processing

This module contains functions that computes new geographies by processing existing geographies.

ST_DELAUNAYLINES

ST_DELAUNAYLINES(points)

Description

Calculates the Delaunay triangulation of the points provided. An array of line strings is returned.

• points: ARRAY<GEOGRAPHY> input to the Delaunay triangulation.

Due to technical limitations of the underlying libraries used, the input points' coordinates are truncated to 5 decimal places in order to avoid problems that happen with close but distinct input points. This limits the precision of the results and can alter slightly the position of the resulting polygons (about 1 meter). This can also result in some points being merged together, so that fewer polygons than expected may result.

warning

The maximum number of points typically used to compute Delaunay diagrams is 300,000. This limit ensures efficient computation while maintaining accuracy in delineating regions based on proximity to specified points.

Return type

ARRAY<GEOGRAPHY>

Examples

carto-un

SELECT `carto-un`.carto.ST_DELAUNAYLINES(
  [
    ST_GEOGPOINT(-74.5366825512491, 43.6889777784079),
    ST_GEOGPOINT(-74.4821382017478, 43.3096147774153),
    ST_GEOGPOINT(-70.7632814028801, 42.9679602005825),
    ST_GEOGPOINT(-73.3262122666779, 41.2706174323278),
    ST_GEOGPOINT(-70.2005131676838, 43.8455720129728),
    ST_GEOGPOINT(-73.9704330709753, 35.3953164724094),
    ST_GEOGPOINT(-72.3402283537205, 35.8941454568627),
    ST_GEOGPOINT(-72.514071762468, 36.5823995124737)
  ]
);
-- LINESTRING(-74.5366825512491 43.6889777784079, -70.7632814028801 ...
-- LINESTRING(-74.4821382017478 43.3096147774153, -74.5366825512491  ...
-- LINESTRING(-73.3262122666779 41.2706174323278, -74.4821382017478 ...
-- LINESTRING(-73.9704330709753 35.3953164724094, -72.3402283537205 ...
-- LINESTRING(-73.9704330709753 35.3953164724094, -72.514071762468 ...
-- LINESTRING(-72.514071762468 36.5823995124737, -73.3262122666779 ...

carto-un-eu

manual

Note that if some points are very close together (about 1 meter) they may be merged and the result may have fewer lines than expected, for example these four points result in two lines:

carto-un

SELECT `carto-un`.carto.ST_DELAUNAYLINES(
     [
          ST_GEOGPOINT(4.1829523, 43.6347910),
          ST_GEOGPOINT(4.1829967, 43.6347137),
          ST_GEOGPOINT(4.1829955, 43.6347143),
          ST_GEOGPOINT(4.1829321, 43.6347500)
     ]
);
-- [
--   LINESTRING(4.18293 43.63475, 4.183 43.63471, 4.18295 43.63479, 4.18293 43.63475)
-- ]

carto-un-eu

manual

Additional examples

• A NYC subway connection graph using Delaunay triangulation

ST_DELAUNAYPOLYGONS

ST_DELAUNAYPOLYGONS(points)

Description

Calculates the Delaunay triangulation of the points provided. An array of polygons is returned.

• points: ARRAY<GEOGRAPHY> input to the Delaunay triangulation.

Due to technical limitations of the underlying libraries used, the input points' coordinates are truncated to 5 decimal places in order to avoid problems that happen with close but distinct input points. This limits the precision of the results and can alter slightly the position of the resulting polygons (about 1 meter). This can also result in some points being merged together, so that fewer polygons than expected may result.

warning

The maximum number of points typically used to compute Delaunay diagrams is 300,000. This limit ensures efficient computation while maintaining accuracy in delineating regions based on proximity to specified points.

