计算外环PostGIS（多边形和多边形）的角度

Question

示例数据：

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
);

我有一个多边形和多边形的表格，我正在尝试使用ST_Azimuth计算表格中外环的内角（即没有内环......）。有没有办法修改附加查询以在线串的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函数会产生错误，因为您不能将两个generate_series用作单个函数的参数。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麻烦。

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;

我添加了一些复杂性，因为我想识别每个多边形，以避免混合线进行角度计算。

由于sqlfiddle不支持PostGIS我已经将这个例子上传了一些补充代码给github here

Answer 2

您可以将方位角计算添加到子查询中，如下所示。请注意，ST_Azimuth从下到上顺时针计算角度，因此需要更多工作来确保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;

Answer 3

我只需要多边形的内角。对于任意形状的多边形，vamaq所接受的解决方案并不总是给出内角，但有时会给出外角。这是因为它计算两条线之间的角度，而不考虑这两条线的哪一侧是内部的，所以如果内部角度是钝的，则vamaq的解决方案会改为给出外部角度。

在我的解决方案中，我使用余弦规则来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，以便我可以确保角度是内部的。 / p>

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;