ST_CatmullRomSmoothing
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Name

ST_CatmullRomSmoothing — Returns a smoothed version of a geometry, using the Catmull-Rom spline algorithm

Synopsis

geometry ST_CatmullRomSmoothing(geometry geom, integer nSegments = 5);

Description

Smoothes a linear or polygonal geometry using the Catmull-Rom spline algorithm. Unlike ST_ChaikinSmoothing, this is an interpolating spline: the output curve passes through every original vertex. Between each pair of consecutive original vertices, nSegments - 1 new intermediate points are inserted.

The nSegments parameter controls the density of the output. With nSegments = 5 (the default), each original span is divided into 5 sub-segments (inserting 4 new points per span). The minimum value is 2.

At least 4 input vertices are required to apply smoothing; geometries with fewer vertices are returned unchanged. Points and multipoints are always returned unchanged.

[Note]

The output vertex count grows as 1 + (N-1) * nSegments for open lines, and 1 + N * nSegments for closed rings, where N is the number of input vertices. For large geometries, use a simplification function on the result to reduce the number of points (see ST_Simplify, ST_SimplifyPreserveTopology and ST_SimplifyVW).

The result has interpolated values for the Z and M dimensions when present.

This function supports 3d and will not drop the z-index.

Availability: 3.6.0

Examples

Smoothing a LineString using nSegments = 5 and 10.

Code
WITH input(geom) AS (VALUES
  ('LINESTRING (10 140,80 130,100 190,190 150,140 20,120 120,50 30,30 100)'::geometry)
)
SELECT ST_CatmullRomSmoothing(geom, 5) AS segments_5,
  ST_CatmullRomSmoothing(geom, 10) AS segments_10
FROM input;
Output
LINESTRING(10 140,24.8 136.88,40.4 132.64,55.6 128.96,69.2 127.52,80 130,86.08 139.12,88.24 153.76,89.36 169.84,92.32 183.28,100 190,115.76 189.84,137.68 185.52,160.72 177.28,179.84 165.36,190 150,188.48 126.08,178.64 93.44,164.56 59.76,150.32 32.72,140 20,134.88 28.32,132.24 52.56,130.16 82.64,126.72 108.48,120 120,108.4 111.6,93.2 90,76.8 63.6,61.6 40.8,50 30,42.8 33.76,38.4 46.48,35.6 64.32,33.2 83.44,30 100) | LINESTRING(10 140,17.225 138.685,24.8 136.88,32.575 134.795,40.4 132.64,48.125 130.625,55.6 128.96,62.675 127.855,69.2 127.52,75.025 128.165,80 130,83.71 133.615,86.08 139.12,87.47 146.005,88.24 153.76,88.75 161.875,89.36 169.84,90.43 177.145,92.32 183.28,95.39 187.735,100 190,106.795 190.455,115.76 189.84,126.265 188.185,137.68 185.52,149.375 181.875,160.72 177.28,171.085 171.765,179.84 165.36,186.355 158.095,190 150,190.535 139.61,188.48 126.08,184.345 110.37,178.64 93.44,171.875 76.25,164.56 59.76,157.205 44.93,150.32 32.72,144.415 24.09,140 20,137.01 21.54,134.88 28.32,133.37 39.08,132.24 52.56,131.25 67.5,130.16 82.64,128.73 96.72,126.72 108.48,123.89 116.66,120 120,114.8 117.975,108.4 111.6,101.1 101.925,93.2 90,85 76.875,76.8 63.6,68.9 51.225,61.6 40.8,55.2 33.375,50 30,45.975 30.52,42.8 33.76,40.325 39.24,38.4 46.48,36.875 55,35.6 64.32,34.425 73.96,33.2 83.44,31.775 92.28,30 100)
Figure
Geometry figure for visual-st-catmullromsmoothing-01

Smoothing a 4-point collinear line with default nSegments=5 shows the minimal change case.

Code
SELECT ST_CatmullRomSmoothing('LINESTRING(0 0,5 0,10 0,15 0)');
Output
LINESTRING(0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 0,10 0,11 0,12 0,13 0,14 0,15 0)
Figure
Geometry figure for visual-st-catmullromsmoothing-02

Smoothing a Polygon using nSegments = 5 and 10. This larger example is kept last.

Code
WITH input(geom) AS (VALUES
  ('POLYGON ((20 20,60 90,10 150,100 190,190 160,130 120,190 50,140 70,120 10,90 60,20 20))'::geometry)
)
SELECT ST_CatmullRomSmoothing(geom, 5) AS segments_5,
  ST_CatmullRomSmoothing(geom, 10) AS segments_10
FROM input;
Output
POLYGON((20 20,22.4 27.12,32.4 40.56,45.2 57.44,56 74.88,60 90,53.52 102.96,39.76 115.68,24.24 127.92,12.48 139.44,10 150,19.04 160.4,35.92 170.8,57.28 180,79.76 186.8,100 190,120.4 188.64,143.2 183.52,164.8 176.08,181.6 167.76,190 160,185.68 153.12,171.04 146.16,152.56 138.64,136.72 130.08,130 120,136.08 106.48,150.64 89.84,168.16 72.96,183.12 58.72,190 50,186.56 49.52,176.48 55.36,163.12 63.44,149.84 69.68,140 70,134.24 61.36,130.32 46.48,127.28 29.92,124.16 16.24,120 10,115.28 14.4,110.64 26.4,105.36 41.2,98.72 54,90 60,76.8 56,59.6 45.2,42 32.4,27.6 22.4,20 20)) | POLYGON((20 20,19.95 22.59,22.4 27.12,26.75 33.23,32.4 40.56,38.75 48.75,45.2 57.44,51.15 66.27,56 74.88,59.15 82.91,60 90,58.015 96.495,53.52 102.96,47.205 109.365,39.76 115.68,31.875 121.875,24.24 127.92,17.545 133.785,12.48 139.44,9.735 144.855,10 150,13.33 155.125,19.04 160.4,26.71 165.675,35.92 170.8,46.25 175.625,57.28 180,68.59 183.775,79.76 186.8,90.37 188.925,100 190,109.675 189.88,120.4 188.64,131.725 186.46,143.2 183.52,154.375 180,164.8 176.08,174.025 171.94,181.6 167.76,187.075 163.72,190 160,189.535 156.54,185.68 153.12,179.245 149.68,171.04 146.16,161.875 142.5,152.56 138.64,143.905 134.52,136.72 130.08,131.815 125.26,130 120,131.635 113.81,136.08 106.48,142.645 98.37,150.64 89.84,159.375 81.25,168.16 72.96,176.305 65.33,183.12 58.72,187.915 53.49,190 50,189.32 48.715,186.56 49.52,182.14 51.905,176.48 55.36,170 59.375,163.12 63.44,156.26 67.045,149.84 69.68,144.28 70.835,140 70,136.83 66.745,134.24 61.36,132.11 54.415,130.32 46.48,128.75 38.125,127.28 29.92,125.79 22.435,124.16 16.24,122.27 11.905,120 10,117.585 10.95,115.28 14.4,112.995 19.75,110.64 26.4,108.125 33.75,105.36 41.2,102.255 48.15,98.72 54,94.665 58.15,90 60,84.125 59.15,76.8 56,68.475 51.15,59.6 45.2,50.625 38.75,42 32.4,34.175 26.75,27.6 22.4,22.725 19.95,20 20))
Figure
Geometry figure for visual-st-catmullromsmoothing-03