geo_polygon_densify()

Converts polygon or multipolygon planar edges to geodesics by adding intermediate points.

Syntax

geo_polygon_densify(polygon, tolerance)

geo_polygon_densify(polygon, tolerance, preserve_crossing)

Arguments

• polygon: Polygon or multipolygon in the GeoJSON format and of a dynamic data type.
• tolerance: An optional numeric that defines maximum distance in meters between the original planar edge and the converted geodesic edge chain. Supported values are in the range [0.1, 10000]. If unspecified, the default value is 10.
• preserve_crossing: An optional boolean that preserves edge crossing over antimeridian. If unspecified, the default value False is used.

Polygon definition

dynamic({"type": "Polygon","coordinates": [ LinearRingShell, LinearRingHole_1 ,..., LinearRingHole_N ]})

dynamic({"type": "MultiPolygon","coordinates": [[ LinearRingShell, LinearRingHole_1 ,..., LinearRingHole_N ] ,..., [LinearRingShell, LinearRingHole_1 ,..., LinearRingHole_M]]})

• LinearRingShell is required and defined as a counterclockwise ordered array of coordinates [[lng_1,lat_1],...,[lng_i,lat_i],...,[lng_j,lat_j],...,[lng_1,lat_1]]. There can be only one shell.
• LinearRingHole is optional and defined as a clockwise ordered array of coordinates [[lng_1,lat_1],...,[lng_i,lat_i],...,[lng_j,lat_j],...,[lng_1,lat_1]]. There can be any number of interior rings and holes.
• LinearRing vertices must be distinct with at least three coordinates. The first coordinate must be equal to the last. At least four entries are required.
• Coordinates [longitude,latitude] must be valid. Longitude must be a real number in the range [-180, +180] and latitude must be a real number in the range [-90, +90].
• LinearRingShell encloses at most half of the sphere. LinearRing divides the sphere into two regions. The smaller of the two regions will be chosen.
• LinearRing edge length must be less than 180 degrees. The shortest edge between the two vertices will be chosen.

Constraints

• The maximum number of points in the densified polygon is limited to 10485760.
• Storing polygons in dynamic format has size limits.
• Densifying a valid polygon may invalidate the polygon. The algorithm adds points in a non-uniform manner, and as such may cause edges to intertwine with each other.

Motivation

• GeoJSON format defines an edge between two points as a straight cartesian line while Azure Data Explorer uses geodesic.
• The decision to use geodesic or planar edges might depend on the dataset and is especially relevant in long edges.

Returns

Densified polygon in the GeoJSON format and of a dynamic data type. If either the polygon or tolerance is invalid, the query will produce a null result.

Note

• The geospatial coordinates are interpreted as represented by the WGS-84 coordinate reference system.

Examples

The following example densifies Manhattan Central Park polygon. The edges are short and the distance between planar edges and their geodesic counterparts is less than the distance specified by tolerance. As such, the result remains unchanged.

print densified_polygon = tostring(geo_polygon_densify(dynamic({"type":"Polygon","coordinates":[[[-73.958244,40.800719],[-73.949146,40.79695],[-73.973093,40.764226],[-73.982062,40.768159],[-73.958244,40.800719]]]})))

densified_polygon
{"type":"Polygon","coordinates":[[[-73.958244,40.800719],[-73.949146,40.79695],[-73.973093,40.764226],[-73.982062,40.768159],[-73.958244,40.800719]]]}

The following example densifies two edges of the polygon. Densified edges length is ~110 km

print densified_polygon = tostring(geo_polygon_densify(dynamic({"type":"Polygon","coordinates":[[[10,10],[11,10],[11,11],[10,11],[10,10]]]})))

densified_polygon
{"type":"Polygon","coordinates":[[[10,10],[10.25,10],[10.5,10],[10.75,10],[11,10],[11,11],[10.75,11],[10.5,11],[10.25,11],[10,11],[10,10]]]}

The following example returns a null result because of the invalid coordinate input.

print densified_polygon = geo_polygon_densify(dynamic({"type":"Polygon","coordinates":[[[10,900],[11,10],[11,11],[10,11],[10,10]]]}))

densified_polygon

The following example returns a null result because of the invalid tolerance input.

print densified_polygon = geo_polygon_densify(dynamic({"type":"Polygon","coordinates":[[[10,10],[11,10],[11,11],[10,11],[10,10]]]}), 0)

densified_polygon