PostgreSQL+PostGIS時態分析

背景

假設我們有一些物體的軌跡資料（經緯度、measure(通常存為epoch時間戳)），比如車輛、人、感測器等。

給定一個物體在某個時間範圍的軌跡資料，查詢有沒有與這個物體接觸的軌跡，並按親密度排序。

http://postgis.net/docs/manual-2.4/geometry_distance_cpa.html

需求：

1、判斷兩個軌跡是否有親密接觸的可能。

2、如果有親密接觸的可能，那麼是在什麼時間點（measure）發生的。

3、如果有親密接觸的可能，那麼他們接觸的距離有多近。

4、如果有親密接觸的可能，那麼他們最近距離接觸的點是哪個。

使用PostGIS，可以滿足相應的需求。

http://postgis.net/docs/manual-2.4/reference.html

8.13. Temporal Support  
  
ST_IsValidTrajectory — Returns true if the geometry is a valid trajectory.  
  
ST_ClosestPointOfApproach — Returns the measure at which points interpolated along two lines are closest.  
  
ST_DistanceCPA — Returns the distance between closest points of approach in two trajectories.  
  
ST_CPAWithin — Returns true if the trajectories` closest points of approach are within the specified distance.

時態分析可以做很多事情，比如地下情，嘿嘿。

1、軌跡格式

軌跡為帶有measure的linestring，包括：經緯度(支援Z軸，3D座標)、measure(遞增)。

通常使用時間戳epoch來儲存measure的內容。

例如：

postgres=# select extract(epoch from now());  
    date_part       
------------------  
 1528347341.02161  
(1 row)  
  
postgres=# select extract(epoch from now());  
    date_part       
------------------  
 1528347342.99521  
(1 row)  
  
postgres=# select ST_MakeLine(ST_MakePointM(-350,300,1528347341),ST_MakePointM(-410,490,1528347342));  
                                                    st_makeline                                                       
--------------------------------------------------------------------------------------------------------------------  
 0102000040020000000000000000E075C00000000000C07240000040B32EC6D6410000000000A079C00000000000A07E40000080B32EC6D641  
(1 row)  
  
postgres=# select st_astext(ST_MakeLine(ST_MakePointM(-350,300,1528347341),ST_MakePointM(-410,490,1528347342)));  
                       st_astext                          
--------------------------------------------------------  
 LINESTRING M (-350 300 1528347341,-410 490 1528347342)  
(1 row)

2、計算兩個軌跡是否有近距離接觸

指定距離閾值，判斷兩個軌跡是否有近距離接觸。

http://postgis.net/docs/manual-2.4/ST_CPAWithin.html

Name

ST_CPAWithin — Returns true if the trajectories` closest points of approach are within the specified distance.

Synopsis

float8 ST_CPAWithin(geometry track1, geometry track2, float8 maxdist);

例子

WITH inp AS ( SELECT  
  ST_AddMeasure(`LINESTRING Z (0 0 0, 10 0 5)`::geometry,  
    extract(epoch from `2015-05-26 10:00`::timestamptz),  
    extract(epoch from `2015-05-26 11:00`::timestamptz)  
  ) a,  
  ST_AddMeasure(`LINESTRING Z (0 2 10, 12 1 2)`::geometry,  
    extract(epoch from `2015-05-26 10:00`::timestamptz),  
    extract(epoch from `2015-05-26 11:00`::timestamptz)  
  ) b  
)  
SELECT ST_CPAWithin(a,b,2), ST_DistanceCPA(a,b) distance FROM inp;  
  
 st_cpawithin |     distance  
--------------+------------------  
 t            | 1.96521473776207

3、計算兩個軌跡近距離接觸的MEASURE(時間戳)

http://postgis.net/docs/manual-2.4/ST_ClosestPointOfApproach.html

Name

ST_ClosestPointOfApproach — Returns the measure at which points interpolated along two lines are closest.

