Chapter 15. Spatial Extensions
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## Chapter 15. Spatial Extensions

MySQL 4.1 introduces spatial extensions to allow the generation, storage, and analysis of geographic features. Currently, these features are available for `MyISAM` tables only.

This chapter covers the following topics:

- The basis of these spatial extensions in the OpenGIS geometry model

- Data formats for representing spatial data

- How to use spatial data in MySQL

- Use of indexing for spatial data

- MySQL differences from the OpenGIS specification

Additional resources

- The Open Geospatial Consortium publishes the OpenGIS® Simple Features Specifications For SQL, a document that proposes several conceptual ways for extending an SQL RDBMS to support spatial data. This specification is available from the OGC Web site at http://www.opengis.org/docs/99-049.pdf.

- If you have questions or concerns about the use of the spatial extensions to MySQL, you can discuss them in the GIS forum: http://forums.mysql.com/list.php?23.

## 15.1. Introduction to MySQL Spatial Support

MySQL implements spatial extensions following the specification of the Open Geospatial Consortium (OGC). This is an international consortium of more than 250 companies, agencies, and universities participating in the development of publicly available conceptual solutions that can be useful with all kinds of applications that manage spatial data. The OGC maintains a Web site at http://www.opengis.org/.

In 1997, the Open Geospatial Consortium published the OpenGIS® Simple Features Specifications For SQL, a document that proposes several conceptual ways for extending an SQL RDBMS to support spatial data. This specification is available from the OGC Web site at http://www.opengis.org/docs/99-049.pdf. It contains additional information relevant to this chapter.

MySQL implements a subset of the SQL with Geometry Types environment proposed by OGC. This term refers to an SQL environment that has been extended with a set of geometry types. A geometry-valued SQL column is implemented as a column that has a geometry type. The specification describe a set of SQL geometry types, as well as functions on those types to create and analyze geometry values.

A geographic feature is anything in the world that has a location. A feature can be:

- An entity. For example, a mountain, a pond, a city.

- A space. For example, town district, the tropics.

- A definable location. For example, a crossroad, as a particular place where two streets intersect.

Some documents use the term geospatial feature to refer to geographic features.

Geometry is another word that denotes a geographic feature. Originally the word geometry meant measurement of the earth. Another meaning comes from cartography, referring to the geometric features that cartographers use to map the world.

This chapter uses all of these terms synonymously: geographic feature, geospatial feature, feature, or geometry. Here, the term most commonly used is geometry, defined as a point or an aggregate of points representing anything in the world that has a location.

## 15.2. The OpenGIS Geometry Model

The set of geometry types proposed by OGC's SQL with Geometry Types environment is based on the OpenGIS Geometry Model. In this model, each geometric object has the following general properties:

- It is associated with a Spatial Reference System, which describes the coordinate space in which the object is defined.

- It belongs to some geometry class.

### 15.2.1. The Geometry Class Hierarchy

The geometry classes define a hierarchy as follows:

- `Geometry` (non-instantiable)

  - `Point` (instantiable)

  - `Curve` (non-instantiable)

    - `LineString` (instantiable)

      - `Line`

      - `LinearRing`

  - `Surface` (non-instantiable)

    - `Polygon` (instantiable)

  - `GeometryCollection` (instantiable)

    - `MultiPoint` (instantiable)

    - `MultiCurve` (non-instantiable)

      - `MultiLineString` (instantiable)

    - `MultiSurface` (non-instantiable)

      - `MultiPolygon` (instantiable)

It is not possible to create objects in non-instantiable classes. It is possible to create objects in instantiable classes. All classes have properties, and instantiable classes may also have assertions (rules that define valid class instances).

`Geometry` is the base class. It is an abstract class. The instantiable subclasses of `Geometry` are restricted to zero-, one-, and two-dimensional geometric objects that exist in two-dimensional coordinate space. All instantiable geometry classes are defined so that valid instances of a geometry class are topologically closed (that is, all defined geometries include their boundary).

The base `Geometry` class has subclasses for `Point`, `Curve`, `Surface`, and `GeometryCollection`:

- `Point` represents zero-dimensional objects.

- `Curve` represents one-dimensional objects, and has subclass `LineString`, with sub-subclasses `Line` and `LinearRing`.

- `Surface` is designed for two-dimensional objects and has subclass `Polygon`.

- `GeometryCollection` has specialized zero-, one-, and two-dimensional collection classes named `MultiPoint`, `MultiLineString`, and `MultiPolygon` for modeling geometries corresponding to collections of `Points`, `LineStrings`, and `Polygons`, respectively. `MultiCurve` and `MultiSurface` are introduced as abstract superclasses that generalize the collection interfaces to handle `Curves` and `Surfaces`.

`Geometry`, `Curve`, `Surface`, `MultiCurve`, and `MultiSurface` are defined as non-instantiable classes. They define a common set of methods for their subclasses and are included for extensibility.

`Point`, `LineString`, `Polygon`, `GeometryCollection`, `MultiPoint`, `MultiLineString`, and `MultiPolygon` are instantiable classes.

### 15.2.2. Class `Geometry`

`Geometry` is the root class of the hierarchy. It is a non-instantiable class but has a number of properties that are common to all geometry values created from any of the `Geometry` subclasses. These properties are described in the following list. Particular subclasses have their own specific properties, described later.

Geometry Properties

A geometry value has the following properties:

- Its type. Each geometry belongs to one of the instantiable classes in the hierarchy.

- Its SRID, or Spatial Reference Identifier. This value identifies the geometry's associated Spatial Reference System that describes the coordinate space in which the geometry object is defined.

  In MySQL, the SRID value is just an integer associated with the geometry value. All calculations are done assuming Euclidean (planar) geometry.

- Its coordinates in its Spatial Reference System, represented as double-precision (eight-byte) numbers. All non-empty geometries include at least one pair of (X,Y) coordinates. Empty geometries contain no coordinates.

