数据库内核月报－ 2018/06 - PgSQL · 应用案例 · PostgreSQL + PostGIS 时态分析 - 《数据库内核月报》

背景
1、轨迹格式
2、计算两个轨迹是否有近距离接触
3、计算两个轨迹近距离接触的MEASURE(时间戳)
4、计算两个轨迹近距离接触的位置
5、计算两个轨迹近距离接触的最近的距离
6、索引加速
压测
小结
参考

背景

假设我们有一些物体的轨迹数据（经纬度、measure(通常存为epoch时间戳)），比如车辆、人、传感器等。

给定一个物体在某个时间范围的轨迹数据，查找有没有与这个物体接触的轨迹，并按亲密度排序。

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

需求：

1、判断两个轨迹是否有亲密接触的可能。

2、如果有亲密接触的可能，那么是在什么时间点（measure）发生的。

3、如果有亲密接触的可能，那么他们接触的距离有多近。

4、如果有亲密接触的可能，那么他们最近距离接触的点是哪个。

使用PostGIS，可以满足相应的需求。

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


1. 8.13. Temporal Support

3. ST_IsValidTrajectory — Returns true if the geometry is a valid trajectory.

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

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

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

时态分析可以做很多事情，比如地下活动。

1、轨迹格式

轨迹为带有measure的linestring，包括：经纬度(支持Z轴，3D坐标)、measure(递增)。

通常使用时间戳epoch来存储measure的内容。

例如：


1. postgres=# select extract(epoch from now());
2. date_part
3. ------------------
4. 1528347341.02161
5. (1 row)

7. postgres=# select extract(epoch from now());
8. date_part
9. ------------------
10. 1528347342.99521
11. (1 row)

13. postgres=# select ST_MakeLine(ST_MakePointM(-350,300,1528347341),ST_MakePointM(-410,490,1528347342));
14. st_makeline
15. --------------------------------------------------------------------------------------------------------------------
16. 0102000040020000000000000000E075C00000000000C07240000040B32EC6D6410000000000A079C00000000000A07E40000080B32EC6D641
17. (1 row)

19. postgres=# select st_astext(ST_MakeLine(ST_MakePointM(-350,300,1528347341),ST_MakePointM(-410,490,1528347342)));
20. st_astext
21. --------------------------------------------------------
22. LINESTRING M (-350 300 1528347341,-410 490 1528347342)
23. (1 row)

2、计算两个轨迹是否有近距离接触

指定距离阈值，判断两个轨迹是否有近距离接触。

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

Name


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

Synopsis


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

例子


1. WITH inp AS ( SELECT
2. ST_AddMeasure('LINESTRING Z (0 0 0, 10 0 5)'::geometry,
3. extract(epoch from '2015-05-26 10:00'::timestamptz),
4. extract(epoch from '2015-05-26 11:00'::timestamptz)
5. ) a,
6. ST_AddMeasure('LINESTRING Z (0 2 10, 12 1 2)'::geometry,
7. extract(epoch from '2015-05-26 10:00'::timestamptz),
8. extract(epoch from '2015-05-26 11:00'::timestamptz)
9. ) b
10. )
11. SELECT ST_CPAWithin(a,b,2), ST_DistanceCPA(a,b) distance FROM inp;

13. st_cpawithin |     distance
14. --------------+------------------
15. t            | 1.96521473776207

3、计算两个轨迹近距离接触的MEASURE(时间戳)

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

Name


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

Synopsis


1. float8 ST_ClosestPointOfApproach(geometry track1, geometry track2);

例子


1. -- Return the time in which two objects moving between 10:00 and 11:00
2. -- are closest to each other and their distance at that point
3. WITH inp AS ( SELECT
4. ST_AddMeasure('LINESTRING Z (0 0 0, 10 0 5)'::geometry,
5. extract(epoch from '2015-05-26 10:00'::timestamptz),
6. extract(epoch from '2015-05-26 11:00'::timestamptz)
7. ) a,
8. ST_AddMeasure('LINESTRING Z (0 2 10, 12 1 2)'::geometry,
9. extract(epoch from '2015-05-26 10:00'::timestamptz),
10. extract(epoch from '2015-05-26 11:00'::timestamptz)
11. ) b
12. ), cpa AS (
13. SELECT ST_ClosestPointOfApproach(a,b) m FROM inp
14. ), points AS (
15. SELECT ST_Force3DZ(ST_GeometryN(ST_LocateAlong(a,m),1)) pa,
16. ST_Force3DZ(ST_GeometryN(ST_LocateAlong(b,m),1)) pb
17. FROM inp, cpa
18. )
19. SELECT to_timestamp(m) t,
20. ST_Distance(pa,pb) distance
21. FROM points, cpa;

23. t               |     distance
24. -------------------------------+------------------
25. 2015-05-26 10:45:31.034483+02 | 1.96036833151395