Synopsis

float8 ST_ClosestPointOfApproach(geometry track1, geometry track2);

例子

-- Return the time in which two objects moving between 10:00 and 11:00  
-- are closest to each other and their distance at that point  
WITH inp AS ( SELECT  
  ST_AddMeasure(`LINESTRING Z (0 0 0, 10 0 5)`::geometry,  
    extract(epoch from `2015-05-26 10:00`::timestamptz),  
    extract(epoch from `2015-05-26 11:00`::timestamptz)  
  ) a,  
  ST_AddMeasure(`LINESTRING Z (0 2 10, 12 1 2)`::geometry,  
    extract(epoch from `2015-05-26 10:00`::timestamptz),  
    extract(epoch from `2015-05-26 11:00`::timestamptz)  
  ) b  
), cpa AS (  
  SELECT ST_ClosestPointOfApproach(a,b) m FROM inp  
), points AS (  
  SELECT ST_Force3DZ(ST_GeometryN(ST_LocateAlong(a,m),1)) pa,  
         ST_Force3DZ(ST_GeometryN(ST_LocateAlong(b,m),1)) pb  
  FROM inp, cpa  
)  
SELECT to_timestamp(m) t,  
       ST_Distance(pa,pb) distance  
FROM points, cpa;  
  
               t               |     distance  
-------------------------------+------------------  
 2015-05-26 10:45:31.034483+02 | 1.96036833151395

4、計算兩個軌跡近距離接觸的位置

http://postgis.net/docs/manual-2.4/ST_LocateAlong.html

Name

ST_LocateAlong — Return a derived geometry collection value with elements that match the specified measure. Polygonal elements are not supported.

Synopsis

geometry ST_LocateAlong(geometry ageom_with_measure, float8 a_measure, float8 offset);

例子1

SELECT ST_AsText(the_geom)  
		FROM  
		(SELECT ST_LocateAlong(  
			ST_GeomFromText(`MULTILINESTRINGM((1 2 3, 3 4 2, 9 4 3),  
		(1 2 3, 5 4 5))`),3) As the_geom) As foo;  
  
						 st_asewkt  
-----------------------------------------------------------  
 MULTIPOINT M (1 2 3)  
  
--Geometry collections are difficult animals so dump them  
--to make them more digestable  
SELECT ST_AsText((ST_Dump(the_geom)).geom)  
	FROM  
	(SELECT ST_LocateAlong(  
			ST_GeomFromText(`MULTILINESTRINGM((1 2 3, 3 4 2, 9 4 3),  
	(1 2 3, 5 4 5))`),3) As the_geom) As foo;  
  
   st_asewkt  
---------------  
 POINTM(1 2 3)  
 POINTM(9 4 3)  
 POINTM(1 2 3)

例子2

postgres=# WITH inp AS ( SELECT  
postgres(#   ST_AddMeasure(`LINESTRING Z (0 0 0, 10 0 5)`::geometry,  
postgres(#     extract(epoch from `2015-05-26 10:00`::timestamptz),  
postgres(#     extract(epoch from `2015-05-26 11:00`::timestamptz)  
postgres(#   ) a,  
postgres(#   ST_AddMeasure(`LINESTRING Z (0 2 10, 12 1 2)`::geometry,  
postgres(#     extract(epoch from `2015-05-26 10:00`::timestamptz),  
postgres(#     extract(epoch from `2015-05-26 11:00`::timestamptz)  
postgres(#   ) b  
postgres(# ), cpa AS (  
postgres(#   SELECT ST_ClosestPointOfApproach(a,b) m FROM inp  
postgres(# ) select ST_LocateAlong(a, m), ST_LocateAlong(b, m) from inp,cpa;  
                                        st_locatealong                                        |                                        st_locatealong                                          
----------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------  
 01040000C00100000001010000C03A8EE39E46581E4000000000000000003A8EE39E46580E40F734C292F758D541 | 01040000C00100000001010000C02222222CF7342240E9933E8DB0DCF33FA44FFA34C2720F40F734C292F758D541  
(1 row)  
  
postgres=# WITH inp AS ( SELECT  
  ST_AddMeasure(`LINESTRING Z (0 0 0, 10 0 5)`::geometry,  
    extract(epoch from `2015-05-26 10:00`::timestamptz),  
    extract(epoch from `2015-05-26 11:00`::timestamptz)  
  ) a,  
  ST_AddMeasure(`LINESTRING Z (0 2 10, 12 1 2)`::geometry,  
    extract(epoch from `2015-05-26 10:00`::timestamptz),  
    extract(epoch from `2015-05-26 11:00`::timestamptz)  
  ) b  
), cpa AS (  
  SELECT ST_ClosestPointOfApproach(a,b) m FROM inp  
) select st_astext(ST_LocateAlong(a, m)), st_astext(ST_LocateAlong(b, m)) from inp,cpa;  
                              st_astext                               |                                      st_astext                                        
----------------------------------------------------------------------+-------------------------------------------------------------------------------------  
 MULTIPOINT ZM (7.58620689643754 0 3.79310344821877 1432608331.03448) | MULTIPOINT ZM (9.10344827572505 1.24137931035625 3.93103448284997 1432608331.03448)  
(1 row)

5、計算兩個軌跡近距離接觸的最近的距離

http://postgis.net/docs/manual-2.4/ST_DistanceCPA.html

Name

ST_DistanceCPA — Returns the distance between closest points of approach in two trajectories.