  Coordinates are related to the SRID. For example, in different coordinate systems, the distance between two objects may differ even when objects have the same coordinates, because the distance on the planar coordinate system and the distance on the geocentric system (coordinates on the Earth's surface) are different things.

- Its interior, boundary, and exterior.

  Every geometry occupies some position in space. The exterior of a geometry is all space not occupied by the geometry. The interior is the space occupied by the geometry. The boundary is the interface between the geometry's interior and exterior.

- Its MBR (Minimum Bounding Rectangle), or Envelope. This is the bounding geometry, formed by the minimum and maximum (X,Y) coordinates:

      ((MINX MINY, MAXX MINY, MAXX MAXY, MINX MAXY, MINX MINY))

- Whether the value is simple or non-simple. Geometry values of types (`LineString`, `MultiPoint`, `MultiLineString`) are either simple or non-simple. Each type determines its own assertions for being simple or non-simple.

- Whether the value is closed or not closed. Geometry values of types (`LineString`, `MultiString`) are either closed or not closed. Each type determines its own assertions for being closed or not closed.

- Whether the value is empty or non-empty A geometry is empty if it does not have any points. Exterior, interior, and boundary of an empty geometry are not defined (that is, they are represented by a `NULL` value). An empty geometry is defined to be always simple and has an area of 0.

- Its dimension. A geometry can have a dimension of –1, 0, 1, or 2:

  - –1 for an empty geometry.

  - 0 for a geometry with no length and no area.

  - 1 for a geometry with non-zero length and zero area.

  - 2 for a geometry with non-zero area.

  `Point` objects have a dimension of zero. `LineString` objects have a dimension of 1. `Polygon` objects have a dimension of 2. The dimensions of `MultiPoint`, `MultiLineString`, and `MultiPolygon` objects are the same as the dimensions of the elements they consist of.

### 15.2.3. Class `Point`

A `Point` is a geometry that represents a single location in coordinate space.

`Point` Examples

- Imagine a large-scale map of the world with many cities. A `Point` object could represent each city.

- On a city map, a `Point` object could represent a bus stop.

`Point` Properties

- X-coordinate value.

- Y-coordinate value.

- `Point` is defined as a zero-dimensional geometry.

- The boundary of a `Point` is the empty set.

### 15.2.4. Class `Curve`

A `Curve` is a one-dimensional geometry, usually represented by a sequence of points. Particular subclasses of `Curve` define the type of interpolation between points. `Curve` is a non-instantiable class.

`Curve` Properties

- A `Curve` has the coordinates of its points.

- A `Curve` is defined as a one-dimensional geometry.

- A `Curve` is simple if it does not pass through the same point twice.

- A `Curve` is closed if its start point is equal to its endpoint.

- The boundary of a closed `Curve` is empty.

- The boundary of a non-closed `Curve` consists of its two endpoints.

- A `Curve` that is simple and closed is a `LinearRing`.

### 15.2.5. Class `LineString`

A `LineString` is a `Curve` with linear interpolation between points.

`LineString` Examples

- On a world map, `LineString` objects could represent rivers.

- In a city map, `LineString` objects could represent streets.

`LineString` Properties

- A `LineString` has coordinates of segments, defined by each consecutive pair of points.

- A `LineString` is a `Line` if it consists of exactly two points.

- A `LineString` is a `LinearRing` if it is both closed and simple.

### 15.2.6. Class `Surface`

A `Surface` is a two-dimensional geometry. It is a non-instantiable class. Its only instantiable subclass is `Polygon`.

`Surface` Properties

- A `Surface` is defined as a two-dimensional geometry.

- The OpenGIS specification defines a simple `Surface` as a geometry that consists of a single “patch” that is associated with a single exterior boundary and zero or more interior boundaries.

- The boundary of a simple `Surface` is the set of closed curves corresponding to its exterior and interior boundaries.

### 15.2.7. Class `Polygon`

A `Polygon` is a planar `Surface` representing a multisided geometry. It is defined by a single exterior boundary and zero or more interior boundaries, where each interior boundary defines a hole in the `Polygon`.

`Polygon` Examples

- On a region map, `Polygon` objects could represent forests, districts, and so on.

`Polygon` Assertions

- The boundary of a `Polygon` consists of a set of `LinearRing` objects (that is, `LineString` objects that are both simple and closed) that make up its exterior and interior boundaries.

- A `Polygon` has no rings that cross. The rings in the boundary of a `Polygon` may intersect at a `Point`, but only as a tangent.

- A `Polygon` has no lines, spikes, or punctures.

- A `Polygon` has an interior that is a connected point set.

- A `Polygon` may have holes. The exterior of a `Polygon` with holes is not connected. Each hole defines a connected component of the exterior.

The preceding assertions make a `Polygon` a simple geometry.

### 15.2.8. Class `GeometryCollection`

A `GeometryCollection` is a geometry that is a collection of one or more geometries of any class.

All the elements in a `GeometryCollection` must be in the same Spatial Reference System (that is, in the same coordinate system). There are no other constraints on the elements of a `GeometryCollection`, although the subclasses of `GeometryCollection` described in the following sections may restrict membership. Restrictions may be based on:

- Element type (for example, a `MultiPoint` may contain only `Point` elements)

- Dimension

- Constraints on the degree of spatial overlap between elements

### 15.2.9. Class `MultiPoint`

A `MultiPoint` is a geometry collection composed of `Point` elements. The points are not connected or ordered in any way.

`MultiPoint` Examples

- On a world map, a `MultiPoint` could represent a chain of small islands.

- On a city map, a `MultiPoint` could represent the outlets for a ticket office.

`MultiPoint` Properties

- A `MultiPoint` is a zero-dimensional geometry.

