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ST_Relate translator edit
The PostGIS (and similar by OGC standards) offer the ST_relate function for the DE-9IM analysis,
http://www.postgis.org/documentation/manual-2.0/ST_Relate.html
If the DE-9IM article is correct, the "or list" for each spatial predicate (binary operator) is
Equals T*F**FFF* Disjoint FF*FF**** Intersects T******** *T******* ***T***** ****T**** Touches FT******* F**T***** F***T**** Crosses T*T****** T*****T** 0******** Within T*F**F*** Contains T*****FF* Overlaps T*T***T** 1*T***T** Covers T*****FF* *T****FF* ***T**FF* ****T*FF* CoveredBy T*F**F*** *TF**F*** **FT*F*** **F*TF***
Then, we can translate the result of the ST_Replate() function into a summarized and human-readable string,
http://code.google.com/p/postgis-st-relate-summary/
Number of possible cases edit
The number of possible results in a binary DE-9IM matrix is 512, but, all results that ends with '0' or '1' (EE) starts with '1' or '0', since EE is the opposite of II. This correlation reduces the number of possible results to 256. Calculating the probability of each predicate in a context of possible matrix results,
Equals T*F**FFF = 2^3 = 8 (3.1% of 256) or T*F**FFF* = 2^4 = 16 (3.1% of 512)
Disjoint FF*FF*** = 2^4 = 16 (6.3% of 256)
Intersects T******* *T****** ***T**** ****T***
P1 = = 2^7 = 128 (50% of 256), P2 = 50% - P2(P1), P3 = ...
P1+P2+P3+P4 = 240 (93.8% of 256)
Touches FT****** F**T**** F***T*** 112 (43.8%)
Crosses T*T***** T*****T* 0******* changes with combination of input dimensions
2^6 = 64 (25% of 256) and 0% for inputs with equal dimensions, except lines.
Within T*F**F** = 2^5 = 32 (12.5% of 256)
Contains T*****FF = 2^5 = 32 (12.5% of 256)
Overlaps T*T***T* 1*T***T* changes with combination of input dimensions
for both cases, 2^5 = 32 (12.5% of 256)
Covers T*****FF *T****FF ***T**FF ****T*FF 60 (23.4%)
CoveredBy T*F**F** *TF**F** **FT*F** **F*TF** 60 (23.4%)
You can demonstrate by Combinatorics or by software. Example:
CREATE FUNCTION bit8checkmask(bit(8),bit(8),bit(8)) RETURNS boolean AS
$func$
SELECT COALESCE(($1 & $2 = $3),false);
$func$ LANGUAGE SQL IMMUTABLE;
CREATE FUNCTION testmask(bit[],bit[]) RETURNS table (s integer,perc float) AS
$func$
select s, round(100.0*s::float/256.0,1) as perc FROM (
select sum((
bit8checkmask(v::bit(8),$1[1],$2[1])
OR bit8checkmask(v::bit(8),$1[2],$2[2])
OR bit8checkmask(v::bit(8),$1[3],$2[3])
OR bit8checkmask(v::bit(8),$1[4],$2[4])
)::integer)::integer as s from (
select generate_series(0,255) as v
) as t ) as t2;
$func$ LANGUAGE SQL;
-- -- EXAMPLE:
select * from testmask( -- Intersects
-- 'T*******', '*T******', '***T****', '****T***'
array[b'10000000',b'01000000',b'00010000',b'00001000'],
array[b'10000000',b'01000000',b'00010000',b'00001000']
); -- 240 | 93.8%
For the {0,1,2,F} domain of the DE-9IM matrix, generating sequences from 0 to 3^8=6561, falls into same percentuals for masks of {T,*} domain, like Intersects, Equals, etc. and lower values for masks of {0,1,2,T,*} domain.
Illustrations for predicates edit
Work to do, add some of these illustrations...
- Spatial relation
- ...
External links modified edit
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- Added archive https://web.archive.org/web/20110321145301/http://www.vividsolutions.com:80/jts/javadoc/com/vividsolutions/jts/geom/IntersectionMatrix.html to http://www.vividsolutions.com/jts/javadoc/com/vividsolutions/jts/geom/IntersectionMatrix.html
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Featured article nomination edit
An incomplete nomination for a Wikipedia:Featured article candidates has been placed on this page.
In my view the article is a long way from where it would need to be to stand a chance. The main criticism which would be encountered is its accessibility. Even as someone with a mathematics background I've found to hard to follow.--Salix alba (talk): 14:13, 1 October 2018 (UTC)
- Hi @Salix alba: thanks to comment (!). Well, I agree that more didatic will be good, can you show "didactic articles" as example?
- External didactic article about DE-9IM, as this one or this other: what characteristics you see there that you not see here? We need more illustrations? .. Show any paragraph or section that is better there (tham here), so if it is easy I can try to change here in the correct direction.
- Internal featured didactic article with mathematical background: any article, to show as "reference model" to this kind of content.
- Krauss (talk) 01:02, 17 November 2018 (UTC)