Synopsis

float8 ST_DistanceCPA(geometry track1, geometry track2);

例子

-- Return the minimum distance of two objects moving between 10:00 and 11:00  
WITH inp AS ( SELECT  
  ST_AddMeasure(`LINESTRING Z (0 0 0, 10 0 5)`::geometry,  
    extract(epoch from `2015-05-26 10:00`::timestamptz),  
    extract(epoch from `2015-05-26 11:00`::timestamptz)  
  ) a,  
  ST_AddMeasure(`LINESTRING Z (0 2 10, 12 1 2)`::geometry,  
    extract(epoch from `2015-05-26 10:00`::timestamptz),  
    extract(epoch from `2015-05-26 11:00`::timestamptz)  
  ) b  
)  
SELECT ST_DistanceCPA(a,b) distance FROM inp;  
  
     distance  
------------------  
 1.96036833151395

6、索引加速

http://postgis.net/docs/manual-2.4/geometry_distance_cpa.html

Name

|=| — Returns the distance between A and B trajectories at their closest point of approach.

Synopsis

double precision |=|( geometry A , geometry B );

Description

The |=| operator returns the 3D distance between two trajectories (See ST_IsValidTrajectory).   
  
This is the same as ST_DistanceCPA but as an operator it can be used for doing nearest   
neightbor searches using an N-dimensional index   
  
(requires PostgreSQL 9.5.0 or higher).

例子

-- Save a literal query trajectory in a psql variable...  
set qt `ST_AddMeasure(ST_MakeLine(ST_MakePointM(-350,300,0),ST_MakePointM(-410,490,0)),10,20)`  
-- Run the query !  
SELECT track_id, dist FROM (  
  SELECT track_id, ST_DistanceCPA(tr,:qt) dist  
  FROM trajectories  
  ORDER BY tr |=| :qt  
  LIMIT 5  
) foo;  
 track_id        dist  
----------+-------------------  
      395 | 0.576496831518066  
      380 |  5.06797130410151  
      390 |  7.72262293958322  
      385 |   9.8004461358071  
      405 |  10.9534397988433  
(5 rows)

壓測

1、建立一個生成隨機軌跡的函式

create or replace function gen_rand_linestring (  
  seedx float8,    -- 起點x座標  
  seedy float8,    -- 起點y座標  
  seedstep float8, -- 運動步調最大值  
  seedts float8,   -- 時間，measure 步調(second 單位)  
  ts1 timestamp,   -- 時間區間最小值  
  ts2 timestamp,   -- 時間區間最大值  
  cnt int          -- 在軌跡中生成幾個POINT  
) returns geometry as $$  
declare  
  ts timestamp := ts1 + ((random()*extract(epoch from (ts2-ts1)))||` sec`)::interval;  
  ts_epo float8;  
  geo geometry[];  
begin  
  for i in 1..cnt loop   
    ts_epo := extract(epoch from ts+((i*seedts)||` sec`)::interval) ;  
    geo := array_cat(geo, array[st_makepointm(seedx + i*(random()*seedstep), seedy + i*(random()*seedstep), ts_epo)]) ;  
  end loop;   
  return st_makeline(geo);   
end;  
$$ language plpgsql strict stable;

2、例子

postgres=# select gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval `1 day`)::timestamp,10);  
-[ RECORD 1 ]-------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------  
gen_rand_linestring | 01020000400A0000000000503BA9CB124000004062BCE20940A4E1CEC382C6D6410000C0637DE10B400000C0C50AB82F40A4E1CEE182C6D64100005057B1D511400000C4CBE74C3040A4E1CEFF82C6D6410000C0558CD11C400000C09177B72940A4E1CE1D83C6D64100004067EAE646400000884E67E02C40A4E1CE3B83C6D641000088FAE5AA4240000000AD26AF2740A4E1CE5983C6D64100007CD8F8274F400000B8B89E4D2F40A4E1CE7783C6D641000000823E6B27400000902247B34C40A4E1CE9583C6D6410000D863843C56400000C06676921440A4E1CEB383C6D64100000C90922455400000386AD2743D40A4E1CED183C6D641  
  