- A `MultiPoint` is simple if no two of its `Point` values are equal (have identical coordinate values).

- The boundary of a `MultiPoint` is the empty set.

### 15.2.10. Class `MultiCurve`

A `MultiCurve` is a geometry collection composed of `Curve` elements. `MultiCurve` is a non-instantiable class.

`MultiCurve` Properties

- A `MultiCurve` is a one-dimensional geometry.

- A `MultiCurve` is simple if and only if all of its elements are simple; the only intersections between any two elements occur at points that are on the boundaries of both elements.

- A `MultiCurve` boundary is obtained by applying the “mod 2 union rule” (also known as the “odd-even rule”): A point is in the boundary of a `MultiCurve` if it is in the boundaries of an odd number of `MultiCurve` elements.

- A `MultiCurve` is closed if all of its elements are closed.

- The boundary of a closed `MultiCurve` is always empty.

### 15.2.11. Class `MultiLineString`

A `MultiLineString` is a `MultiCurve` geometry collection composed of `LineString` elements.

`MultiLineString` Examples

- On a region map, a `MultiLineString` could represent a river system or a highway system.

### 15.2.12. Class `MultiSurface`

A `MultiSurface` is a geometry collection composed of surface elements. `MultiSurface` is a non-instantiable class. Its only instantiable subclass is `MultiPolygon`.

`MultiSurface` Assertions

- Two `MultiSurface` surfaces have no interiors that intersect.

- Two `MultiSurface` elements have boundaries that intersect at most at a finite number of points.

### 15.2.13. Class `MultiPolygon`

A `MultiPolygon` is a `MultiSurface` object composed of `Polygon` elements.

`MultiPolygon` Examples

- On a region map, a `MultiPolygon` could represent a system of lakes.

`MultiPolygon` Assertions

- A `MultiPolygon` has no two `Polygon` elements with interiors that intersect.

- A `MultiPolygon` has no two `Polygon` elements that cross (crossing is also forbidden by the previous assertion), or that touch at an infinite number of points.

- A `MultiPolygon` may not have cut lines, spikes, or punctures. A `MultiPolygon` is a regular, closed point set.

- A `MultiPolygon` that has more than one `Polygon` has an interior that is not connected. The number of connected components of the interior of a `MultiPolygon` is equal to the number of `Polygon` values in the `MultiPolygon`.

`MultiPolygon` Properties

- A `MultiPolygon` is a two-dimensional geometry.

- A `MultiPolygon` boundary is a set of closed curves (`LineString` values) corresponding to the boundaries of its `Polygon` elements.

- Each `Curve` in the boundary of the `MultiPolygon` is in the boundary of exactly one `Polygon` element.

- Every `Curve` in the boundary of an `Polygon` element is in the boundary of the `MultiPolygon`.

## 15.3. Supported Spatial Data Formats

This section describes the standard spatial data formats that are used to represent geometry objects in queries. They are:

- Well-Known Text (WKT) format

- Well-Known Binary (WKB) format

Internally, MySQL stores geometry values in a format that is not identical to either WKT or WKB format.

### 15.3.1. Well-Known Text (WKT) Format

The Well-Known Text (WKT) representation of Geometry is designed to exchange geometry data in ASCII form.

Examples of WKT representations of geometry objects:

- A `Point`:

      POINT(15 20)

  Note that point coordinates are specified with no separating comma.

- A `LineString` with four points:

      LINESTRING(0 0, 10 10, 20 25, 50 60)

  Note that point coordinate pairs are separated by commas.

- A `Polygon` with one exterior ring and one interior ring:

      POLYGON((0 0,10 0,10 10,0 10,0 0),(5 5,7 5,7 7,5 7, 5 5))

- A `MultiPoint` with three `Point` values:

      MULTIPOINT(0 0, 20 20, 60 60)

- A `MultiLineString` with two `LineString` values:

      MULTILINESTRING((10 10, 20 20), (15 15, 30 15))

- A `MultiPolygon` with two `Polygon` values:

      MULTIPOLYGON(((0 0,10 0,10 10,0 10,0 0)),((5 5,7 5,7 7,5 7, 5 5)))

- A `GeometryCollection` consisting of two `Point` values and one `LineString`:

      GEOMETRYCOLLECTION(POINT(10 10), POINT(30 30), LINESTRING(15 15, 20 20))

A Backus-Naur grammar that specifies the formal production rules for writing WKT values can be found in the OpenGIS specification document referenced near the beginning of this chapter.

### 15.3.2. Well-Known Binary (WKB) Format

The Well-Known Binary (WKB) representation for geometric values is defined by the OpenGIS specification. It is also defined in the ISO SQL/MM Part 3: Spatial standard.

WKB is used to exchange geometry data as binary streams represented by `BLOB` values containing geometric WKB information.

WKB uses one-byte unsigned integers, four-byte unsigned integers, and eight-byte double-precision numbers (IEEE 754 format). A byte is eight bits.

For example, a WKB value that corresponds to `POINT(1 1)` consists of this sequence of 21 bytes (each represented here by two hex digits):

    0101000000000000000000F03F000000000000F03F

The sequence may be broken down into these components:

    Byte order : 01
    WKB type   : 01000000
    X          : 000000000000F03F
    Y          : 000000000000F03F

Component representation is as follows:

- The byte order may be either 1 or 0 to indicate little-endian or big-endian storage. The little-endian and big-endian byte orders are also known as Network Data Representation (NDR) and External Data Representation (XDR), respectively.

- The WKB type is a code that indicates the geometry type. Values from 1 through 7 indicate `Point`, `LineString`, `Polygon`, `MultiPoint`, `MultiLineString`, `MultiPolygon`, and `GeometryCollection`.

- A `Point` value has X and Y coordinates, each represented as a double-precision value.

WKB values for more complex geometry values are represented by more complex data structures, as detailed in the OpenGIS specification.

