====================
Geospatial Functions
====================

Presto Geospatial functions that begin with the ``ST_`` prefix support the SQL/MM specification
and are compliant with the Open Geospatial Consortium’s (OGC) OpenGIS Specifications.
As such, many Presto Geospatial functions require, or more accurately, assume that
geometries that are operated on are both simple and valid. For example, it does not
make sense to calculate the area of a polygon that has a hole defined outside of the
polygon, or to construct a polygon from a non-simple boundary line.

Presto Geospatial functions support the Well-Known Text (WKT) and Well-Known Binary (WKB) form of spatial objects:

* ``POINT (0 0)``
* ``LINESTRING (0 0, 1 1, 1 2)``
* ``POLYGON ((0 0, 4 0, 4 4, 0 4, 0 0), (1 1, 2 1, 2 2, 1 2, 1 1))``
* ``MULTIPOINT (0 0, 1 2)``
* ``MULTILINESTRING ((0 0, 1 1, 1 2), (2 3, 3 2, 5 4))``
* ``MULTIPOLYGON (((0 0, 4 0, 4 4, 0 4, 0 0), (1 1, 2 1, 2 2, 1 2, 1 1)), ((-1 -1, -1 -2, -2 -2, -2 -1, -1 -1)))``
* ``GEOMETRYCOLLECTION (POINT(2 3), LINESTRING (2 3, 3 4))``

Use :func:`ST_GeometryFromText` and :func:`ST_GeomFromBinary` functions to create geometry
objects from WKT or WKB.

The ``SphericalGeography`` type provides native support for spatial features represented on
*geographic* coordinates (sometimes called *geodetic* coordinates, or *lat/lon*, or *lon/lat*).
Geographic coordinates are spherical coordinates expressed in angular units (degrees).

The basis for the ``Geometry`` type is a plane. The shortest path between two points on the plane is a
straight line. That means calculations on geometries (areas, distances, lengths, intersections, etc)
can be calculated using cartesian mathematics and straight line vectors.

The basis for the ``SphericalGeography`` type is a sphere. The shortest path between two points on the
sphere is a great circle arc. That means that calculations on geographies (areas, distances,
lengths, intersections, etc) must be calculated on the sphere, using more complicated mathematics.
More accurate measurements that take the actual spheroidal shape of the world into account are not
supported.

Values returned by the measurement functions :func:`ST_Distance` and :func:`ST_Length` are in the unit of meters;
values returned by :func:`ST_Area` are in square meters.

Use :func:`to_spherical_geography()` function to convert a geometry object to geography object.

For example, ``ST_Distance(ST_Point(-71.0882, 42.3607), ST_Point(-74.1197, 40.6976))`` returns
``3.4577`` in the unit of the passed-in values on the euclidean plane, while
``ST_Distance(to_spherical_geography(ST_Point(-71.0882, 42.3607)), to_spherical_geography(ST_Point(-74.1197, 40.6976)))``
returns ``312822.179`` in meters.


Constructors
------------

.. function:: ST_AsBinary(Geometry) -> varbinary

    Returns the WKB representation of the geometry.

.. function:: ST_AsText(Geometry) -> varchar

    Returns the WKT representation of the geometry. For empty geometries,
    ``ST_AsText(ST_LineFromText('LINESTRING EMPTY'))`` will produce ``'MULTILINESTRING EMPTY'``
    and ``ST_AsText(ST_Polygon('POLYGON EMPTY'))`` will produce ``'MULTIPOLYGON EMPTY'``.

.. function:: ST_GeometryFromText(varchar) -> Geometry

    Returns a geometry type object from WKT representation.

.. function:: ST_GeomFromBinary(varbinary) -> Geometry

    Returns a geometry type object from WKB representation.

.. function:: geometry_from_hadoop_shape(varbinary) -> Geometry

    Returns a geometry type object from Spatial Framework for Hadoop representation.

.. function:: ST_LineFromText(varchar) -> LineString

    Returns a geometry type linestring object from WKT representation.

.. function:: ST_LineString(array(Point)) -> LineString

    Returns a LineString formed from an array of points. If there are fewer than
    two non-empty points in the input array, an empty LineString will be returned.
    Array elements must not be ``NULL`` or the same as the previous element.
    The returned geometry may not be simple, e.g. may self-intersect or may contain
    duplicate vertexes depending on the input.

.. function:: ST_MultiPoint(array(Point)) -> MultiPoint

    Returns a MultiPoint geometry object formed from the specified points. Returns ``NULL`` if input array is empty.
    Array elements must not be ``NULL`` or empty.
    The returned geometry may not be simple and may contain duplicate points if input array has duplicates.

