I tried some functions in postgis. Scope of work, get the equality of two shapes, independently of their orientation in the space. I detect the shapes from autocad and of course in lifetime of a project, can happen that two shapes in two different draws are oriented int different way. so i tried the very first relationship, get difference of mirrored shapes(this was my very first trouble):

select st_equals(
ST_GeomFromEWKT('TRIANGLE ((0 0, 5 10, 30 0, 0 0))'),
ST_GeomFromEWKT('TRIANGLE ((0 0, 5 -10, 30 0, 0 0))')) 

And i get False. Perfect. But I was not more happy, when i just tried to rotate the geometry:

select st_equals(
ST_GeomFromEWKT('TRIANGLE ((0 0, 5 10, 30 0, 0 0))'),
ST_GeomFromEWKT('TRIANGLE ((0 0, -10 5, 0 30, 0 0))'))

These are the same triangle, just rotate of 90°,I get also False. Is postgis able to define the equality of shapes, also if are rotate in the space?

  • You could try comparing the area and the angles. Since angles won't necessarily be in the same order, you'll need to sort them with array functions before comparison.
    – ffflabs
    Jul 5, 2015 at 2:18
  • Also do you consider traslated geometries as equals?, that is a geometry with the same angles and area but in different positions in space. To measure angles probably you can use something like this gis.stackexchange.com/questions/78665/… Jul 5, 2015 at 8:58
  • I would need to define an unique reference point. And this becomes hard. Currently, I wrote a routine that detect the most significantly side. But if you have a square you have 4 significantly sides. And if you have an hole inside, no way to know where is going to fall.
    – jurhas
    Jul 5, 2015 at 9:55
  • @Amenadiel : these are mechanical parts, think shape H or C-shape, or more complex, all the angles are equal and a lot of sides are also equal. The best way is to define diagonals. But the comparison is ok. The problem is the mirrored shape. Until now the only thing, is a make analysis of the new shape, identify his 0-point, and than runa comparison point by point. But for square or something with high symmetry which is 0 point? Becomes something pervert...
    – jurhas
    Jul 5, 2015 at 10:48

1 Answer 1


There are a couple of questions about equality in this site

What is the PostGIS 2.x equivalent of the pre-PostGIS 1.5 ~= operator?

ST_Equals Postgis problems

The geometries of your example are not "spatially equals", not share the same space, so st_equals will return always false. What output do you expect?

enter image description here

Code used to generate the image:

from matplotlib import pyplot as plt
from shapely.geometry.polygon import LinearRing, Polygon

poly = Polygon ([(0, 0), (5, 10), (30, 0), (0, 0)])
x,y = poly.exterior.xy
fig = plt.figure(1, figsize=(5,5), dpi=90)
ax = fig.add_subplot(111)
ax.plot(x, y)
poly2 = Polygon ([(0, 0), (5, -10), (30, 0), (0, 0)])
x2,y2 = poly2.exterior.xy
ax.plot(x2, y2)
  • My target is to define if two shapes are equal. Doesn't not matter the absolute position, or rotation. I achived it with my code, but I cannot find an easy way to detect if a shape is " mirrored" such in your picture. For my code these two shapes are the same because all the sides and angles are equal. It should be if I could turn it on the other site. But not ever it is possible.
    – jurhas
    Jul 4, 2015 at 11:11
  • 1
    ST_NPoints(), ST_Area() and ST_Perimeter() taken together will provide a bit of a "signature" of particular shapes, though if you also allow scale to vary you're down to having to analyze angles, etc, which you'll have to write your own routines for. Jul 8, 2015 at 11:49

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