## 15.4. Creating a Spatially Enabled MySQL Database

This section describes the data types you can use for representing spatial data in MySQL, and the functions available for creating and retrieving spatial values.

### 15.4.1. MySQL Spatial Data Types

MySQL has data types that correspond to OpenGIS classes. Some of these types hold single geometry values:

- `GEOMETRY`

- `POINT`

- `LINESTRING`

- `POLYGON`

`GEOMETRY` can store geometry values of any type. The other single-value types (`POINT`, `LINESTRING`, and `POLYGON`) restrict their values to a particular geometry type.

The other data types hold collections of values:

- `MULTIPOINT`

- `MULTILINESTRING`

- `MULTIPOLYGON`

- `GEOMETRYCOLLECTION`

`GEOMETRYCOLLECTION` can store a collection of objects of any type. The other collection types (`MULTIPOINT`, `MULTILINESTRING`, `MULTIPOLYGON`, and `GEOMETRYCOLLECTION`) restrict collection members to those having a particular geometry type.

### 15.4.2. Creating Spatial Values

This section describes how to create spatial values using Well-Known Text and Well-Known Binary functions that are defined in the OpenGIS standard, and using MySQL-specific functions.

#### 15.4.2.1. Creating Geometry Values Using WKT Functions

MySQL provides a number of functions that take as input parameters a Well-Known Text representation and, optionally, a spatial reference system identifier (SRID). They return the corresponding geometry.

`GeomFromText()` accepts a WKT of any geometry type as its first argument. An implementation also provides type-specific construction functions for construction of geometry values of each geometry type.

- `GeomCollFromText(`wkt`[,`srid`])`, `GeometryCollectionFromText(`wkt`[,`srid`])`

  Constructs a `GEOMETRYCOLLECTION` value using its WKT representation and SRID.

- `GeomFromText(`wkt`[,`srid`])`, `GeometryFromText(`wkt`[,`srid`])`

  Constructs a geometry value of any type using its WKT representation and SRID.

- `LineFromText(`wkt`[,`srid`])`, `LineStringFromText(`wkt`[,`srid`])`

  Constructs a `LINESTRING` value using its WKT representation and SRID.

- `MLineFromText(`wkt`[,`srid`])`, `MultiLineStringFromText(`wkt`[,`srid`])`

  Constructs a `MULTILINESTRING` value using its WKT representation and SRID.

- `MPointFromText(`wkt`[,`srid`])`, `MultiPointFromText(`wkt`[,`srid`])`

  Constructs a `MULTIPOINT` value using its WKT representation and SRID.

- `MPolyFromText(`wkt`[,`srid`])`, `MultiPolygonFromText(`wkt`[,`srid`])`

  Constructs a `MULTIPOLYGON` value using its WKT representation and SRID.

- `PointFromText(`wkt`[,`srid`])`

  Constructs a `POINT` value using its WKT representation and SRID.

- `PolyFromText(`wkt`[,`srid`])`, `PolygonFromText(`wkt`[,`srid`])`

  Constructs a `POLYGON` value using its WKT representation and SRID.

The OpenGIS specification also defines the following optional functions, which MySQL does not implement. These functions construct `Polygon` or `MultiPolygon` values based on the WKT representation of a collection of rings or closed `LineString` values. These values may intersect.

- `BdMPolyFromText(`wkt`,`srid`)`

  Constructs a `MultiPolygon` value from a `MultiLineString` value in WKT format containing an arbitrary collection of closed `LineString` values.

- `BdPolyFromText(`wkt`,`srid`)`

  Constructs a `Polygon` value from a `MultiLineString` value in WKT format containing an arbitrary collection of closed `LineString` values.

#### 15.4.2.2. Creating Geometry Values Using WKB Functions

MySQL provides a number of functions that take as input parameters a `BLOB` containing a Well-Known Binary representation and, optionally, a spatial reference system identifier (SRID). They return the corresponding geometry.

`GeomFromWKB()` accepts a WKB of any geometry type as its first argument. An implementation also provides type-specific construction functions for construction of geometry values of each geometry type.

- `GeomCollFromWKB(`wkb`[,`srid`])`, `GeometryCollectionFromWKB(`wkb`[,`srid`])`

  Constructs a `GEOMETRYCOLLECTION` value using its WKB representation and SRID.

- `GeomFromWKB(`wkb`[,`srid`])`, `GeometryFromWKB(`wkb`[,`srid`])`

  Constructs a geometry value of any type using its WKB representation and SRID.

- `LineFromWKB(`wkb`[,`srid`])`, `LineStringFromWKB(`wkb`[,`srid`])`

  Constructs a `LINESTRING` value using its WKB representation and SRID.

- `MLineFromWKB(`wkb`[,`srid`])`, `MultiLineStringFromWKB(`wkb`[,`srid`])`

  Constructs a `MULTILINESTRING` value using its WKB representation and SRID.

- `MPointFromWKB(`wkb`[,`srid`])`, `MultiPointFromWKB(`wkb`[,`srid`])`

  Constructs a `MULTIPOINT` value using its WKB representation and SRID.

- `MPolyFromWKB(`wkb`[,`srid`])`, `MultiPolygonFromWKB(`wkb`[,`srid`])`

  Constructs a `MULTIPOLYGON` value using its WKB representation and SRID.

- `PointFromWKB(`wkb`[,`srid`])`

  Constructs a `POINT` value using its WKB representation and SRID.

- `PolyFromWKB(`wkb`[,`srid`])`, `PolygonFromWKB(`wkb`[,`srid`])`

  Constructs a `POLYGON` value using its WKB representation and SRID.

