# Need to enhance a function for creating quadrants within polygons

I wrote a function that creates arbitrary quadrants within a polygon

``````SELECT (quadrant(20,0.0,90)).*
``````

The first parameter is the polygon ID, the second one is the start angle and with the third one the quadrant is finally spanned.

First the `TYPE`

``````CREATE TYPE quadrant AS (id smallint,geom geometry(polygon,31468))
``````

Here is the function

``````CREATE OR REPLACE FUNCTION quadrant(id integer,start double precision, stop integer) RETURNS SETOF quadrant AS \$\$
WITH centroid AS
(SELECT
accumulation.partnumber,
(ST_Centroid(accumulation.geom)) AS vertex
FROM accumulation
WHERE partnumber=\$1
),
newline AS
(SELECT
ST_SetSRID(ST_Translate(
ST_Rotate(
ST_MakeLine(
ST_MakePoint(0.0,2000.0),
ST_MakePoint(0.0,0.0)),
ST_X(vertex), ST_Y(vertex)),
ST_SRID(vertex)) AS geom
FROM centroid, generate_series(0,\$3,\$3) AS s(a)
),
span AS
(SELECT
centroid.partnumber,
ST_LineMerge(ST_Union(newline.geom)) AS geom
FROM newline, centroid
GROUP BY partnumber),
multiobject AS
(SELECT
span.partnumber,
ST_Split(accumulation.geom,span.geom) AS geom,
generate_series(1,100) AS n
FROM span, accumulation
WHERE accumulation.partnumber=\$1),
objects AS
(SELECT
n,
ST_GeometryN(multiobject.geom,n) AS geom
FROM multiobject
WHERE n <= ST_NumGeometries(multiobject.geom))

SELECT
partnumber AS id,
objects.geom
FROM objects, multiobject
WHERE multiobject.n <= ST_NumGeometries(multiobject.geom)
ORDER BY LEAST(ST_Area(ST_GeometryN(objects.geom,multiobject.n)))
LIMIT 1
\$\$ LANGUAGE 'sql';
``````

I applied this function for 300 polygons and I noticed a problem. My last query results the smallest piece from the split. But in some cases, when the first newline (see subquery `newline`) crosses the polygon more than one time, there is a smaller piece that represents the quadrant (see the most right object in the picture below).

The query doesn't calculate the right quadrant for the left object in the picture. In this case the smaller area of the split is not the quadrant, because the polygon is plumped to the northeast direction.

So my question is, how I can enhance my query to avoid these incorrect quadrants. Maybe I have to overthink the function generally.

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