4、计算两个轨迹近距离接触的位置

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

Name


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

Synopsis


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

例子1


1. SELECT ST_AsText(the_geom)
2. FROM
3. (SELECT ST_LocateAlong(
4. ST_GeomFromText('MULTILINESTRINGM((1 2 3, 3 4 2, 9 4 3),
5. (1 2 3, 5 4 5))'),3) As the_geom) As foo;

7. st_asewkt
8. -----------------------------------------------------------
9. MULTIPOINT M (1 2 3)

11. --Geometry collections are difficult animals so dump them
12. --to make them more digestable
13. SELECT ST_AsText((ST_Dump(the_geom)).geom)
14. FROM
15. (SELECT ST_LocateAlong(
16. ST_GeomFromText('MULTILINESTRINGM((1 2 3, 3 4 2, 9 4 3),
17. (1 2 3, 5 4 5))'),3) As the_geom) As foo;

19. st_asewkt
20. ---------------
21. POINTM(1 2 3)
22. POINTM(9 4 3)
23. POINTM(1 2 3)

例子2


1. postgres=# WITH inp AS ( SELECT
2. postgres(#   ST_AddMeasure('LINESTRING Z (0 0 0, 10 0 5)'::geometry,
3. postgres(#     extract(epoch from '2015-05-26 10:00'::timestamptz),
4. postgres(#     extract(epoch from '2015-05-26 11:00'::timestamptz)
5. postgres(#   ) a,
6. postgres(#   ST_AddMeasure('LINESTRING Z (0 2 10, 12 1 2)'::geometry,
7. postgres(#     extract(epoch from '2015-05-26 10:00'::timestamptz),
8. postgres(#     extract(epoch from '2015-05-26 11:00'::timestamptz)
9. postgres(#   ) b
10. postgres(# ), cpa AS (
11. postgres(#   SELECT ST_ClosestPointOfApproach(a,b) m FROM inp
12. postgres(# ) select ST_LocateAlong(a, m), ST_LocateAlong(b, m) from inp,cpa;
13. st_locatealong                                        |                                        st_locatealong
14. ----------------------------------------------------------------------------------------------+----------------------------------------------------------------------------------------------
15. 01040000C00100000001010000C03A8EE39E46581E4000000000000000003A8EE39E46580E40F734C292F758D541 | 01040000C00100000001010000C02222222CF7342240E9933E8DB0DCF33FA44FFA34C2720F40F734C292F758D541
16. (1 row)

18. postgres=# WITH inp AS ( SELECT
19. ST_AddMeasure('LINESTRING Z (0 0 0, 10 0 5)'::geometry,
20. extract(epoch from '2015-05-26 10:00'::timestamptz),
21. extract(epoch from '2015-05-26 11:00'::timestamptz)
22. ) a,
23. ST_AddMeasure('LINESTRING Z (0 2 10, 12 1 2)'::geometry,
24. extract(epoch from '2015-05-26 10:00'::timestamptz),
25. extract(epoch from '2015-05-26 11:00'::timestamptz)
26. ) b
27. ), cpa AS (
28. SELECT ST_ClosestPointOfApproach(a,b) m FROM inp
29. ) select st_astext(ST_LocateAlong(a, m)), st_astext(ST_LocateAlong(b, m)) from inp,cpa;
30. st_astext                               |                                      st_astext
31. ----------------------------------------------------------------------+-------------------------------------------------------------------------------------
32. MULTIPOINT ZM (7.58620689643754 0 3.79310344821877 1432608331.03448) | MULTIPOINT ZM (9.10344827572505 1.24137931035625 3.93103448284997 1432608331.03448)
33. (1 row)

5、计算两个轨迹近距离接触的最近的距离

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

Name


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

Synopsis


1. float8 ST_DistanceCPA(geometry track1, geometry track2);

例子


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

14. distance
15. ------------------
16. 1.96036833151395

6、索引加速

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

Name


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

Synopsis


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

Description


1. The |=| operator returns the 3D distance between two trajectories (See ST_IsValidTrajectory).

3. This is the same as ST_DistanceCPA but as an operator it can be used for doing nearest
4. neightbor searches using an N-dimensional index

6. (requires PostgreSQL 9.5.0 or higher).

例子


1. -- Save a literal query trajectory in a psql variable...
2. \set qt 'ST_AddMeasure(ST_MakeLine(ST_MakePointM(-350,300,0),ST_MakePointM(-410,490,0)),10,20)'
3. -- Run the query !
4. SELECT track_id, dist FROM (
5. SELECT track_id, ST_DistanceCPA(tr,:qt) dist
6. FROM trajectories
7. ORDER BY tr |=| :qt
8. LIMIT 5
9. ) foo;
10. track_id        dist
11. ----------+-------------------
12. 395 | 0.576496831518066
13. 380 |  5.06797130410151
14. 390 |  7.72262293958322
15. 385 |   9.8004461358071
16. 405 |  10.9534397988433
17. (5 rows)

