计算外环的角度 PostGIS（多边形和多多边形）

Question

样本数据：

CREATE TABLE poly_and_multipoly (
  "id" SERIAL NOT NULL PRIMARY KEY,
  "name" char(1) NOT NULL,
  "the_geom" geometry NOT NULL
);
-- add data, A is a polygon, B is a multipolygon
INSERT INTO poly_and_multipoly (name, the_geom) VALUES (
    'A', 'POLYGON((7.7 3.8,7.7 5.8,9.0 5.8,7.7 3.8))'::geometry
    ), (
    'B',
    'MULTIPOLYGON(((0 0,4 0,4 4,0 4,0 0),(1 1,2 1,2 2,1 2,1 1)), ((-1 -1,-1 -2,-2 -2,-2 -1,-1 -1)))'::geometry
);

我有一个多面体和多边形表，我正在尝试使用ST_Azimuth 计算表中外环的内角（即没有内环...）。有什么方法可以修改附加的查询以在线串的 sp 和 ep 上使用ST_Azimuth？

    SELECT id, name, ST_AsText( ST_MakeLine(sp,ep) )
FROM
   -- extract the endpoints for every 2-point line segment for each linestring
   (SELECT id, name,
      ST_PointN(geom, generate_series(1, ST_NPoints(geom)-1)) as sp,
      ST_PointN(geom, generate_series(2, ST_NPoints(geom)  )) as ep
    FROM
       -- extract the individual linestrings
      (SELECT id, name, (ST_Dump(ST_Boundary(the_geom))).geom
       FROM poly_and_multipoly
       ) AS linestrings
    ) AS segments;

1;"A";"LINESTRING(7.7 3.8,7.7 5.8)"
1;"A";"LINESTRING(7.7 5.8,9 5.8)"
1;"A";"LINESTRING(9 5.8,7.7 3.8)"
2;"B";"LINESTRING(0 0,4 0)"

Answer 1

在 aengus 示例中使用 ST_Azimuth 函数会出错，因为您不能使用两个 generate_series 作为单个函数的参数。如果您在另一个子查询中使用 ep / sp 值，那么您将不会遇到任何问题。

这是我的解决方案：

-- 3.- Create segments from points and calculate azimuth for each line.
--     two calls of generate_series for a single function wont work (azimuth).
select id,
       name,
       polygon_num,
       point_order as vertex,
       --
       case when point_order = 1
         then last_value(ST_Astext(ST_Makeline(sp,ep))) over (partition by id, polygon_num)
         else lag(ST_Astext(ST_Makeline(sp,ep)),1) over (partition by id, polygon_num order by point_order)
       end ||' - '||ST_Astext(ST_Makeline(sp,ep)) as lines,
       --
       abs(abs(
       case when point_order = 1
         then last_value(degrees(ST_Azimuth(sp,ep))) over (partition by id, polygon_num)
         else lag(degrees(ST_Azimuth(sp,ep)),1) over (partition by id, polygon_num order by point_order)
       end - degrees(ST_Azimuth(sp,ep))) -180 ) as ang
from (-- 2.- extract the endpoints for every 2-point line segment for each linestring
      --     Group polygons from multipolygon
      select id,
             name,
             coalesce(path[1],0) as polygon_num,
             generate_series(1, ST_Npoints(geom)-1) as point_order,
             ST_Pointn(geom, generate_series(1, ST_Npoints(geom)-1)) as sp,
             ST_Pointn(geom, generate_series(2, ST_Npoints(geom)  )) as ep
      from ( -- 1.- Extract the individual linestrings and the Polygon number for later identification
             select id,
                    name,
                    (ST_Dump(ST_Boundary(the_geom))).geom as geom,
                    (ST_Dump(ST_Boundary(the_geom))).path as path -- To identify the polygon
              from poly_and_multipoly ) as pointlist ) as segments;

