afd0>
```

As a result, we now have only those grid cells that intersect with the Helsinki borders. As we can see **the grid cells are clipped based on the boundary.**

- Whatabout the data attributes? Let’s see what we have:

```
[6]:
```

```
print(intersection.head())
```

```
car_m_d car_m_t car_r_d car_r_t from_id pt_m_d pt_m_t pt_m_tt \
0 29476 41 29483 46 5876274 29990 76 95
1 29456 41 29462 46 5876275 29866 74 95
2 36772 50 36778 56 5876278 33541 116 137
3 36898 49 36904 56 5876279 33720 119 141
4 29411 40 29418 44 5878128 29944 75 95
pt_r_d pt_r_t pt_r_tt to_id walk_d walk_t GML_ID NAMEFIN \
0 24984 77 99 5975375 25532 365 27517366 Helsinki
1 24860 75 93 5975375 25408 363 27517366 Helsinki
2 44265 130 146 5975375 31110 444 27517366 Helsinki
3 44444 132 155 5975375 31289 447 27517366 Helsinki
4 24938 76 99 5975375 25486 364 27517366 Helsinki
NAMESWE NATCODE geometry
0 Helsingfors 091 POLYGON ((402250.0001322526 6685750.000039577,...
1 Helsingfors 091 POLYGON ((402367.8898583531 6685750.000039573,...
2 Helsingfors 091 POLYGON ((403250.000132058 6685750.000039549, ...
3 Helsingfors 091 POLYGON ((403456.4840652301 6685750.000039542,...
4 Helsingfors 091 POLYGON ((402000.0001323065 6685500.000039622,...
```

As we can see, due to the overlay analysis, the dataset contains the attributes from both input layers.

- Let’s save our result grid as a GeoJSON file that is commonly used file format nowadays for storing spatial data.

```
[7]:
```

```
# Output filepath
outfp = "data/TravelTimes_to_5975375_RailwayStation_Helsinki.geojson"
# Use GeoJSON driver
intersection.to_file(outfp, driver="GeoJSON")
```

There are many more examples for different types of overlay analysis in Geopandas documentation where you can go and learn more.

## Aggregating data¶

Data aggregation refers to a process where we combine data into groups. When doing spatial data aggregation, we merge the geometries together into coarser units (based on some attribute), and can also calculate summary statistics for these combined geometries from the original, more detailed values. For example, suppose that we are interested in studying continents, but we only have country-level data like the country dataset. If we aggregate the data by continent, we would convert the country-level data into a continent-level dataset.

In this tutorial, we will aggregate our travel time data by car travel times (column `car_r_t`

), i.e. the grid cells that have the same travel time to Railway Station will be merged together.

- For doing the aggregation we will use a function called
`dissolve()`

that takes as input the column that will be used for conducting the aggregation:

```
[8]:
```

```
# Conduct the aggregation
dissolved = intersection.dissolve(by="car_r_t")
# What did we get
print(dissolved.head())
```

```
geometry car_m_d car_m_t \
car_r_t
-1 (POLYGON ((388000.0001354803 6668750.0000429, ... -1 -1
0 POLYGON ((386000.0001357812 6672000.000042388,... 0 0
7 POLYGON ((386250.0001357396 6671750.000042424,... 1051 7
8 (POLYGON ((386250.0001357467 6671500.000042468... 1286 8
9 (POLYGON ((387000.0001355996 6671500.000042449... 1871 9
car_r_d from_id pt_m_d pt_m_t pt_m_tt pt_r_d pt_r_t pt_r_tt \
car_r_t
-1 -1 5913094 -1 -1 -1 -1 -1 -1
0 0 5975375 0 0 0 0 0 0
7 1051 5973739 617 5 6 617 5 6
8 1286 5973736 706 10 10 706 10 10
9 1871 5970457 1384 11 13 1394 11 12
to_id walk_d walk_t GML_ID NAMEFIN NAMESWE NATCODE
car_r_t
-1 -1 -1 -1 27517366 Helsinki Helsingfors 091
0 5975375 0 0 27517366 Helsinki Helsingfors 091
7 5975375 448 6 27517366 Helsinki Helsingfors 091
8 5975375 706 10 27517366 Helsinki Helsingfors 091
9 5975375 1249 18 27517366 Helsinki Helsingfors 091
```

- Let’s compare the number of cells in the layers before and after the aggregation:

```
[9]:
```

```
print('Rows in original intersection GeoDataFrame:', len(intersection))
print('Rows in dissolved layer:', len(dissolved))
```

```
Rows in original intersection GeoDataFrame: 3826
Rows in dissolved layer: 51
```

Indeed the number of rows in our data has decreased and the Polygons were merged together.

What actually happened here? Let’s take a closer look.

- Let’s see what columns we have now in our GeoDataFrame:

