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对于GIS业务来说,路径规划是非常基础的一个业务,一般公司如果处理,都会直接选择调用已经成熟的第三方的接口,比如高德、百度等。当然其实路径规划的算法非常多,像比较著名的Dijkstra、A*算法等。当然本篇文章不是介绍算法的,本文作者会根据pgrouting已经集成的Dijkstra算法来,结合postgresql数据库来处理最短路径。
一、数据处理
路径规划的核心是数据,数据是一般的路网数据,但是我们拿到路网数据之后,需要对数据进行处理,由于算法的思想是基于有向图的原理,因此首先需要对数据做topo处理,通过topo我们其实就建立了路网中各条道路的顶点关系,下面是主要命令:
--开启执行路网topo的插件
create extension postgis;
create extension postgis\_topology;
--数据创建拓扑
ALTER TABLE test\_road ADD COLUMN source integer;
ALTER TABLE test\_road ADD COLUMN target integer;
SELECT pgr\_createTopology('test\_road',0.00001, 'geom', 'gid');
其中test_road是将路网数据导入到postgresql中的表名。
处理完topo之后,基本就够用了,我们就可以借助pgrouting自带的函数,其实有很多,我们选择pgr_dijkstra
CREATE OR REPLACE FUNCTION public.pgr\_dijkstra(
IN edges\_sql text,
IN start\_vid bigint,
IN end\_vid bigint,
IN directed boolean,
OUT seq integer,
OUT path\_seq integer,
OUT node bigint,
OUT edge bigint,
OUT cost double precision,
OUT agg\_cost double precision)
RETURNS SETOF record AS
$BODY$
DECLARE
BEGIN
RETURN query SELECT *
FROM \_pgr\_dijkstra(\_pgr\_get\_statement($1), start\_vid, end\_vid, directed, false);
END
$BODY$
LANGUAGE plpgsql VOLATILE
COST 100
ROWS 1000;
ALTER FUNCTION public.pgr\_dijkstra(text, bigint, bigint, boolean)
OWNER TO postgres;
从函数输入参数可以看到,我们需要一个查询sql,一个起始点、一个结束点、以及是否考虑方向,好了了解到调用函数输入参数,我们就来写这个函数。
二、原理分析
一般路径规划,基本都是输入一个起点位置、一个终点位置然后直接规划,那么对于我们来说,要想套用上面的函数,必须找出起点位置target ,以及终点位置的source,然后规划根据找出的这两个topo点,调用上面的函数,来返回自己所需要的结果。
如何根据起始点找到对应的target呢,其实就是找离起点最近线的target,同理终点的source,其实就是找离终点最近线的source,当然将这两个点规划规划好之后,基本就可以了,但是最后还需要将起点到起点最近先的target连接起来,终点到终点最近线的source连接起来,这样整个路径规划就算完成了。
下面我们来看具体的实现存储过程:
CREATE OR REPLACE FUNCTION public.pgr\_shortest\_road(
IN startx double precision,
IN starty double precision,
IN endx double precision,
IN endy double precision,
OUT road\_name character varying,
OUT v\_shpath character varying,
OUT cost double precision)
RETURNS SETOF record AS
$BODY$
declare
v\_startLine geometry;--离起点最近的线
v\_endLine geometry;--离终点最近的线
v\_startTarget integer;--距离起点最近线的终点
v\_endSource integer;--距离终点最近线的起点
v\_statpoint geometry;--在v\_startLine上距离起点最近的点
v\_endpoint geometry;--在v\_endLine上距离终点最近的点
v\_res geometry;--最短路径分析结果
v\_perStart float;--v\_statpoint在v\_res上的百分比
v\_perEnd float;--v\_endpoint在v\_res上的百分比
v\_rec record;
first\_name varchar;
end\_name varchar;
first\_cost double precision;
end\_cost double precision;
begin
--查询离起点最近的线
execute 'select geom,target,name from china\_road where
ST\_DWithin(geom,ST\_Geometryfromtext(''point('|| startx ||' ' || starty||')''),0.01)
order by ST\_Distance(geom,ST\_GeometryFromText(''point('|| startx ||' '|| starty ||')'')) limit 1'
into v\_startLine ,v\_startTarget,first\_name;
--查询离终点最近的线
execute 'select geom,source,name from china\_road
where ST\_DWithin(geom,ST\_Geometryfromtext(''point('|| endx || ' ' || endy ||')''),0.01)
order by ST\_Distance(geom,ST\_GeometryFromText(''point('|| endx ||' ' || endy ||')'')) limit 1'
into v\_endLine,v\_endSource,end\_name;
--如果没找到最近的线,就返回null
if (v\_startLine is null) or (v\_endLine is null) then
return;
end if ;
select ST\_ClosestPoint(v\_startLine, ST\_Geometryfromtext('point('|| startx ||' ' || starty ||')')) into v\_statpoint;