我增加了一些复杂性，因为我想识别每个多边形以避免混合线以进行角度计算。

由于 sqlfiddle 不支持 PostGIS，我已将此示例和一些补充代码上传到 github here

Answer 2

我只需要多边形的内角。 vamaq 接受的解决方案并没有始终如一地给我一个任意形状的多边形的内角，但有时是外角。这是因为它计算两条线之间的角度，而不考虑两条线的哪一侧是内角，所​​以如果内角是钝角，vamaq 的解决方案会给出外角。

在我的解决方案中，我使用余弦规则确定两条线之间的角度而不参考方位角，然后使用 ST_Contains 检查多边形的角度是锐角还是钝角，以便确保角度是内部的。

CREATE OR REPLACE FUNCTION is_internal(polygon geometry, p2 geometry, p3 geometry)
RETURNS boolean as
$$
    BEGIN
        return st_contains(polygon, st_makeline(p2, p3));
    END
$$ language plpgsql;


CREATE OR REPLACE FUNCTION angle(p1 geometry, p2 geometry, p3 geometry)
RETURNS float AS
$$
    DECLARE
        p12 float;
        p23 float;
        p13 float;
    BEGIN
        select st_distance(p1, p2) into p12;
        select st_distance(p1, p3) into p13;
        select st_distance(p2, p3) into p23;
        return acos((p12^2 + p13^2 - p23^2) / (2*p12*p13));
    END
$$ language plpgsql;

CREATE OR REPLACE FUNCTION internal_angle(polygon geometry, p1 geometry, p2 geometry, p3 geometry)
RETURNS float as
$$
    DECLARE
        ang float;
        is_intern boolean;
    BEGIN
        select angle(p1, p2, p3) into ang;
        select is_internal(polygon, p2, p3) into is_intern;
        IF not is_intern THEN
            select 6.28318530718 - ang into ang;
        END IF;
        return ang;
    END
$$ language plpgsql;


CREATE OR REPLACE FUNCTION corner_triplets(geom geometry)
RETURNS table(corner_number integer, p1 geometry, p2 geometry, p3 geometry) AS
$$
    DECLARE
        max_corner_number integer;
    BEGIN
        create temp table corners on commit drop as select path[2] as corner_number, t1.geom as point from (select (st_dumppoints($1)).*) as t1 where path[1] = 1;
        select max(corners.corner_number) into max_corner_number from corners;
        insert into corners (corner_number, point) select 0, point from corners where corners.corner_number = max_corner_number - 1;
        create temp table triplets on commit drop as select t1.corner_number, t1.point as p1, t2.point as p2,  t3.point as p3 from corners as t1, corners as t2, corners as t3 where t1.corner_number = t2.corner_number + 1 and t1.corner_number = t3.corner_number - 1;
        return QUERY TABLE triplets;
    END;
$$
LANGUAGE plpgsql;

CREATE OR REPLACE FUNCTION internal_angles(geom geometry)
RETURNS table(corner geometry, angle float)
AS $$
    BEGIN
        create temp table internal_angs on commit drop as select p1, internal_angle(geom, p1, p2, p3) from (select (c).* from (select corner_triplets(geom) as c) as t1) as t2;
        return QUERY TABLE internal_angs;
    END;
$$
LANGUAGE plpgsql;

用法：

select (c).* into temp from (select internal_angles(geom) as c from my_table) as t;

Answer 3

您可以将方位角计算添加到您的子查询中，如下所示。请注意，ST_Azimuth 从下到上计算顺时针角度，因此需要做更多工作来确保 az 实际上是内角。

     SELECT id, name, ST_AsText( ST_MakeLine(sp,ep) ), az
    FROM
      -- extract the endpoints for every 2-point line segment for each      linestring
 (SELECT id, name,
  ST_PointN(geom, generate_series(1, ST_NPoints(geom)-1)) as sp,
  ST_PointN(geom, generate_series(2, ST_NPoints(geom)  )) as ep,
    ST_Azimuth(ST_PointN(geom, generate_series(1, ST_NPoints(geom)-1)),
    ST_PointN(geom, generate_series(2, ST_NPoints(geom)  ))) as az
FROM
   -- extract the individual linestrings
  (SELECT id, name, (ST_Dump(ST_Boundary(the_geom))).geom
   FROM poly_and_multipoly
   ) AS linestrings
) AS segments;