Return type

ARRAY<GEOGRAPHY>

Examples

carto-un

SELECT `carto-un`.carto.ST_DELAUNAYPOLYGONS(
  [
    ST_GEOGPOINT(-74.5366825512491, 43.6889777784079),
    ST_GEOGPOINT(-74.4821382017478, 43.3096147774153),
    ST_GEOGPOINT(-70.7632814028801, 42.9679602005825),
    ST_GEOGPOINT(-73.3262122666779, 41.2706174323278),
    ST_GEOGPOINT(-70.2005131676838, 43.8455720129728),
    ST_GEOGPOINT(-73.9704330709753, 35.3953164724094),
    ST_GEOGPOINT(-72.3402283537205, 35.8941454568627),
    ST_GEOGPOINT(-72.514071762468, 36.5823995124737)
  ]
);
-- [
--   POLYGON((-74.5366825512491 43.6889777784079, -70.7632814028801 42.9679602005825, -70.2005131676838 43.8455720129728, -74.5366825512491 43.6889777784079)),
--   POLYGON((-70.7632814028801 42.9679602005825, -74.5366825512491 43.6889777784079, -74.4821382017478 43.3096147774153, -70.7632814028801 42.9679602005825)),
--   POLYGON((-70.7632814028801 42.9679602005825, -74.4821382017478 43.3096147774153, -73.3262122666779 41.2706174323278, -70.7632814028801 42.9679602005825)),
--   POLYGON((-73.9704330709753 35.3953164724094, -72.3402283537205 35.8941454568627, -72.514071762468 36.5823995124737, -73.9704330709753 35.3953164724094)),
--   POLYGON((-73.9704330709753 35.3953164724094, -72.514071762468 36.5823995124737, -73.3262122666779 41.2706174323278, -73.9704330709753 35.3953164724094)),
--  POLYGON((-70.7632814028801 42.9679602005825, -73.3262122666779 41.2706174323278, -72.514071762468 36.5823995124737, -70.7632814028801 42.9679602005825))]
-- ]

carto-un-eu

manual

Note that if some points are very close together (about 1 meter) they may be merged and the result may have fewer triangles than expected, for example these four points result in one triangle:

carto-un

SELECT `carto-un`.carto.ST_DELAUNAYPOLYGONS(
     [
          ST_GEOGPOINT(4.1829523, 43.6347910),
          ST_GEOGPOINT(4.1829967, 43.6347137),
          ST_GEOGPOINT(4.1829955, 43.6347143),
          ST_GEOGPOINT(4.1829321, 43.6347500)
     ]
);
-- [ POLYGON((4.18293 43.63475, 4.183 43.63471, 4.18295 43.63479, 4.18293 43.63475)) ]

carto-un-eu

manual

ST_POLYGONIZE

ST_POLYGONIZE(lines)

Description

Creates a set of polygons from geographies which contain lines that represent the their edges.

• lines: ARRAY<GEOGRAPHY> array of lines which represent the polygons edges.

Return type

ARRAY<GEOGRAPHY>

Example

carto-un

SELECT `carto-un`.carto.ST_POLYGONIZE(
  [
    ST_GEOGFROMTEXT('LINESTRING(-74.5366825512491 43.6889777784079, -70.7632814028801 42.9679602005825, -70.2005131676838 43.8455720129728, -74.5366825512491 43.6889777784079)'),
    ST_GEOGFROMTEXT('LINESTRING(-73.9704330709753 35.3953164724094, -72.514071762468 36.5823995124737, -73.3262122666779 41.2706174323278, -73.9704330709753 35.3953164724094)')
  ]
);
-- POLYGON((-74.5366825512491 43.6889777784079, -70.7632814028801 42.9679602005825, -70.2005131676838 43.8455720129728, -74.5366825512491 43.6889777784079))
-- POLYGON((-73.9704330709753 35.3953164724094, -72.514071762468 36.5823995124737, -73.3262122666779 41.2706174323278, -73.9704330709753 35.3953164724094))

carto-un-eu

manual

Additional examples

• Identifying earthquake-prone areas in the state of California

ST_VORONOILINES

ST_VORONOILINES(points, bbox)

Description

Calculates the Voronoi diagram of the points provided. An array of lines is returned.

• points: ARRAY<GEOGRAPHY> input to the Voronoi diagram.

• bbox: ARRAY<FLOAT64>|NULL clipping bounding box. If NULL a default [-180,-85,180,-85] bbox will be used.

Due to technical limitations of the underlying libraries used, the input points' coordinates are truncated to 5 decimal places in order to avoid problems that happen with close but distinct input points. This limits the precision of the results and can alter slightly the position of the resulting lines (about 1 meter). This can also result in some points being merged together, so that fewer lines than input points may result.

warning

The maximum number of points typically used to compute Voronoi diagrams is 300,000. This limit ensures efficient computation while maintaining accuracy in delineating regions based on proximity to specified points.

