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# Section 18: Geometry Constructing Functions

All the functions we have seen so far work with geometries "as they are" and returns

analyses of the objects (:command:`ST_Length(geometry)`, :command:`ST_Area(geometry)`),

serializations of the objects (:command:`ST_AsText(geometry)`, :command:`ST_AsGML(geometry)`),

parts of the object (:command:`ST_RingN(geometry,n)`) or

true/false tests (:command:`ST_Contains(geometry,geometry)`, :command:`ST_Intersects(geometry,geometry)`).

"Geometry constructing functions" take geometries as inputs and output new shapes.

# ST_Centroid / ST_PointOnSurface

A common need when composing a spatial query is to replace a polygon feature with a point representation of the feature. This is useful for spatial joins (as discussed in :ref:`polypolyjoins`) because using :command:`ST_Intersects(geometry,geometry)` on two polygon layers often results in double-counting: a polygon on a boundary will intersect an object on both sides; replacing it with a point forces it to be on one side or the other, not both.

:command:`ST_Centroid(geometry)` returns a point that is approximately on the center of mass of the input argument. This simple calculation is very fast, but sometimes not desirable, because the returned point is not necessarily in the feature itself. If the input feature has a convexity (imagine the letter 'C') the returned centroid might not be in the interior of the feature.

:command:`ST_PointOnSurface(geometry)` returns a point that is guaranteed to be inside the input argument. It is substantially more computationally expensive than the centroid operation.

# ST_Buffer

The buffering operation is common in GIS workflows, and is also available in PostGIS. :command:`ST_Buffer(geometry,distance)` takes in a buffer distance and geometry type and outputs a polygon with a boundary the buffer distance away from the input geometry.

For example, if the US Park Service wanted to enforce a marine traffic zone around Liberty Island, they might build a 500 meter buffer polygon around the island. Liberty Island is a single census block in our `nyc_census_blocks` table, so we can easily extract and buffer it.

-- Make a new table with a Liberty Island 500m buffer zone CREATE TABLE libery_island_zone AS SELECT ST_Buffer(the_geom,500) AS the_geom FROM nyc_census_blocks WHERE blkid = '360610001009000'; -- Update the geometry_columns table SELECT Populate_Geometry_Columns();

The :command:`ST_Buffer` function also accepts negative distances and builds inscribed polygons within polygonal inputs. For lines and points you will just get an empty return.

# ST_Intersection

Another classic GIS operation -- the "overlay" -- creates a new coverage by calculating the intersection of two superimposed polygons. The resultant has the property that any polygon in either of the parents can be built by merging polygons in the resultant.

The :command:`ST_Intersection(geometry A, geometry B)` function returns the spatial area (or line, or point) that both arguments have in common. If the arguments are disjoint, the function returns an empty geometry.

-- What is the area these two circles have in common? -- Using ST_Buffer to make the circles! SELECT ST_AsText(ST_Intersection( ST_Buffer('POINT(0 0)', 2), ST_Buffer('POINT(3 0)', 2) ));

# ST_Union

In the previous example we intersected geometries, creating a new geometry that had lines from both the inputs. The :command:`ST_Union` does the reverse; it takes inputs and removes common lines. There are two forms of the :command:`ST_Union` function:

:command:`ST_Union(geometry, geometry)`: A two-argument version that takes in two geometries and returns the merged union. For example, our two-circle example from the previous section looks like this when you replace the intersection with a union.

-- What is the total area these two circles cover? -- Using ST_Buffer to make the circles! SELECT ST_AsText(ST_Union( ST_Buffer('POINT(0 0)', 2), ST_Buffer('POINT(3 0)', 2) ));:command:`ST_Union([geometry])`: An aggregate version that takes in a set of geometries and returns the merged geometry for the entire group. The aggregate ST_Union can be used with the

GROUP BYSQL statement to create carefully merged subsets of basic geometries. It is very powerful,

As an example of :command:`ST_Union` aggregation, consider our `nyc_census_blocks` table. Census geography is carefully constructed so that larger geographies can be built up from smaller ones. So, we can create a census tracts map by merging the blocks that form each tract (as we do later in :ref:`creatingtractstable`). Or, we can create a county map by merging blocks that fall within each county.

To carry out the merge, note that the unique key `blkid` actually embeds information about the higher level geographies. Here are the parts of the key for Liberty Island we used earlier:

360610001009000 = 36 061 00100 9000 36 = State of New York 061 = New York County (Manhattan) 000100 = Census Tract 9 = Census Block Group 000 = Census Block

So, we can create a county map by merging all geometries that share the same first 5 digits of their `blkid`.

-- Create a nyc_census_counties table by merging census blocks CREATE TABLE nyc_census_counties AS SELECT ST_Union(the_geom) AS the_geom, SubStr(blkid,1,5) AS countyid FROM nyc_census_blocks GROUP BY countyid; -- Update the geometry_columns table SELECT Populate_Geometry_Columns();

An area test can confirm that our union operation did not lose any geometry. First, we calculate the area of each individual census block, and sum those areas grouping by census county id.

SELECT SubStr(blkid,1,5) AS countyid, Sum(ST_Area(the_geom)) AS area FROM nyc_census_blocks GROUP BY countyid;

countyid | area ----------+------------------ 36005 | 109807439.720947 36047 | 184906575.839355 36061 | 58973521.6225586 36081 | 283764734.207275 36085 | 149806077.958252

Then we calculate the area of each of our new county polygons from the county table:

SELECT countyid, ST_Area(the_geom) AS area FROM nyc_census_counties;

countyid | area ----------+------------------ 36005 | 109807439.720947 36047 | 184906575.839355 36061 | 58973521.6225586 36081 | 283764734.207275 36085 | 149806077.958252

The same answer! We have successfully built an NYC county table from our census blocks data.

# Function List

ST_AsText(text): Returns the Well-Known Text (WKT) representation of the geometry/geography without SRID metadata.

ST_Buffer(geometry, distance): For geometry: Returns a geometry that represents all points whose distance from this Geometry is less than or equal to distance. Calculations are in the Spatial Reference System of this Geometry. For geography: Uses a planar transform wrapper.

ST_Intersection(geometry A, geometry B): Returns a geometry that represents the shared portion of geomA and geomB. The geography implementation does a transform to geometry to do the intersection and then transform back to WGS84.

ST_Union(): Returns a geometry that represents the point set union of the Geometries.

substring(string [from int] [for int]): PostgreSQL string function to extract substring matching SQL regular expression.

sum(expression): PostgreSQL aggregate function that returns the sum of records in a set of records.

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