Extended topological relations for line objects

This repository contains SQL functions which enable the extended topological relations for line objects to be computed. These relations extend on the 9 Intersection Model (9IM) in order to show if the relations of the line object with other objects are symmetrical (i.e. present on both sides) or not.

Reference:

Majic I., Naghizade E., Winter S., & Tomko M. (2019) Discovery of topological constraints on spatial object classes using an extended topological model. Journal of Spatial Information Science, 2019(18).

Examples

All the examples below show how the functions for the extended topological relations work on a simple scenario with bridge that crosses a river and is connected to roads on both sides.

Function relate_simple

Function relate_simple transforms the result of the PostGIS function ST_Relate from the Dimensionally Extended 9 Intersection Model (DE-9IM) into the 9IM.

SELECT relate_simple(st_geomfromtext('LINESTRING(3 2, 5 2)'), geom), object_class
FROM (VALUES 
		(st_geomfromtext('LINESTRING(0 2, 3 2)'), 'road1'),
		(st_geomfromtext('LINESTRING(5 2, 7 4)'), 'road2'),
		(st_geomfromtext('LINESTRING(5 2, 7 0)'), 'road3'),
		(st_geomfromtext('LINESTRING(4 4, 4 0)'), 'river')
	) AS v (geom, object_class);

relate_simple	object_class
FFTFTTTTT	road1
FFTFTTTTT	road2
FFTFTTTTT	road3
TFTFFTTTT	river

Function relate_line

Function relate_line looks at the topological relations that a given line object has with other objects, and determines if they are related to its start point, to its end point, or both.

SELECT relate_line(st_geomfromtext('LINESTRING(3 2, 5 2)'), geom), object_class
FROM (VALUES 
		(st_geomfromtext('LINESTRING(0 2, 3 2)'), 'road1'),
		(st_geomfromtext('LINESTRING(5 2, 7 4)'), 'road2'),
		(st_geomfromtext('LINESTRING(5 2, 7 0)'), 'road3'),
		(st_geomfromtext('LINESTRING(4 4, 4 0)'), 'river')
	) AS v (geom, object_class);

relate_line	object_class
FFTFSETTT	road1
FFTFESTTT	road2
FFTFESTTT	road3
TFTFFBTTT	river

Function bridge_relations_sides

Function bridge_relations_sides then determines if the relations are present on the both sides of the given line object or not. If the relation is present on both sides, it gets the appendix 'both', and if it is present only on one side of the given line object it gets the appendix 'single'.

The first SQL example shows how the topological relations of a single line object need to be arranged for input in the bridge_relations_sides function.

SELECT array_agg(relate_line(st_geomfromtext('LINESTRING(3 2, 5 2)'), geom))
FROM (VALUES 
		(st_geomfromtext('LINESTRING(0 2, 3 2)'), 'road1'),
		(st_geomfromtext('LINESTRING(5 2, 7 4)'), 'road2'),
		(st_geomfromtext('LINESTRING(5 2, 7 0)'), 'road3'),
		(st_geomfromtext('LINESTRING(4 4, 4 0)'), 'river')
	) AS v (geom, object_class);

array_agg
{FFTFSETTT,FFTFESTTT,FFTFESTTT,TFTFFBTTT}

WITH rels AS (SELECT array_agg(relate_line(st_geomfromtext('LINESTRING(3 2, 5 2)'), geom)) AS relations
FROM (VALUES 
		(st_geomfromtext('LINESTRING(0 2, 3 2)'), 'road1'),
		(st_geomfromtext('LINESTRING(5 2, 7 4)'), 'road2'),
		(st_geomfromtext('LINESTRING(5 2, 7 0)'), 'road3'),
		(st_geomfromtext('LINESTRING(4 4, 4 0)'), 'river')
		) AS v (geom, object_class))
SELECT bridge_relations_sides(relations) FROM rels;

bridge_relations_sides
{FFTFTTTTT-both,FFTFTTTTT-single,TFTFFBTTT}