The OpenGIS specification also describes optional functions for constructing `Polygon` or `MultiPolygon` values based on the WKB representation of a collection of rings or closed `LineString` values. These values may intersect. MySQL does not implement these functions:

- `BdMPolyFromWKB(`wkb`,`srid`)`

  Constructs a `MultiPolygon` value from a `MultiLineString` value in WKB format containing an arbitrary collection of closed `LineString` values.

- `BdPolyFromWKB(`wkb`,`srid`)`

  Constructs a `Polygon` value from a `MultiLineString` value in WKB format containing an arbitrary collection of closed `LineString` values.

#### 15.4.2.3. Creating Geometry Values Using MySQL-Specific Functions

MySQL provides a set of useful non-standard functions for creating geometry WKB representations. The functions described in this section are MySQL extensions to the OpenGIS specification. The results of these functions are `BLOB` values containing WKB representations of geometry values with no SRID. The results of these functions can be substituted as the first argument for any function in the `GeomFromWKB()` function family.

- `GeometryCollection(`g1`,`g2`,...)`

  Constructs a WKB `GeometryCollection`. If any argument is not a well-formed WKB representation of a geometry, the return value is `NULL`.

- `LineString(`pt1`,`pt2`,...)`

  Constructs a WKB `LineString` value from a number of WKB `Point` arguments. If any argument is not a WKB `Point`, the return value is `NULL`. If the number of `Point` arguments is less than two, the return value is `NULL`.

- `MultiLineString(`ls1`,`ls2`,...)`

  Constructs a WKB `MultiLineString` value using WKB `LineString` arguments. If any argument is not a WKB `LineString`, the return value is `NULL`.

- `MultiPoint(`pt1`,`pt2`,...)`

  Constructs a WKB `MultiPoint` value using WKB `Point` arguments. If any argument is not a WKB `Point`, the return value is `NULL`.

- `MultiPolygon(`poly1`,`poly2`,...)`

  Constructs a WKB `MultiPolygon` value from a set of WKB `Polygon` arguments. If any argument is not a WKB `Polygon`, the return value is `NULL`.

- `Point(`x`,`y`)`

  Constructs a WKB `Point` using its coordinates.

- `Polygon(`ls1`,`ls2`,...)`

  Constructs a WKB `Polygon` value from a number of WKB `LineString` arguments. If any argument does not represent the WKB of a `LinearRing` (that is, not a closed and simple `LineString`) the return value is `NULL`.

### 15.4.3. Creating Spatial Columns

MySQL provides a standard way of creating spatial columns for geometry types, for example, with `CREATE TABLE` or `ALTER TABLE`. Currently, spatial columns are supported only for `MyISAM` tables.

- Use the `CREATE TABLE` statement to create a table with a spatial column:

      CREATE TABLE geom (g GEOMETRY);

- Use the `ALTER TABLE` statement to add or drop a spatial column to or from an existing table:

      ALTER TABLE geom ADD pt POINT;
      ALTER TABLE geom DROP pt;

### 15.4.4. Populating Spatial Columns

After you have created spatial columns, you can populate them with spatial data.

Values should be stored in internal geometry format, but you can convert them to that format from either Well-Known Text (WKT) or Well-Known Binary (WKB) format. The following examples demonstrate how to insert geometry values into a table by converting WKT values into internal geometry format:

- Perform the conversion directly in the `INSERT` statement:

      INSERT INTO geom VALUES (GeomFromText('POINT(1 1)'));

      SET @g = 'POINT(1 1)';
      INSERT INTO geom VALUES (GeomFromText(@g));

- Perform the conversion prior to the `INSERT`:

      SET @g = GeomFromText('POINT(1 1)');
      INSERT INTO geom VALUES (@g);

The following examples insert more complex geometries into the table:

    SET @g = 'LINESTRING(0 0,1 1,2 2)';
    INSERT INTO geom VALUES (GeomFromText(@g));

    SET @g = 'POLYGON((0 0,10 0,10 10,0 10,0 0),(5 5,7 5,7 7,5 7, 5 5))';
    INSERT INTO geom VALUES (GeomFromText(@g));

    SET @g =
    'GEOMETRYCOLLECTION(POINT(1 1),LINESTRING(0 0,1 1,2 2,3 3,4 4))';
    INSERT INTO geom VALUES (GeomFromText(@g));

The preceding examples all use `GeomFromText()` to create geometry values. You can also use type-specific functions:

    SET @g = 'POINT(1 1)';
    INSERT INTO geom VALUES (PointFromText(@g));

    SET @g = 'LINESTRING(0 0,1 1,2 2)';
    INSERT INTO geom VALUES (LineStringFromText(@g));

    SET @g = 'POLYGON((0 0,10 0,10 10,0 10,0 0),(5 5,7 5,7 7,5 7, 5 5))';
    INSERT INTO geom VALUES (PolygonFromText(@g));

    SET @g =
    'GEOMETRYCOLLECTION(POINT(1 1),LINESTRING(0 0,1 1,2 2,3 3,4 4))';
    INSERT INTO geom VALUES (GeomCollFromText(@g));

Note that if a client application program wants to use WKB representations of geometry values, it is responsible for sending correctly formed WKB in queries to the server. However, there are several ways of satisfying this requirement. For example:

- Inserting a `POINT(1 1)` value with hex literal syntax:

      mysql> INSERT INTO geom VALUES
          -> (GeomFromWKB(0x0101000000000000000000F03F000000000000F03F));

- An ODBC application can send a WKB representation, binding it to a placeholder using an argument of `BLOB` type:

      INSERT INTO geom VALUES (GeomFromWKB(?))

  Other programming interfaces may support a similar placeholder mechanism.

- In a C program, you can escape a binary value using `mysql_real_escape_string()` and include the result in a query string that is sent to the server. See Section 16.2.3.51, “`mysql_real_escape_string()`”.

### 15.4.5. Fetching Spatial Data

Geometry values stored in a table can be fetched in internal format. You can also convert them into WKT or WKB format.