.. function:: ST_Point(double, double) -> Point

    Returns a geometry type point object with the given coordinate values.

.. function:: ST_Polygon(varchar) -> Polygon

    Returns a geometry type polygon object from WKT representation.

.. function:: to_spherical_geography(Geometry) -> SphericalGeography

    Converts a Geometry object to a SphericalGeography object on the sphere of the Earth's radius. This
    function is only applicable to ``POINT``, ``MULTIPOINT``, ``LINESTRING``, ``MULTILINESTRING``,
    ``POLYGON``, ``MULTIPOLYGON`` geometries defined in 2D space, or ``GEOMETRYCOLLECTION`` of such
    geometries. For each point of the input geometry, it verifies that ``point.x`` is within
    ``[-180.0, 180.0]`` and ``point.y`` is within ``[-90.0, 90.0]``, and uses them as (longitude, latitude)
    degrees to construct the shape of the ``SphericalGeography`` result.

.. function:: to_geometry(SphericalGeography) -> Geometry

    Converts a SphericalGeography object to a Geometry object.

Relationship Tests
------------------

.. function:: ST_Contains(Geometry, Geometry) -> boolean

    Returns ``true`` if and only if no points of the second geometry lie in the exterior
    of the first geometry, and at least one point of the interior of the first geometry
    lies in the interior of the second geometry.

.. function:: ST_Crosses(Geometry, Geometry) -> boolean

    Returns ``true`` if the supplied geometries have some, but not all, interior points in common.

.. function:: ST_Disjoint(Geometry, Geometry) -> boolean

    Returns ``true`` if the give geometries do not *spatially intersect* --
    if they do not share any space together.

.. function:: ST_Equals(Geometry, Geometry) -> boolean

    Returns ``true`` if the given geometries represent the same geometry.

.. function:: ST_Intersects(Geometry, Geometry) -> boolean

    Returns ``true`` if the given geometries spatially intersect in two dimensions
    (share any portion of space) and ``false`` if they do not (they are disjoint).

.. function:: ST_Overlaps(Geometry, Geometry) -> boolean

    Returns ``true`` if the given geometries share space, are of the same dimension,
    but are not completely contained by each other.

.. function:: ST_Relate(Geometry, Geometry) -> boolean

    Returns ``true`` if first geometry is spatially related to second geometry.

.. function:: ST_Touches(Geometry, Geometry) -> boolean

    Returns ``true`` if the given geometries have at least one point in common,
    but their interiors do not intersect.

.. function:: ST_Within(Geometry, Geometry) -> boolean

    Returns ``true`` if first geometry is completely inside second geometry.

Operations
----------

.. function:: geometry_union(array(Geometry)) -> Geometry

    Returns a geometry that represents the point set union of the input geometries. Performance
    of this function, in conjunction with :func:`array_agg` to first aggregate the input geometries,
    may be better than :func:`geometry_union_agg`, at the expense of higher memory utilization.

.. function:: ST_Boundary(Geometry) -> Geometry

    Returns the closure of the combinatorial boundary of this geometry.

.. function:: ST_Buffer(Geometry, distance) -> Geometry

    Returns the geometry that represents all points whose distance from the specified geometry
    is less than or equal to the specified distance.

.. function:: ST_Difference(Geometry, Geometry) -> Geometry

    Returns the geometry value that represents the point set difference of the given geometries.

.. function:: ST_Envelope(Geometry) -> Geometry

    Returns the bounding rectangular polygon of a geometry.

.. function:: ST_EnvelopeAsPts(Geometry) -> array(Geometry)

    Returns an array of two points: the lower left and upper right corners of the bounding
    rectangular polygon of a geometry. Returns ``NULL`` if input geometry is empty.

.. function:: ST_ExteriorRing(Geometry) -> Geometry

    Returns a line string representing the exterior ring of the input polygon.

.. function:: ST_Intersection(Geometry, Geometry) -> Geometry

    Returns the geometry value that represents the point set intersection of two geometries.

.. function:: ST_SymDifference(Geometry, Geometry) -> Geometry

    Returns the geometry value that represents the point set symmetric difference of two geometries.

.. function:: ST_Union(Geometry, Geometry) -> Geometry

    Returns a geometry that represents the point set union of the input geometries.

    See also:  :func:`geometry_union`, :func:`geometry_union_agg`


Accessors
---------

.. function:: ST_Area(Geometry) -> double

    Returns the 2D Euclidean area of a geometry.

    For Point and LineString types, returns 0.0.
    For GeometryCollection types, returns the sum of the areas of the individual
    geometries.

.. function:: ST_Area(SphericalGeography) -> double

    Returns the area of a polygon or multi-polygon in square meters using a spherical model for Earth.