压测

1、创建一个生成随机轨迹的函数


1. create or replace function gen_rand_linestring (
2. seedx float8,    -- 起点x坐标
3. seedy float8,    -- 起点y坐标
4. seedstep float8, -- 运动步调最大值
5. seedts float8,   -- 时间，measure 步调(second 单位)
6. ts1 timestamp,   -- 时间区间最小值
7. ts2 timestamp,   -- 时间区间最大值
8. cnt int          -- 在轨迹中生成几个POINT
9. ) returns geometry as $$
10. declare
11. ts timestamp := ts1 + ((random()*extract(epoch from (ts2-ts1)))||' sec')::interval;
12. ts_epo float8;
13. geo geometry[];
14. begin
15. for i in 1..cnt loop
16. ts_epo := extract(epoch from ts+((i*seedts)||' sec')::interval) ;
17. geo := array_cat(geo, array[st_makepointm(seedx + i*(random()*seedstep), seedy + i*(random()*seedstep), ts_epo)]) ;
18. end loop;
19. return st_makeline(geo);
20. end;
21. $$ language plpgsql strict stable;

2、例子


1. postgres=# select gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10);
2. -[ RECORD 1 ]-------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3. gen_rand_linestring | 01020000400A0000000000503BA9CB124000004062BCE20940A4E1CEC382C6D6410000C0637DE10B400000C0C50AB82F40A4E1CEE182C6D64100005057B1D511400000C4CBE74C3040A4E1CEFF82C6D6410000C0558CD11C400000C09177B72940A4E1CE1D83C6D64100004067EAE646400000884E67E02C40A4E1CE3B83C6D641000088FAE5AA4240000000AD26AF2740A4E1CE5983C6D64100007CD8F8274F400000B8B89E4D2F40A4E1CE7783C6D641000000823E6B27400000902247B34C40A4E1CE9583C6D6410000D863843C56400000C06676921440A4E1CEB383C6D64100000C90922455400000386AD2743D40A4E1CED183C6D641

5. postgres=# select gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10);
6. -[ RECORD 1 ]-------+-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
7. gen_rand_linestring | 01020000400A0000000000D007926420400000D089B6B52540115366F26EC6D6410000200020CB16400000C83382CD3540115366106FC6D6410000481EF79F32400000643974B938401153662E6FC6D6410000B0230B473C400000806A901F3C401153664C6FC6D6410000F4DE658733400000B85EDB112E401153666A6FC6D6410000C0C5B30603400000802221A63F40115366886FC6D6410000E4045AF23B4000001EDEDB0E4A40115366A66FC6D64100007089A6E048400000D0AD8FBB5140115366C46FC6D641000090384ED9534000007A4EF7515440115366E26FC6D641000084005E3153400000102214F72B401153660070C6D641

10. postgres=# select st_astext(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10));
11. -[ RECORD 1 ]---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
12. 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)

14. postgres=# select st_astext(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10));
15. -[ RECORD 1 ]-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
16. 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)

19. postgres=# select st_isvalidtrajectory(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10));
20. st_isvalidtrajectory
21. ----------------------
22. t
23. (1 row)

25. postgres=# select st_isvalidtrajectory(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10));
26. st_isvalidtrajectory
27. ----------------------
28. t
29. (1 row)

31. postgres=# select st_isvalidtrajectory(gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10));
32. st_isvalidtrajectory
33. ----------------------
34. t
35. (1 row)

3、建表


1. create table tbl_trc(uid int, tc geometry);

4、创建空间索引


1. create index idx_tbl_trc_1 on tbl_trc using gist (tc);

5、压测

每600秒跟踪60个点。


1. vi test.sql

4. \set uid random(1,100000000)
5. \set x random(1,1000)
6. \set y random(1,1000)
7. insert into tbl_trc values (:uid, gen_rand_linestring(:x,:y,10,600,now()::timestamp,(now()+interval '1 day')::timestamp,60));


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

6、查询测试


1. with a as (select gen_rand_linestring(1,2,10,120,now()::timestamp,(now()+interval '1 day')::timestamp,10) tc)
2. 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;


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

5. NOTICE:  Could not find point with M=1.52839e+09 on first geom
6. NOTICE:  Could not find point with M=1.52839e+09 on first geom
7. NOTICE:  Could not find point with M=1.52839e+09 on first geom
8. NOTICE:  Could not find point with M=1.52839e+09 on first geom
9. NOTICE:  Could not find point with M=1.5284e+09 on first geom
10. NOTICE:  Could not find point with M=1.52839e+09 on first geom
11. NOTICE:  Could not find point with M=1.52839e+09 on first geom
12. uid    |     ?column?
13. ----------+------------------
14. 97041413 | 47.2605527818083
15. 627623 | 89.2835207317297
16. 65446299 |  75.474589493268
17. 86176035 | 52.5219858940626
18. 81450777 | 63.8253100431266
19. 97175328 | 61.8835334486386
20. 99585779 | 34.6884977809673
21. 73552807 | 17.7467079053642
22. 27098713 | 68.9482850607433
23. 84443616 | 62.2849622517964
24. (10 rows)