select ST\_ClosestPoint(v\_endLine, ST\_GeometryFromText('point('|| endx ||' ' || endy ||')')) into v\_endpoint;
--计算距离起点最近线上的点在该线中的位置
select ST\_Line\_Locate\_Point(st\_linemerge(v\_startLine), v\_statpoint) into v\_perStart;
select ST\_Line\_Locate\_Point(st\_linemerge(v\_endLine), v\_endpoint) into v\_perEnd;
select ST\_Distance\_Sphere(v\_statpoint,ST\_PointN(ST\_GeometryN(v\_startLine,1), ST\_NumPoints(ST\_GeometryN(v\_startLine,1)))) into first\_cost;
select ST\_Distance\_Sphere(ST\_PointN(ST\_GeometryN(v\_endLine,1),1),v\_endpoint) into end\_cost;
if (ST\_Intersects(st\_geomfromtext('point('|| startx ||' '|| starty ||') '), v\_startLine) and ST\_Intersects(st\_geomfromtext('point('|| endx ||' '|| endy ||') '), v\_startLine)) then
select ST\_Distance\_Sphere(v\_statpoint, v\_endpoint) into first\_cost;
select ST\_Line\_Locate\_Point(st\_linemerge(v\_startLine), v\_endpoint) into v\_perEnd;
for v\_rec in
select ST\_Line\_SubString(st\_linemerge(v\_startLine), v\_perStart,v\_perEnd) as point,COALESCE(end\_name,'无名路') as name,end\_cost as cost loop
v\_shPath:= ST\_AsGeoJSON(v\_rec.point);
cost:= v\_rec.cost;
road\_name:= v\_rec.name;
return next;
end loop;
return;
end if;
--最短路径
for v\_rec in
(select ST\_Line\_SubString(st\_linemerge(v\_startLine),v\_perStart,1) as point,COALESCE(first\_name,'无名路') as name,first\_cost as cost
union all
SELECT st\_linemerge(b.geom) as point,COALESCE(b.name,'无名路') as name,b.length as cost
FROM pgr\_dijkstra(
'SELECT gid as id, source, target, length as cost FROM china\_road
where st\_intersects(geom,st\_buffer(st\_linefromtext(''linestring('||startx||' ' || starty ||','|| endx ||' ' || endy ||')''),0.05))',
v\_startTarget, v\_endSource , false
) a, china\_road b
WHERE a.edge = b.gid
union all
select ST\_Line\_SubString(st\_linemerge(v\_endLine),0,v\_perEnd) as point,COALESCE(end\_name,'无名路') as name,end\_cost as cost)
loop
v\_shPath:= ST\_AsGeoJSON(v\_rec.point);
cost:= v\_rec.cost;
road\_name:= v\_rec.name;
return next;
end loop;
end;
$BODY$
LANGUAGE plpgsql VOLATILE STRICT;
上面这种实现,是将所有查询道路返回一个集合,然后客户端来将各个线路进行合并,这种方式对最终效率影响比较大,所以一般会在函数中将道路何合并为一条道路,我们可以使用postgis的st_union函数来处理,小编经过长时间的试验,在保证效率和准确性的情况下,对上面的存储过程做了很多优化,最终得出了如下:
CREATE OR REPLACE FUNCTION public.pgr\_shortest\_road(
startx double precision,
starty double precision,
endx double precision,
endy double precision)
RETURNS geometry AS
$BODY$
declare
v\_startLine geometry;--离起点最近的线
v\_endLine geometry;--离终点最近的线
v\_perStart float;--v\_statpoint在v\_res上的百分比
v\_perEnd float;--v\_endpoint在v\_res上的百分比
v\_shpath geometry;
distance double precision;
bufferInstance double precision;
bufferArray double precision[];
begin
execute 'select geom,
case china\_road.direction
when ''3'' then
source
else
target
end
from china\_road where
ST\_DWithin(geom,ST\_Geometryfromtext(''point('|| startx ||' ' || starty||')'',4326),0.05)
AND width::double precision >= '||roadWidth||'
order by ST\_Distance(geom,ST\_GeometryFromText(''point('|| startx ||' '|| starty ||')'',4326)) limit 1'
into v\_startLine;
execute 'select geom,
case china\_road.direction
when ''3'' then
target
else
source
end
from china\_road
where ST\_DWithin(geom,ST\_Geometryfromtext(''point('|| endx || ' ' || endy ||')'',4326),0.05)