.. function:: ST_Centroid(Geometry) -> Geometry

    Returns the point value that is the mathematical centroid of a geometry.

.. function:: ST_ConvexHull(Geometry) -> Geometry

    Returns the minimum convex geometry that encloses all input geometries.

.. function:: ST_CoordDim(Geometry) -> bigint

    Returns the coordinate dimension of the geometry.

.. function:: ST_Dimension(Geometry) -> bigint

    Returns the inherent dimension of this geometry object, which must be
    less than or equal to the coordinate dimension.

.. function:: ST_Distance(Geometry, Geometry) -> double

    Returns the 2-dimensional cartesian minimum distance (based on spatial ref)
    between two geometries in projected units.

.. function:: ST_Distance(SphericalGeography, SphericalGeography) -> double

    Returns the great-circle distance in meters between two SphericalGeography points.

.. function:: ST_GeometryN(Geometry, index) -> Geometry

    Returns the geometry element at a given index (indices start at 1).
    If the geometry is a collection of geometries (e.g., GEOMETRYCOLLECTION or MULTI*),
    returns the geometry at a given index.
    If the given index is less than 1 or greater than the total number of elements in the collection,
    returns ``NULL``.
    Use :func:`ST_NumGeometries` to find out the total number of elements.
    Singular geometries (e.g., POINT, LINESTRING, POLYGON), are treated as collections of one element.
    Empty geometries are treated as empty collections.

.. function:: ST_InteriorRingN(Geometry, index) -> Geometry

   Returns the interior ring element at the specified index (indices start at 1). If
   the given index is less than 1 or greater than the total number of interior rings
   in the input geometry, returns ``NULL``. The input geometry must be a polygon.
   Use :func:`ST_NumInteriorRing` to find out the total number of elements.

.. function:: ST_GeometryType(Geometry) -> varchar

    Returns the type of the geometry.

.. function:: ST_IsClosed(Geometry) -> boolean

    Returns ``true`` if the linestring's start and end points are coincident.

.. function:: ST_IsEmpty(Geometry) -> boolean

    Returns ``true`` if this Geometry is an empty geometrycollection, polygon, point etc.

.. function:: ST_IsSimple(Geometry) -> boolean

    Returns ``true`` if this Geometry has no anomalous geometric points, such as self intersection or self tangency.

.. function:: ST_IsRing(Geometry) -> boolean

    Returns ``true`` if and only if the line is closed and simple.

.. function:: ST_IsValid(Geometry) -> boolean

    Returns ``true`` if and only if the input geometry is well formed.
    Use :func:`geometry_invalid_reason` to determine why the geometry is not well formed.

.. function:: ST_Length(Geometry) -> double

    Returns the length of a linestring or multi-linestring using Euclidean measurement on a
    two dimensional plane (based on spatial ref) in projected units.

.. function:: ST_Length(SphericalGeography) -> double

    Returns the length of a linestring or multi-linestring on a spherical model of the Earth.
    This is equivalent to the sum of great-circle distances between adjacent points on the linestring.

.. function:: ST_PointN(LineString, index) -> Point

    Returns the vertex of a linestring at a given index (indices start at 1).
    If the given index is less than 1 or greater than the total number of elements in the collection,
    returns ``NULL``.
    Use :func:`ST_NumPoints` to find out the total number of elements.

.. function:: ST_Points(Geometry) -> array(Point)

    Returns an array of points in a linestring.

.. function:: ST_XMax(Geometry) -> double

    Returns X maxima of a bounding box of a geometry.

.. function:: ST_YMax(Geometry) -> double

    Returns Y maxima of a bounding box of a geometry.

.. function:: ST_XMin(Geometry) -> double

    Returns X minima of a bounding box of a geometry.

.. function:: ST_YMin(Geometry) -> double

    Returns Y minima of a bounding box of a geometry.

.. function:: ST_StartPoint(Geometry) -> point

    Returns the first point of a LineString geometry as a Point.
    This is a shortcut for ``ST_PointN(geometry, 1)``.

.. function:: simplify_geometry(Geometry, double) -> Geometry

    Returns a "simplified" version of the input geometry using the Douglas-Peucker algorithm.
    Will avoid creating derived geometries (polygons in particular) that are invalid.

.. function:: ST_EndPoint(Geometry) -> point

    Returns the last point of a LineString geometry as a Point.
    This is a shortcut for ``ST_PointN(geometry, ST_NumPoints(geometry))``.

.. function:: ST_X(Point) -> double

    Returns the X coordinate of the point.

.. function:: ST_Y(Point) -> double

    Returns the Y coordinate of the point.