- Fetching spatial data in internal format:

  Fetching geometry values using internal format can be useful in table-to-table transfers:

      CREATE TABLE geom2 (g GEOMETRY) SELECT g FROM geom;

- Fetching spatial data in WKT format:

  The `AsText()` function converts a geometry from internal format into a WKT string.

      SELECT AsText(g) FROM geom;

- Fetching spatial data in WKB format:

  The `AsBinary()` function converts a geometry from internal format into a `BLOB` containing the WKB value.

      SELECT AsBinary(g) FROM geom;

## 15.5. Analyzing Spatial Information

After populating spatial columns with values, you are ready to query and analyze them. MySQL provides a set of functions to perform various operations on spatial data. These functions can be grouped into four major categories according to the type of operation they perform:

- Functions that convert geometries between various formats

- Functions that provide access to qualitative or quantitative properties of a geometry

- Functions that describe relations between two geometries

- Functions that create new geometries from existing ones

Spatial analysis functions can be used in many contexts, such as:

- Any interactive SQL program, such as mysql or MySQL Query Browser

- Application programs written in any language that supports a MySQL client API

### 15.5.1. Geometry Format Conversion Functions

MySQL supports the following functions for converting geometry values between internal format and either WKT or WKB format:

- `AsBinary(`g`)`

  Converts a value in internal geometry format to its WKB representation and returns the binary result.

      SELECT AsBinary(g) FROM geom;

- `AsText(`g`)`

  Converts a value in internal geometry format to its WKT representation and returns the string result.

      mysql> SET @g = 'LineString(1 1,2 2,3 3)';
      mysql> SELECT AsText(GeomFromText(@g));
      +--------------------------+
      | AsText(GeomFromText(@g)) |
      +--------------------------+
      | LINESTRING(1 1,2 2,3 3)  |
      +--------------------------+

- `GeomFromText(`wkt`[,`srid`])`

  Converts a string value from its WKT representation into internal geometry format and returns the result. A number of type-specific functions are also supported, such as `PointFromText()` and `LineFromText()`. See Section 15.4.2.1, “Creating Geometry Values Using WKT Functions”.

- `GeomFromWKB(`wkb`[,`srid`])`

  Converts a binary value from its WKB representation into internal geometry format and returns the result. A number of type-specific functions are also supported, such as `PointFromWKB()` and `LineFromWKB()`. See Section 15.4.2.2, “Creating Geometry Values Using WKB Functions”.

### 15.5.2. `Geometry` Functions

Each function that belongs to this group takes a geometry value as its argument and returns some quantitative or qualitative property of the geometry. Some functions restrict their argument type. Such functions return `NULL` if the argument is of an incorrect geometry type. For example, `Area()` returns `NULL` if the object type is neither `Polygon` nor `MultiPolygon`.

#### 15.5.2.1. General Geometry Functions

The functions listed in this section do not restrict their argument and accept a geometry value of any type.

- `Dimension(`g`)`

  Returns the inherent dimension of the geometry value `g`. The result can be –1, 0, 1, or 2. The meaning of these values is given in Section 15.2.2, “Class `Geometry`”.

      mysql> SELECT Dimension(GeomFromText('LineString(1 1,2 2)'));
      +------------------------------------------------+
      | Dimension(GeomFromText('LineString(1 1,2 2)')) |
      +------------------------------------------------+
      |                                              1 |
      +------------------------------------------------+

- `Envelope(`g`)`

  Returns the Minimum Bounding Rectangle (MBR) for the geometry value `g`. The result is returned as a `Polygon` value.

  The polygon is defined by the corner points of the bounding box:

      POLYGON((MINX MINY, MAXX MINY, MAXX MAXY, MINX MAXY, MINX MINY))

      mysql> SELECT AsText(Envelope(GeomFromText('LineString(1 1,2 2)')));
      +-------------------------------------------------------+
      | AsText(Envelope(GeomFromText('LineString(1 1,2 2)'))) |
      +-------------------------------------------------------+
      | POLYGON((1 1,2 1,2 2,1 2,1 1))                        |
      +-------------------------------------------------------+

- `GeometryType(`g`)`

  Returns as a string the name of the geometry type of which the geometry instance `g` is a member. The name corresponds to one of the instantiable `Geometry` subclasses.

      mysql> SELECT GeometryType(GeomFromText('POINT(1 1)'));
      +------------------------------------------+
      | GeometryType(GeomFromText('POINT(1 1)')) |
      +------------------------------------------+
      | POINT                                    |
      +------------------------------------------+

- `SRID(`g`)`

  Returns an integer indicating the Spatial Reference System ID for the geometry value `g`.

  In MySQL, the SRID value is just an integer associated with the geometry value. All calculations are done assuming Euclidean (planar) geometry.

      mysql> SELECT SRID(GeomFromText('LineString(1 1,2 2)',101));
      +-----------------------------------------------+
      | SRID(GeomFromText('LineString(1 1,2 2)',101)) |
      +-----------------------------------------------+
      |                                           101 |
      +-----------------------------------------------+

The OpenGIS specification also defines the following functions, which MySQL does not implement:

- `Boundary(`g`)`

  Returns a geometry that is the closure of the combinatorial boundary of the geometry value `g`.

- `IsEmpty(`g`)`

  Returns 1 if the geometry value `g` is the empty geometry, 0 if it is not empty, and –1 if the argument is `NULL`. If the geometry is empty, it represents the empty point set.

- `IsSimple(`g`)`

  Currently, this function is a placeholder and should not be used. If implemented, its behavior will be as described in the next paragraph.

  Returns 1 if the geometry value `g` has no anomalous geometric points, such as self-intersection or self-tangency. `IsSimple()` returns 0 if the argument is not simple, and –1 if it is `NULL`.

