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ST_SimplifyPreserveTopology

Signature

GEOMETRY ST_SimplyPreserveTopology(GEOMETRY geom, DOUBLE distance);

Description

Simplifies geom with a distance tolerance of distance ensuring that the result is a valid geometry (if the input is) having the same dimension and number of components as the input, and with the components having the same topological relationship. Uses a maximum-distance difference algorithm similar to the Douglas-Peuker algorithm.

If the input is a POLYGON or a MULTIPOLYGON:

  • The result has the same number of shells and holes as the input, with the same topological structure
  • The result rings touch at no more than the number of touching points in the input (although they may touch at fewer points). The key implication of this statement is that if the input is topologically valid, so is the simplified output.

For linear geometries, if the input does not contain any intersecting line segments, this property will be preserved in the output.

For all geometry types, the result will contain enough vertices to ensure validity. For polygons and closed linear geometries, the result will have at least 4 vertices; for open linestrings the result will have at least 2 vertices.

All geometry types are handled. Empty and point geometries are returned unchanged.

KNOWN BUGS

If a small hole is very near an edge, it is possible for the edge to be moved by a relatively large tolerance value and end up with the hole outside the result shell. Similarly, it is possible for a small polygon component to end up inside a nearby larger polygon. A workaround is to test for this situation in post-processing and remove any invalid holes or polygons.

Examples

-- The following three examples use the same input POLYGON.
SELECT ST_SimplyPreserveTopology(
           POLYGON((8 25, 28 22, 28 20, 15 11, 33 3, 56 30, 46 33,
                    46 34, 47 44, 35 36, 45 33, 43 19, 29 21, 29 22,
                    35 26, 24 39, 8 25)), 10);
-- Answer: POLYGON((8 25, 28 22, 28 20, 15 11, 33 3, 56 30, 46 33,
--                  46 34, 47 44, 35 36, 45 33, 43 19, 29 21, 29 22,
--                  35 26, 24 39, 8 25))

SELECT ST_SimplyPreserveTopology(
           POLYGON((8 25, 28 22, 28 20, 15 11, 33 3, 56 30, 46 33,
                    46 34, 47 44, 35 36, 45 33, 43 19, 29 21, 29 22,
                    35 26, 24 39, 8 25)), 20);
-- Answer:POLYGON((8 25, 33 3, 56 30, 47 44, 43 19, 8 25))

SELECT ST_SimplyPreserveTopology(
           POLYGON((8 25, 28 22, 28 20, 15 11, 33 3, 56 30, 46 33,
                    46 34, 47 44, 35 36, 45 33, 43 19, 29 21, 29 22,
                    35 26, 24 39, 8 25)), 30);
-- Answer: POLYGON((8 25, 33 3, 56 30, 47 44, 8 25))

-- POINTs and MULTIPOINTs cannot be further simplified:
SELECT ST_SimplifyPreserveTopology(
            'MULTIPOINT((190 300), (10 11))', 4);
-- Answer:   MULTIPOINT((190 300), (10 11))

-- Simplify a LINESTRING:
SELECT ST_SimplifyPreserveTopology(
            'LINESTRING(250 250, 280 290, 300 230, 340 300, 360 260,
                        440 310, 470 360, 604 286)',
            40);
-- Answer:   LINESTRING(250 250, 280 290, 300 230, 470 360, 604 286)
Comparison with ST_Simplify
CREATE TABLE INPUT_TABLE(geom GEOMETRY);
INSERT INTO INPUT_TABLE VALUES (
    'POLYGON((8 25, 28 22, 28 20, 15 11, 33 3, 56 30,
              46 33, 46 34, 47 44, 35 36, 45 33, 43 19,
              29 21, 29 22, 35 26, 24 39, 8 25))');

-- Notice that the result of ST_SimplifyPreserveTopology contains
-- more vertices than the result of ST_Simplify. In general, it will
-- contain enough to ensure validity.
SELECT ST_SimplifyPreserveTopology(geom, 20) SPT,
       ST_Simplify(geom, 20) S FROM INPUT_TABLE;

-- Answer:
-- |               SPT              |            S          |
-- |--------------------------------|-----------------------|
-- | POLYGON((8 25, 33 3, 56 30,    | POLYGON((8 25, 56 30, |
-- |          47 44, 43 19, 8 25))  |          33 3, 8 25)) |

CREATE TABLE INPUT_TABLE(geom GEOMETRY);
INSERT INTO INPUT_TABLE VALUES (
    'POLYGON((5 7, 2 5, 5 4, 13 4, 18 7, 16 11, 7 9, 11 7, 5 7),
             (13 8, 13 6, 14 6, 15 9, 13 8))');

-- Here ST_SimplifyPreserveTopology keeps the hole whereas
-- ST_Simplify removes it:
SELECT ST_SimplifyPreserveTopology(geom, 3) SPT,
       ST_Simplify(geom, 3) S FROM INPUT_TABLE;

-- Answer:
-- |              SPT            |              S             |
-- |-----------------------------|----------------------------|
-- | POLYGON((5 7, 2 5, 13 4,    | POLYGON((5 7, 16 11, 18 7, |
-- |          18 7, 16 11, 5 7), |          2 5, 5 7))        |
-- |         (13 8, 13 6, 14 6,  |                            |
-- |          15 9, 13 8))       |                            |

See also