PostGIS Performance: Simplification

There’s nothing simple about simplification! It is very common to want to slim down the size of geometries, and there are lots of different approaches to the problem.

We will explore different methods starting with ST_Letters for this rendering of the letter “a”.

SELECT ST_Letters('a');

This is a good starting point, but to show the different effects of different algorithms on things like redundant linear points, we need a shape with more vertices along the straights, and fewer along the curves.

SELECT ST_RemoveRepeatedPoints(ST_Segmentize(ST_Letters('a'), 1), 1);

Here we add in vertices every one meter with ST_Segmentize and ST_RemoveRepeatedPoints to thin out the points along the curves. Already we are simplifying!

Lets apply the same “remove repeated” algorithm, with a 10 meter tolerance.

WITH a AS (
  SELECT ST_RemoveRepeatedPoints(ST_Segmentize(ST_Letters('a'), 1), 1) AS a
)
SELECT ST_RemoveRepeatedPoints(a, 10) FROM a;

We do have a lot fewer points, and the constant angle curves are well preserved, but some straight lines are no longer legible as such, and there are redundant vertices in the vertical straight lines.

The ST_Simplify function applies the Douglas-Peuker line simplification algorithm to the rings of the polygon. Because it is a line simplifier it does a cruder job preserving some aspects of the polygon area like squareness of the top ligature.

WITH a AS (
  SELECT ST_RemoveRepeatedPoints(ST_Segmentize(ST_Letters('a'), 1), 1) AS a
)
SELECT ST_Simplify(a, 1) FROM a;

The ST_SimplifyVW function applies the Visvalingam–Whyatt algorithm to the rings of the polygon. Visvalingam–Whyatt is better for preserving the shapes of polygons than Douglas-Peuker, but the differences are subtle.

WITH a AS (
  SELECT ST_RemoveRepeatedPoints(ST_Segmentize(ST_Letters('a'), 1), 1) AS a
)
SELECT ST_SimplifyVW(a, 5) FROM a;

Coercing a shape onto a fixed precision grid is another form of simplification, sometimes used to force the edges of adjacent objects to line up exactly. The original such function, ST_SnapToGrid, does exactly what it says on the name. Every vertex is rounded to a fixed grid point.

WITH a AS (
  SELECT ST_RemoveRepeatedPoints(ST_Segmentize(ST_Letters('a'), 1), 1) AS a
)
SELECT ST_SnapToGrid(a, 5) FROM a;

However, as you can see at the top left, the grid snapper frequently generates invalidity in polygons, such as the self-intersecting ring in this example.

A more modern alternative is precision reduction.

WITH a AS (
  SELECT ST_RemoveRepeatedPoints(ST_Segmentize(ST_Letters('a'), 1), 1) AS a
)
SELECT ST_ReducePrecision(a, 5) FROM a;

The ST_ReducePrecision function not only snaps geometries to a fixed precision grid, it also ensures that outputs are always valid.

Because grid snapping tends to introduce a lot of vertices along straight edges, combining it with a line simplifier makes a lot of sense.

WITH a AS (
  SELECT ST_RemoveRepeatedPoints(ST_Segmentize(ST_Letters('a'), 1), 1) AS a
)
SELECT ST_Simplify(ST_ReducePrecision(a, 5),1) FROM a;

Simplifying single geometries is all well and good, but what about simplifying groups of geometries? Specifically ones that share boundaries?

Fortunately, since PostGIS 3.6 there is now a complete set of functions for that problem.

Starting with a pair of polygons with a non-matched shared boundary.

Non-clean boundaries can be cleaned up with the ST_CoverageClean function.

SELECT ST_CoverageClean OVER() AS geom FROM polys;

And once the coverage is clean, the shapes including their shared borders can be simplified with ST_CoverageSimplify.

WITH clean AS (
  SELECT ST_CoverageClean OVER() AS geom FROM polys
)
SELECT ST_CoverageSimplify(geom, 10) OVER() FROM clean