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SQL (POSTGIS), 286 269 261 240 226 218

This is a query for the PostGIS extension to PostgreSQL. I haven't counted the input values in the total.

SELECT SUM(1)FROM(SELECT(ST_Dump(ST_Polygonize(g))).geom d FROM (SELECT ST_Union(ST_Boundary(ST_MakeEnvelope(a,b,c,d)))g FROM(VALUES
-- Coordinate input
(2, 1, 3, 11)
,(1, 10, 5, 19)
,(6, 10, 11, 3)
,(8, 8, 15, 15)
,(13, 13, 9, 5)
,(15, 1, 19, 7)
,(17, 19, 19, 17)
)i(a,b,c,d))i)a WHERE(ST_XMax(d)-ST_XMin(d))^2+(ST_YMax(d)-ST_YMin(d))^2=ST_Area(d)*2

Explanation

The query builds geometries for each coordinate pair. Unions the exterior rings to properly node the lines. Turns the results into polygons and tests the width against height and the area doubled against the sum of each side squared.

It will run as a standalone query on any PostgreSQL database with the PostGIS Extension.

SQL (POSTGIS), 286 269 261 240 226 218 216

This is a query for the PostGIS extension to PostgreSQL. I haven't counted the input values in the total.

SELECT SUM(1)FROM(SELECT(ST_Dump(ST_Polygonize(g))).geom d FROM(SELECT ST_Union(ST_Boundary(ST_MakeEnvelope(a,b,c,d)))g FROM(VALUES
-- Coordinate input
(2, 1, 3, 11)
,(1, 10, 5, 19)
,(6, 10, 11, 3)
,(8, 8, 15, 15)
,(13, 13, 9, 5)
,(15, 1, 19, 7)
,(17, 19, 19, 17)
)i(a,b,c,d))i)a WHERE(ST_XMax(d)-ST_XMin(d))^2+(ST_YMax(d)-ST_YMin(d))^2=ST_Area(d)*2

Explanation

The query builds geometries for each coordinate pair. Unions the exterior rings to properly node the lines. Turns the results into polygons and tests the width against height and the area doubled against the sum of each side squared.

It will run as a standalone query on any PostgreSQL database with the PostGIS Extension.

Edit Found a couple more.

SQL (POSTGIS), 286 269 261 240 226

This is a query for the PostGIS extension to PostgreSQL. I haven't counted the input values in the total.

WITH I AS(SELECT ST_Union(ST_Boundary(ST_MakeEnvelope(a,b,c,d)))g FROM(VALUES
-- Coordinate input
(2, 1, 3, 11)
,(1, 10, 5, 19)
,(6, 10, 11, 3)
,(8, 8, 15, 15)
,(13, 13, 9, 5)
,(15, 1, 19, 7)
,(17, 19, 19, 17)
)i(a,b,c,d))SELECT SUM(1)FROM(SELECT(ST_Dump(ST_Polygonize(g))).geom d FROM i)a WHERE(ST_XMax(d)-ST_XMin(d))^2+(ST_YMax(d)-ST_YMin(d))^2=ST_Area(d)*2

Explanation

The query builds geometries for each coordinate pair. Unions the exterior rings to properly node the lines. Turns the results into polygons and tests the width against height and the area doubled against the sum of each side squared.

It will run as a standalone query on any PostgreSQL database with the PostGIS Extension.

SQL (POSTGIS), 286 269 261 240 226 218

This is a query for the PostGIS extension to PostgreSQL. I haven't counted the input values in the total.

SELECT SUM(1)FROM(SELECT(ST_Dump(ST_Polygonize(g))).geom d FROM (SELECT ST_Union(ST_Boundary(ST_MakeEnvelope(a,b,c,d)))g FROM(VALUES
-- Coordinate input
(2, 1, 3, 11)
,(1, 10, 5, 19)
,(6, 10, 11, 3)
,(8, 8, 15, 15)
,(13, 13, 9, 5)
,(15, 1, 19, 7)
,(17, 19, 19, 17)
)i(a,b,c,d))i)a WHERE(ST_XMax(d)-ST_XMin(d))^2+(ST_YMax(d)-ST_YMin(d))^2=ST_Area(d)*2

Explanation

The query builds geometries for each coordinate pair. Unions the exterior rings to properly node the lines. Turns the results into polygons and tests the width against height and the area doubled against the sum of each side squared.

It will run as a standalone query on any PostgreSQL database with the PostGIS Extension.

SQL (POSTGIS), 286 269 261 240

This is a query for the PostGIS extension to PostgreSQL. I haven't counted the input values in the total.

WITH I AS(SELECT ST_Union(ST_Boundary(ST_MakeEnvelope(a,b,c,d)))g FROM(VALUES
-- Coordinate input
(2, 1, 3, 11)
,(1, 10, 5, 19)
,(6, 10, 11, 3)
,(8, 8, 15, 15)
,(13, 13, 9, 5)
,(15, 1, 19, 7)
,(17, 19, 19, 17)
)i(a,b,c,d))SELECT COUNT(*)FROM(SELECT(ST_Dump(ST_Polygonize(g))).geom d FROM i)a WHERE ST_Area(d)=(ST_XMax(d)-ST_XMin(d))^2AND(ST_YMax(d)-ST_YMin(d))^2=ST_Area(d)

Explanation

The query builds geometries for each coordinate pair. Unions the exterior rings to properly node the lines. Turns the results into polygons and tests the width against height and the area against each side squared.

It will run as a standalone query on any PostgreSQL database with the PostGIS Extension.

SQL (POSTGIS), 286 269 261 240 226

This is a query for the PostGIS extension to PostgreSQL. I haven't counted the input values in the total.

WITH I AS(SELECT ST_Union(ST_Boundary(ST_MakeEnvelope(a,b,c,d)))g FROM(VALUES
-- Coordinate input
(2, 1, 3, 11)
,(1, 10, 5, 19)
,(6, 10, 11, 3)
,(8, 8, 15, 15)
,(13, 13, 9, 5)
,(15, 1, 19, 7)
,(17, 19, 19, 17)
)i(a,b,c,d))SELECT SUM(1)FROM(SELECT(ST_Dump(ST_Polygonize(g))).geom d FROM i)a WHERE(ST_XMax(d)-ST_XMin(d))^2+(ST_YMax(d)-ST_YMin(d))^2=ST_Area(d)*2

Explanation

The query builds geometries for each coordinate pair. Unions the exterior rings to properly node the lines. Turns the results into polygons and tests the width against height and the area doubled against the sum of each side squared.

It will run as a standalone query on any PostgreSQL database with the PostGIS Extension.