In surveying, we strive for the highest accuracy and precision possible. However, this is not always the case in mapmaking. Too-detailed geometries on small scale (zoomed-out) maps are bad for human perception; edges or lines appear jagged, and cause an unnecessary burden on the computer in trying to render them. For that reason, cartographers generalize the geometries used for mapmaking. There are a few algorithms designed for automated generalization. PostGIS provides an implementation of a widely used Douglas-Peucker algorithm in a ST_Simplify function.

The function accepts two arguments, the first being a geometry to be simplified, and the second being a tolerance parameter defining how aggressive the simplification can be. Tolerance is given in the same units as the geometry's coordinate system, and the bigger it is, the more simplified the output geometry becomes.

Here are some examples of simplification:

River meanders simplified with 50 (green) and 100 (red)...

Invalid geometries are a spatial analyst's nightmare. They can appear in any dataset, and can break a carefully-designed, long-running query in the middle of execution. Or even worse, a failing query might break an application's functionality. Luckily, PostGIS is equipped with the tools to find and repair them.

Simplicity and validity

In PostGIS, there are two concepts: simplicity and validity. For most spatial analyses to succeed, input geometries have to be both simple and valid. Here are some rules:

• Does not have repeated points (with the exception of closed rings, whose first and last point are identical)
• Does not self-intersect

• A point must always be simple and valid
• A MultiPoint must always be valid, and simple when there are no repeated points with identical coordinates
• A LineString or MultiLineString must always be valid, and is simple if the line:

Example of a non-simple line: self-intersecting autogenerated contours.

A polygon is always simple, and is valid if:

• All interior...

In PostGIS, there are two ways in which geometries can be intersected. The first way is checking whether two geometries intersect (at least one point of geometry A lies within the interior of geometry B). That's the ST_Intersects function. It accepts two arguments of the geometry type, and returns a Boolean.

For example, these lines intersect:

SELECT ST_Intersects(
    ST_MakeLine(ST_MakePoint(20,50),ST_MakePoint(21,51)),
    ST_MakeLine(ST_MakePoint(20.5,50.5), ST_MakePoint(22,52))
);

But these lines don't:

 st_intersects
---------------
 t

SELECT ST_Intersects(
    ST_MakeLine(ST_MakePoint(20,50),ST_MakePoint(21,51)),
    ST_MakeLine(ST_MakePoint(21.5,51.5), ST_MakePoint(22,52))
);

 st_intersects
---------------
 f

ST_Intersects can also be used for table joining. The following query will return land features that had at least one earthquake:

SELECT ne_110m_land.* FROM data_import.ne_110m_land JOIN data_import.earthquakes_subset_with_geom ON ST_Intersects(ne_110m_land...

This is a key feature for almost any location-based application: given a current location, it will return the nearest feature (or list of nearest features, ordered by distance).

The naive approach to this problem would be to query the table ordering by ST_Distance. Let's find the five earthquakes closest to San Juan:

SELECT * FROM data_import.earthquakes_subset_with_geom
ORDER BY ST_Distance(geom::geography, ST_SetSRID(ST_MakePoint(-66.11,18.46),4326)::geography)
LIMIT 5;

   id     |           time           | depth | mag | magtype |                       place                       |                        geom                       
------------+--------------------------+-------+-----+---------+---------------------------------------------------+----------------------------------------------------
 pr16281009 | 2016-10-08 01:08:46.4+02 |     5 | 2.5 | Md      | 28km SE of El Negro, Puerto Rico                  | 0101000020E610000062A1D634EF6850C0E561A1D634DF3140...

Spatial analysis functions are a key feature for spatial databases, and PostGIS has a very rich set of them. One can compose geometries from raw coordinates, compose geometries into more complex shapes, break down complex shapes into elementary geometries, calculate spatial metrics, and query features based on their location. Spatial analysis functions require the geometries to conform to a specification, so validation and automated repair functions are also provided.

Most spatial analysis functions are easy to understand, but special attention must be paid to coordinate systems. When using latitude-longitude coordinate systems, it's best to use the geography data type to ensure the calculated measurements are correct.