```
[10]:
```

```
print(dissolved.columns)
```

```
Index(['geometry', 'car_m_d', 'car_m_t', 'car_r_d', 'from_id', 'pt_m_d',
'pt_m_t', 'pt_m_tt', 'pt_r_d', 'pt_r_t', 'pt_r_tt', 'to_id', 'walk_d',
'walk_t', 'GML_ID', 'NAMEFIN', 'NAMESWE', 'NATCODE'],
dtype='object')
```

As we can see, the column that we used for conducting the aggregation (`car_r_t`

) can not be found from the columns list anymore. What happened to it?

- Let’s take a look at the indices of our GeoDataFrame:

```
[11]:
```

```
print(dissolved.index)
```

```
Int64Index([-1, 0, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38,
39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54,
56],
dtype='int64', name='car_r_t')
```

Aha! Well now we understand where our column went. It is now used as index in our `dissolved`

GeoDataFrame.

- Now, we can for example select only such geometries from the layer that are for example exactly 15 minutes away from the Helsinki Railway Station:

```
[12]:
```

```
# Select only geometries that are within 15 minutes away
dissolved.iloc[15]
```

```
[12]:
```

```
geometry (POLYGON ((388250.0001354316 6668750.000042891...
car_m_d 12035
car_m_t 18
car_r_d 11997
from_id 5903886
pt_m_d 11568
pt_m_t 30
pt_m_tt 36
pt_r_d 11568
pt_r_t 34
pt_r_tt 37
to_id 5975375
walk_d 11638
walk_t 166
GML_ID 27517366
NAMEFIN Helsinki
NAMESWE Helsingfors
NATCODE 091
Name: 20, dtype: object
```

```
[13]:
```

```
# See the data type
print(type(dissolved.iloc[15]))
```

```
<class 'pandas.core.series.Series'>
```

```
[14]:
```

```
# See the data
print(dissolved.iloc[15].head())
```

```
geometry (POLYGON ((388250.0001354316 6668750.000042891...
car_m_d 12035
car_m_t 18
car_r_d 11997
from_id 5903886
Name: 20, dtype: object
```

As we can see, as a result, we have now a Pandas `Series`

object containing basically one row from our original aggregated GeoDataFrame.

Let’s also visualize those 15 minute grid cells.

- First, we need to convert the selected row back to a GeoDataFrame:

```
[15]:
```

```
# Create a GeoDataFrame
selection = gpd.GeoDataFrame([dissolved.iloc[15]], crs=dissolved.crs)
```

- Plot the selection on top of the entire grid:

```
[16]:
```

```
# Plot all the grid cells, and the grid cells that are 15 minutes a way from the Railway Station
ax = dissolved.plot(facecolor='gray')
selection.plot(ax=ax, facecolor='red')
```

```
[16]:
```

```
<matplotlib.axes._subplots.AxesSubplot at 0x2552c25be10>
```

## Simplifying geometries¶

Sometimes it might be useful to be able to simplify geometries. This could be something to consider for example when you have very detailed spatial features that cover the whole world. If you make a map that covers the whole world, it is unnecessary to have really detailed geometries because it is simply impossible to see those small details from your map. Furthermore, it takes a long time to actually render a large quantity of features into a map. Here, we will see how it is possible to simplify geometric features in Python.

As an example we will use data representing the Amazon river in South America, and simplify it’s geometries.

- Let’s first read the data and see how the river looks like:

```
[17]:
```

```
import geopandas as gpd
# File path
fp = "data/Amazon_river.shp"
data = gpd.read_file(fp)
# Print crs
print(data.crs)
# Plot the river
data.plot();
```

```
{'ellps': 'GRS80', 'lat_ts': -2, 'y_0': 10000000, 'units': 'm', 'x_0': 5000000, 'proj': 'merc', 'no_defs': True, 'lon_0': -43}
```

The LineString that is presented here is quite detailed, so let’s see how we can generalize them a bit. As we can see from the coordinate reference system, the data is projected in a metric system using Mercator projection based on SIRGAS datum.

- Generalization can be done easily by using a Shapely function called
`.simplify()`

. The`tolerance`

parameter can be used to adjusts how much geometries should be generalized.**The tolerance value is tied to the coordinate system of the geometries**. Hence, the value we pass here is 20 000**meters**(20 kilometers).

```
[18]:
```

```
# Generalize geometry
data['geom_gen'] = data.simplify(tolerance=20000)
# Set geometry to be our new simlified geometry
data = data.set_geometry('geom_gen')
# Plot
data.plot()
```

```
[18]:
```

```
<matplotlib.axes._subplots.AxesSubplot at 0x2552bd5add8>
```

Nice! As a result, now we have simplified our LineString quite significantly as we can see from the map.