  The description of each instantiable geometric class given earlier in the chapter includes the specific conditions that cause an instance of that class to be classified as not simple. (See Section 15.2.1, “The Geometry Class Hierarchy”.)

#### 15.5.2.2. `Point` Functions

A `Point` consists of X and Y coordinates, which may be obtained using the following functions:

- `X(`p`)`

  Returns the X-coordinate value for the point `p` as a double-precision number.

      mysql> SET @pt = 'Point(56.7 53.34)';
      mysql> SELECT X(GeomFromText(@pt));
      +----------------------+
      | X(GeomFromText(@pt)) |
      +----------------------+
      |                 56.7 |
      +----------------------+

- `Y(`p`)`

  Returns the Y-coordinate value for the point `p` as a double-precision number.

      mysql> SET @pt = 'Point(56.7 53.34)';
      mysql> SELECT Y(GeomFromText(@pt));
      +----------------------+
      | Y(GeomFromText(@pt)) |
      +----------------------+
      |                53.34 |
      +----------------------+

#### 15.5.2.3. `LineString` Functions

A `LineString` consists of `Point` values. You can extract particular points of a `LineString`, count the number of points that it contains, or obtain its length.

- `EndPoint(`ls`)`

  Returns the `Point` that is the endpoint of the `LineString` value `ls`.

      mysql> SET @ls = 'LineString(1 1,2 2,3 3)';
      mysql> SELECT AsText(EndPoint(GeomFromText(@ls)));
      +-------------------------------------+
      | AsText(EndPoint(GeomFromText(@ls))) |
      +-------------------------------------+
      | POINT(3 3)                          |
      +-------------------------------------+

- `GLength(`ls`)`

  Returns as a double-precision number the length of the `LineString` value `ls` in its associated spatial reference.

      mysql> SET @ls = 'LineString(1 1,2 2,3 3)';
      mysql> SELECT GLength(GeomFromText(@ls));
      +----------------------------+
      | GLength(GeomFromText(@ls)) |
      +----------------------------+
      |            2.8284271247462 |
      +----------------------------+

  `GLength()` is a non-standard name. It corresponds to the OpenGIS `Length()` function.

- `NumPoints(`ls`)`

  Returns the number of `Point` objects in the `LineString` value `ls`.

      mysql> SET @ls = 'LineString(1 1,2 2,3 3)';
      mysql> SELECT NumPoints(GeomFromText(@ls));
      +------------------------------+
      | NumPoints(GeomFromText(@ls)) |
      +------------------------------+
      |                            3 |
      +------------------------------+

- `PointN(`ls`,`N`)`

  Returns the `N`-th `Point` in the `Linestring` value `ls`. Points are numbered beginning with 1.

      mysql> SET @ls = 'LineString(1 1,2 2,3 3)';
      mysql> SELECT AsText(PointN(GeomFromText(@ls),2));
      +-------------------------------------+
      | AsText(PointN(GeomFromText(@ls),2)) |
      +-------------------------------------+
      | POINT(2 2)                          |
      +-------------------------------------+

- `StartPoint(`ls`)`

  Returns the `Point` that is the start point of the `LineString` value `ls`.

      mysql> SET @ls = 'LineString(1 1,2 2,3 3)';
      mysql> SELECT AsText(StartPoint(GeomFromText(@ls)));
      +---------------------------------------+
      | AsText(StartPoint(GeomFromText(@ls))) |
      +---------------------------------------+
      | POINT(1 1)                            |
      +---------------------------------------+

The OpenGIS specification also defines the following function, which MySQL does not implement:

- `IsRing(`ls`)`

  Returns 1 if the `LineString` value `ls` is closed (that is, its `StartPoint()` and `EndPoint()` values are the same) and is simple (does not pass through the same point more than once). Returns 0 if `ls` is not a ring, and –1 if it is `NULL`.

#### 15.5.2.4. `MultiLineString` Functions

- `GLength(`mls`)`

  Returns as a double-precision number the length of the `MultiLineString` value `mls`. The length of `mls` is equal to the sum of the lengths of its elements.

      mysql> SET @mls = 'MultiLineString((1 1,2 2,3 3),(4 4,5 5))';
      mysql> SELECT GLength(GeomFromText(@mls));
      +-----------------------------+
      | GLength(GeomFromText(@mls)) |
      +-----------------------------+
      |             4.2426406871193 |
      +-----------------------------+

  `GLength()` is a non-standard name. It corresponds to the OpenGIS `Length()` function.

- `IsClosed(`mls`)`

  Returns 1 if the `MultiLineString` value `mls` is closed (that is, the `StartPoint()` and `EndPoint()` values are the same for each `LineString` in `mls`). Returns 0 if `mls` is not closed, and –1 if it is `NULL`.

      mysql> SET @mls = 'MultiLineString((1 1,2 2,3 3),(4 4,5 5))';
      mysql> SELECT IsClosed(GeomFromText(@mls));
      +------------------------------+
      | IsClosed(GeomFromText(@mls)) |
      +------------------------------+
      |                            0 |
      +------------------------------+

#### 15.5.2.5. `Polygon` Functions

- `Area(`poly`)`

  Returns as a double-precision number the area of the `Polygon` value `poly`, as measured in its spatial reference system.

      mysql> SET @poly = 'Polygon((0 0,0 3,3 0,0 0),(1 1,1 2,2 1,1 1))';
      mysql> SELECT Area(GeomFromText(@poly));
      +---------------------------+
      | Area(GeomFromText(@poly)) |
      +---------------------------+
      |                         4 |
      +---------------------------+

- `ExteriorRing(`poly`)`

  Returns the exterior ring of the `Polygon` value `poly` as a `LineString`.

