ST_Equals Geometry Checker

How the ST_Equals Geometry Checker works, and what it assumes

ST_Equals(A, B) is true when the two geometries contain exactly the same points. It compares space, not text: the order the vertices are listed in, the vertex a ring starts at, the direction it runs and extra vertices along a straight edge make no difference. The DE-9IM pattern is T*F**FFF*, which says that neither geometry has any part in the other's exterior.

That makes it the right test for "has this shape changed?", where comparing WKT strings would report a difference for a geometry that was merely rewritten by another program. PostGIS has ST_OrderingEquals for the stricter, vertex-by-vertex comparison.

Two empty geometries are equal in PostGIS, and here, although their DE-9IM matrix on its own would not say so; the page states when that rule has been applied. Elevations are ignored, because the comparison is two-dimensional.

Where this comes up in GIS work

• Checking whether a geometry changed between two versions of a dataset, ignoring harmless reordering.
• Confirming that a round trip through another format or system kept the shape intact.
• Finding duplicate features whose coordinates are written differently.

A worked example

The same square, written from a different corner, in the opposite direction, with an extra vertex half-way up one side:

A: POLYGON ((0 0, 6 0, 6 6, 0 6, 0 0))
B: POLYGON ((6 6, 0 6, 0 3, 0 0, 6 0, 6 6))

ST_Equals(A, B) = true
DE-9IM matrix: 2FFF1FFF2

The texts differ in every position, and an exact vertex-by-vertex comparison says they are different geometries. Lines behave the same way: LINESTRING (0 0, 10 0) equals LINESTRING (10 0, 5 0, 0 0).

Using the ST_Equals Geometry Checker

1. Paste the first geometry into Geometry A, or select Load example.
2. Paste the geometry to compare into Geometry B.
3. Select Check ST_Equals, or press Ctrl + Enter (Cmd + Enter on a Mac).
4. Read the verdict; if they differ, the matrix shows whether one extends beyond the other.

When the output looks wrong

The WKT text differs but ST_Equals is true

That is the point of it. ST_Equals compares the space the geometries cover, so a different starting vertex, the opposite direction or an extra vertex on a straight edge make no difference. For an exact vertex-by-vertex match, PostGIS has ST_OrderingEquals.

The shapes look identical but ST_Equals is false

Somewhere the coordinates differ, perhaps only in the sixth decimal place after a round trip through another system. The matrix shows which part lies outside the other. Rounding both to the same precision before comparing usually settles it.

A polygon and its outline are not equal

They are different dimensions: the polygon is an area and its outline is a line, so they cannot cover the same space.

Questions about the ST_Equals Geometry Checker