.. function:: ST_InteriorRings(Geometry) -> array(Geometry)

   Returns an array of all interior rings found in the input geometry, or an empty
   array if the polygon has no interior rings. Returns ``NULL`` if the input geometry
   is empty. The input geometry must be a polygon.

.. function:: ST_NumGeometries(Geometry) -> bigint

    Returns the number of geometries in the collection.
    If the geometry is a collection of geometries (e.g., GEOMETRYCOLLECTION or MULTI*),
    returns the number of geometries,
    for single geometries returns 1,
    for empty geometries returns 0.

.. function:: ST_Geometries(Geometry) -> array(Geometry)

   Returns an array of geometries in the specified collection. Returns a one-element array
   if the input geometry is not a multi-geometry. Returns ``NULL`` if input geometry is empty.

.. function:: ST_NumPoints(Geometry) -> bigint

    Returns the number of points in a geometry. This is an extension to the SQL/MM
    ``ST_NumPoints`` function which only applies to point and linestring.

.. function:: ST_NumInteriorRing(Geometry) -> bigint

    Returns the cardinality of the collection of interior rings of a polygon.

.. function:: line_interpolate_point(LineString, double) -> double

    Returns a Point interpolated along a LineString at the fraction given. The fraction
    must be between 0 and 1, inclusive.

.. function:: line_interpolate_points(LineString, double, repeated) -> double

    Returns an array of Points interpolated along a LineString. The fraction must be
    between 0 and 1, inclusive.

.. function:: line_locate_point(LineString, Point) -> double

    Returns a float between 0 and 1 representing the location of the closest point on
    the LineString to the given Point, as a fraction of total 2d line length.

    Returns ``NULL`` if a LineString or a Point is empty or ``NULL``.

.. function:: geometry_invalid_reason(Geometry) -> varchar

    Returns the reason for why the input geometry is not valid.
    Returns ``NULL`` if the input is valid.

.. function:: great_circle_distance(latitude1, longitude1, latitude2, longitude2) -> double

    Returns the great-circle distance between two points on Earth's surface in kilometers.

Aggregations
------------
.. function:: convex_hull_agg(Geometry) -> Geometry

    Returns the minimum convex geometry that encloses all input geometries.

.. function:: geometry_union_agg(Geometry) -> Geometry

    Returns a geometry that represents the point set union of all input geometries.

Bing Tiles
----------

These functions convert between geometries and
`Bing tiles <https://msdn.microsoft.com/en-us/library/bb259689.aspx>`_.

.. function:: bing_tile(x, y, zoom_level) -> BingTile

    Creates a Bing tile object from XY coordinates and a zoom level.
    Zoom levels from 1 to 23 are supported.

.. function:: bing_tile(quadKey) -> BingTile

    Creates a Bing tile object from a quadkey.

.. function:: bing_tile_at(latitude, longitude, zoom_level) -> BingTile

    Returns a Bing tile at a given zoom level containing a point at a given latitude
    and longitude. Latitude must be within ``[-85.05112878, 85.05112878]`` range.
    Longitude must be within ``[-180, 180]`` range. Zoom levels from 1 to 23 are supported.

.. function:: bing_tiles_around(latitude, longitude, zoom_level) -> array(BingTile)

    Returns a collection of Bing tiles that surround the point specified
    by the latitude and longitude arguments at a given zoom level.

.. function:: bing_tiles_around(latitude, longitude, zoom_level, radius_in_km) -> array(BingTile)

    Returns a minimum set of Bing tiles at specified zoom level that cover a circle of specified
    radius in km around a specified (latitude, longitude) point.

.. function:: bing_tile_coordinates(tile) -> row<x, y>

    Returns the XY coordinates of a given Bing tile.

.. function:: bing_tile_polygon(tile) -> Geometry

    Returns the polygon representation of a given Bing tile.

.. function:: bing_tile_quadkey(tile) -> varchar

    Returns the quadkey of a given Bing tile.

.. function:: bing_tile_zoom_level(tile) -> tinyint

    Returns the zoom level of a given Bing tile.

.. function:: geometry_to_bing_tiles(geometry, zoom_level) -> array(BingTile)

    Returns the minimum set of Bing tiles that fully covers a given geometry at
    a given zoom level. Zoom levels from 1 to 23 are supported.

Encoded Polylines
-----------------

These functions convert between geometries and
`encoded polylines <https://developers.google.com/maps/documentation/utilities/polylinealgorithm>`_.

.. function:: to_encoded_polyline(Geometry) -> varchar

    Encodes a linestring or multipoint to a polyline.

.. function:: from_encoded_polyline(varchar) -> Geometry

    Decodes a polyline to a linestring.