Return type

ARRAY<GEOGRAPHY>

Examples

carto-un

SELECT `carto-un`.carto.ST_VORONOILINES(
  [
    ST_GEOGPOINT(-75.833, 39.284),
    ST_GEOGPOINT(-75.6, 39.984),
    ST_GEOGPOINT(-75.221, 39.125)
  ],
  [-76.0, 39.0, -75.0, 40.0]
);
-- LINESTRING(-76 39.728365, -75.8598447436013 39.6817133217987, ...
-- LINESTRING(-75 39.7356169965076, -75.2196894872026 39.6386876418512, ...
-- LINESTRING(-75.5801299019608 39, -75.509754438183 39.2708791435974, ...

carto-un-eu

manual

Note that if some points are very close together (about 1 meter) they may be merged and the result may have fewer lines than points, for example these three points result in two lines

carto-un

SELECT `carto-un`.carto.ST_VORONOILINES(
     [
          ST_GEOGPOINT(4.1829523,43.6347910),
          ST_GEOGPOINT(4.1829967,43.6347137),
          ST_GEOGPOINT(4.1829955,43.6347143)
     ],
     [4.182, 43.634, 4.183, 43.635]
);
-- [
--   LINESTRING(4.183 43.634765625, 4.182 43.634140625, 4.182 43.635, 4.183 43.635, 4.183 43.634765625),
--   LINESTRING(4.182 43.634140625, 4.183 43.634765625, 4.183 43.634, 4.182 43.634, 4.182 43.634140625)
--  ]

carto-un-eu

manual

ST_VORONOIPOLYGONS

ST_VORONOIPOLYGONS(points, bbox)

Description

Calculates the Voronoi diagram of the points provided. An array of polygons is returned.

• points: ARRAY<GEOGRAPHY> input to the Voronoi diagram.

• bbox: ARRAY<FLOAT64>|NULL clipping bounding box. If NULL a default [-180,-85,180,-85] bbox will be used.

Due to technical limitations of the underlying libraries used, the input points' coordinates are truncated to 5 decimal places in order to avoid problems that happen with close but distinct input points. This limits the precision of the results and can alter slightly the position of the resulting polygons (about 1 meter). This can also result in some points being merged together, so that fewer polygons than input points may result.

warning

The maximum number of points typically used to compute Voronoi diagrams is 300,000. This limit ensures efficient computation while maintaining accuracy in delineating regions based on proximity to specified points.

Return type

ARRAY<GEOGRAPHY>

Examples

carto-un

SELECT `carto-un`.carto.ST_VORONOIPOLYGONS(
  [
    ST_GEOGPOINT(-75.833, 39.284),
    ST_GEOGPOINT(-75.6, 39.984),
    ST_GEOGPOINT(-75.221, 39.125)
  ],
  [-76.0, 39.0, -75.0, 40.0]
);
-- POLYGON((-76 39, -75.7900649509804 39, -75.5801299019608 39, ...
-- POLYGON((-75 40, -75.25 40, -75.5 40, -75.75 40, -76 40, ...
-- POLYGON((-75.43509742git64706 39, -75.2900649509804 39, ...

carto-un-eu

manual

Note that if some points are very close together (about 1 meter) they may be merged and the result may have fewer polygons than points, for example these three points result in two polygons:

carto-un

SELECT `carto-un`.carto.ST_VORONOIPOLYGONS(
     [
          ST_GEOGPOINT(4.1829523,43.6347910),
          ST_GEOGPOINT(4.1829967,43.6347137),
          ST_GEOGPOINT(4.1829955,43.6347143)
     ],
     [4.182, 43.634, 4.183, 43.635]
);
-- [
--   POLYGON((4.183 43.635, 4.182 43.635, 4.182 43.634140625, 4.183 43.634765625, 4.183 43.635)),
--   POLYGON((4.182 43.634, 4.183 43.634, 4.183 43.634765625, 4.182 43.634140625, 4.182 43.634))
-- ]

carto-un-eu

manual

Additional examples

• Analyzing weather stations coverage using a Voronoi diagram

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 960401.