AND width::double precision >= '||roadWidth||'
order by ST\_Distance(geom,ST\_GeometryFromText(''point('|| endx ||' ' || endy ||')'',4326)) limit 1'
into v\_endLine;
if (v\_startLine is null) or (v\_endLine is null) then
return null;
end if;
if (ST\_equals(v\_startLine,v\_endLine)) then
select ST\_LineLocatePoint(st\_linemerge(v\_startLine), ST\_Geometryfromtext('point('|| startx ||' ' || starty ||')',4326)) into v\_perStart;
select ST\_LineLocatePoint(st\_linemerge(v\_endLine), ST\_Geometryfromtext('point('|| endx ||' ' || endy ||')',4326)) into v\_perEnd;
select ST\_LineSubstring(st\_linemerge(v\_startLine),v\_perStart,v\_perEnd) into v\_shPath;
return v\_shPath;
end if;
select ST\_DistanceSphere(st\_geomfromtext('point('|| startx ||' ' || starty ||')',4326),st\_geomfromtext('point('|| endx ||' ' || endy ||')',4326)) into distance;
if ((distance / 1000) > 50) then
bufferArray := ARRAY[0.1,0.2,0.3,0.5,0.8];
else
bufferArray := ARRAY[0.02,0.05,0.08,0.1];
end if;
forEACH bufferInstance IN ARRAY bufferArray
LOOP
select \_pgr\_shortest\_road(startx,starty,endx,endy,bufferInstance) into v\_shPath;
if (v\_shPath is not null) then
return v\_shPath;
end if;
end loop;
end;
$BODY$
LANGUAGE plpgsql VOLATILE STRICT
COST 100;
ALTER FUNCTION public.pgr\_shortest\_road(double precision, double precision, double precision, double precision )
OWNER TO postgres;
DROP FUNCTION public.\_pgr\_shortest\_road(double precision, double precision, double precision, double precision, double precision);
上面的函数,其实对于大部分情况下的操作,基本可以满足了。
三、效率优化
其实在数据查询方面,我们使用的是起点和终点之间的线性缓冲来提高效率,如下:
SELECT gid as id, source, target, cost,rev\_cost as reverse\_cost FROM china\_road
where geom && st\_buffer(st\_linefromtext(''linestring('||startx||' ' || starty ||','|| endx ||' ' || endy ||')'',4326),'||bufferDistance||')
当然这在大部分情况下,依旧是不错的,然后在有些情况下,并不能起到很好的作用,因为如果起点和终点之间道路偏移较大(比如直线上的山脉较多的时候,路就会比较绕),这个时候,可能会增大缓冲距离,而增加缓冲距离就会导致,部分区域的查询量增大,继而影响效率,因此其实我们可以考虑使用mapid这个参数,这个参数从哪来呢,一般我们拿到的路网数据都会这个字段,我们只需要生成一个区域表,而这个区域表就俩个字段,一个是mapid,一个是这个mapid的polygon范围,这样子,上面的查询条件,就可以换成如下:
SELECT gid as id, source, target, cost,rev\_cost as reverse\_cost FROM china\_road
where mapid in (select mapid from maps where geom && st\_buffer(st\_linefromtext(''linestring('||startx||' ' || starty ||','|| endx ||' ' || endy ||')''),'||bufferDistance||'))
这样就可以在很大程度上提高效率。
四、数据bug处理
其实有时候我们拿到的路网数据,并不是非常的准确,或者说是录入的有瑕疵,我自己遇到的就是生成的topo数据,本来一条路的target应该和它相邻路的source的点重合,然后实际却是不一样,这就导致最终规划处的有问题,因此,简单写了一个处理这种问题的函数
CREATE OR REPLACE FUNCTION public.modity\_road\_data()
RETURNS void AS
$BODY$
declare
n integer;
begin
for n IN (select distinct(source) from china\_road ) loop
update china\_road
set geom = st\_multi(st\_addpoint(ST\_geometryN(geom,1),
(select st\_pointn(ST\_geometryN(geom,1),1) from china\_road where source = n
limit 1),
st\_numpoints(ST\_geometryN(geom,1))))
where target = n;
end loop;
end;
$BODY$
LANGUAGE plpgsql VOLATILE STRICT
COST 100;
ALTER FUNCTION public.modity\_road\_data()
OWNER TO postgres;
五、后续规划
上面的函数已在百万数据中做过验证,后续还会验证千万级别的路网数据,当然这种级别,肯定要在策略上做一些调整了,比如最近测试的全国路网中,先规划起点至起点最近的高速入口,在规划终点至终点最近的高速出口,然后再高速路网上规划高速入口到高速出口的路径,这样发现效率提升不少,当然,这里面还有很多逻辑和业务,等所有东西都验证完毕,会再出一版,千万级别路径规划的文章。
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