postgres=# select gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval `1 day`)::timestamp,10);  
-[ RECORD 1 ]-------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------  
gen_rand_linestring |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
  
  
postgres=# select st_astext(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval `1 day`)::timestamp,10));  
-[ RECORD 1 ]---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------  
st_astext | LINESTRING M (10.2174849007279 11.9571549287066 1528425468.02122,14.630109699443 3.11233511939645 1528425588.02122,21.6466929381713 21.7603580309078 1528425708.02122,4.62157236784697 22.9575021080673 1528425828.02122,47.6620979132131 23.719867666252 1528425948.02122,15.6148129086941 51.1239671874791 1528426068.02122,47.852089674212 18.3603029865772 1528426188.02122,33.4982615187764 36.1437245160341 1528426308.02122,83.4090811889619 7.33796327654272 1528426428.02122,80.737452045083 19.6353993359953 1528426548.02122)  
  
postgres=# select st_astext(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval `1 day`)::timestamp,10));  
-[ RECORD 1 ]-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------  
st_astext | LINESTRING M (3.91523572057486 7.61306651681662 1528390545.99534,16.9645196422935 20.0192420165986 1528390665.99534,13.6881912257522 22.0785792060196 1528390785.99534,32.2743593193591 9.22613327205181 1528390905.99534,40.4555864389986 15.4170794393867 1528391025.99534,7.14410931244493 49.0896332990378 1528391145.99534,67.4892951631919 13.0613004816696 1528391265.99534,38.844025567174 50.6820540204644 1528391385.99534,23.3702098755166 91.7289085481316 1528391505.99534,55.1767633520067 70.295524129644 1528391625.99534)  
  
  
postgres=# select st_isvalidtrajectory(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval `1 day`)::timestamp,10));  
 st_isvalidtrajectory   
----------------------  
 t  
(1 row)  
  
postgres=# select st_isvalidtrajectory(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval `1 day`)::timestamp,10));  
 st_isvalidtrajectory   
----------------------  
 t  
(1 row)  
  
postgres=# select st_isvalidtrajectory(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval `1 day`)::timestamp,10));  
 st_isvalidtrajectory   
----------------------  
 t  
(1 row)

3、建表

create table tbl_trc(uid int, tc geometry);

4、建立空間索引

create index idx_tbl_trc_1 on tbl_trc using gist (tc);

5、壓測

每600秒跟蹤60個點。

vi test.sql  
  
  
set uid random(1,100000000)  
set x random(1,1000)  
set y random(1,1000)  
insert into tbl_trc values (:uid, gen_rand_linestring(:x,:y,10,600,now()::timestamp,(now()+interval `1 day`)::timestamp,60));

pgbench -M prepared -n -r -P 1 -f ./test.sql -c 32 -j 32 -T 1200 -h 127.0.0.1

6、查詢測試

with a as (select gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval `1 day`)::timestamp,10) tc)  
select uid, tbl_trc.tc |=| a.tc, st_astext(tbl_trc.tc), st_astext(a.tc) from tbl_trc,a where ST_CPAWithin(tbl_trc.tc, a.tc, 100) limit 10;

with a as (select gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval `1 day`)::timestamp,10) tc)  
select uid, tbl_trc.tc |=| a.tc from tbl_trc,a where ST_CPAWithin(tbl_trc.tc, a.tc, 100) limit 10;  
  
  
NOTICE:  Could not find point with M=1.52839e+09 on first geom  
NOTICE:  Could not find point with M=1.52839e+09 on first geom  
NOTICE:  Could not find point with M=1.52839e+09 on first geom  
NOTICE:  Could not find point with M=1.52839e+09 on first geom  
NOTICE:  Could not find point with M=1.5284e+09 on first geom  
NOTICE:  Could not find point with M=1.52839e+09 on first geom  
NOTICE:  Could not find point with M=1.52839e+09 on first geom  
   uid    |     ?column?       
----------+------------------  
 97041413 | 47.2605527818083  
   627623 | 89.2835207317297  
 65446299 |  75.474589493268  
 86176035 | 52.5219858940626  
 81450777 | 63.8253100431266  
 97175328 | 61.8835334486386  
 99585779 | 34.6884977809673  
 73552807 | 17.7467079053642  
 27098713 | 68.9482850607433  
 84443616 | 62.2849622517964  
(10 rows)