      mysql> SET @poly =
          -> 'Polygon((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1))';
      mysql> SELECT AsText(ExteriorRing(GeomFromText(@poly)));
      +-------------------------------------------+
      | AsText(ExteriorRing(GeomFromText(@poly))) |
      +-------------------------------------------+
      | LINESTRING(0 0,0 3,3 3,3 0,0 0)           |
      +-------------------------------------------+

- `InteriorRingN(`poly`,`N`)`

  Returns the `N`-th interior ring for the `Polygon` value `poly` as a `LineString`. Rings are numbered beginning with 1.

      mysql> SET @poly =
          -> 'Polygon((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1))';
      mysql> SELECT AsText(InteriorRingN(GeomFromText(@poly),1));
      +----------------------------------------------+
      | AsText(InteriorRingN(GeomFromText(@poly),1)) |
      +----------------------------------------------+
      | LINESTRING(1 1,1 2,2 2,2 1,1 1)              |
      +----------------------------------------------+

- `NumInteriorRings(`poly`)`

  Returns the number of interior rings in the `Polygon` value `poly`.

      mysql> SET @poly =
          -> 'Polygon((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1))';
      mysql> SELECT NumInteriorRings(GeomFromText(@poly));
      +---------------------------------------+
      | NumInteriorRings(GeomFromText(@poly)) |
      +---------------------------------------+
      |                                     1 |
      +---------------------------------------+

#### 15.5.2.6. `MultiPolygon` Functions

- `Area(`mpoly`)`

  Returns as a double-precision number the area of the `MultiPolygon` value `mpoly`, as measured in its spatial reference system.

      mysql> SET @mpoly =
          -> 'MultiPolygon(((0 0,0 3,3 3,3 0,0 0),(1 1,1 2,2 2,2 1,1 1)))';
      mysql> SELECT Area(GeomFromText(@mpoly));
      +----------------------------+
      | Area(GeomFromText(@mpoly)) |
      +----------------------------+
      |                          8 |
      +----------------------------+

The OpenGIS specification also defines the following functions, which MySQL does not implement:

- `Centroid(`mpoly`)`

  Returns the mathematical centroid for the `MultiPolygon` value `mpoly` as a `Point`. The result is not guaranteed to be on the `MultiPolygon`.

- `PointOnSurface(`mpoly`)`

  Returns a `Point` value that is guaranteed to be on the `MultiPolygon` value `mpoly`.

#### 15.5.2.7. `GeometryCollection` Functions

- `GeometryN(`gc`,`N`)`

  Returns the `N`-th geometry in the `GeometryCollection` value `gc`. Geometries are numbered beginning with 1.

      mysql> SET @gc = 'GeometryCollection(Point(1 1),LineString(2 2, 3 3))';
      mysql> SELECT AsText(GeometryN(GeomFromText(@gc),1));
      +----------------------------------------+
      | AsText(GeometryN(GeomFromText(@gc),1)) |
      +----------------------------------------+
      | POINT(1 1)                             |
      +----------------------------------------+

- `NumGeometries(`gc`)`

  Returns the number of geometries in the `GeometryCollection` value `gc`.

      mysql> SET @gc = 'GeometryCollection(Point(1 1),LineString(2 2, 3 3))';
      mysql> SELECT NumGeometries(GeomFromText(@gc));
      +----------------------------------+
      | NumGeometries(GeomFromText(@gc)) |
      +----------------------------------+
      |                                2 |
      +----------------------------------+

### 15.5.3. Functions That Create New Geometries from Existing Ones

#### 15.5.3.1. Geometry Functions That Produce New Geometries

Section 15.5.2, “`Geometry` Functions”, discusses several functions that construct new geometries from existing ones. See that section for descriptions of these functions:

- `Envelope(`g`)`

- `StartPoint(`ls`)`

- `EndPoint(`ls`)`

- `PointN(`ls`,`N`)`

- `ExteriorRing(`poly`)`

- `InteriorRingN(`poly`,`N`)`

- `GeometryN(`gc`,`N`)`

#### 15.5.3.2. Spatial Operators

OpenGIS proposes a number of other functions that can produce geometries. They are designed to implement spatial operators.

These functions are not implemented in MySQL. They may appear in future releases.

- `Buffer(`g`,`d`)`

  Returns a geometry that represents all points whose distance from the geometry value `g` is less than or equal to a distance of `d`.

- `ConvexHull(`g`)`

  Returns a geometry that represents the convex hull of the geometry value `g`.

- `Difference(`g1`,`g2`)`

  Returns a geometry that represents the point set difference of the geometry value `g1` with `g2`.

- `Intersection(`g1`,`g2`)`

  Returns a geometry that represents the point set intersection of the geometry values `g1` with `g2`.

- `SymDifference(`g1`,`g2`)`

  Returns a geometry that represents the point set symmetric difference of the geometry value `g1` with `g2`.

- `Union(`g1`,`g2`)`

  Returns a geometry that represents the point set union of the geometry values `g1` and `g2`.

### 15.5.4. Functions for Testing Spatial Relations Between Geometric Objects

The functions described in these sections take two geometries as input parameters and return a qualitative or quantitative relation between them.

### 15.5.5. Relations on Geometry Minimal Bounding Rectangles (MBRs)

MySQL provides several functions that test relations between minimal bounding rectangles of two geometries `g1` and `g2`. The return values 1 and 0 indicate true and false, respectively.

- `MBRContains(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether the Minimum Bounding Rectangle of `g1` contains the Minimum Bounding Rectangle of `g2`. This tests the opposite relationship as `MBRWithin()`.

      mysql> SET @g1 = GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0))');
      mysql> SET @g2 = GeomFromText('Point(1 1)');
      mysql> SELECT MBRContains(@g1,@g2), MBRContains(@g2,@g1);
      ----------------------+----------------------+
      | MBRContains(@g1,@g2) | MBRContains(@g2,@g1) |
      +----------------------+----------------------+
      |                    1 |                    0 |
      +----------------------+----------------------+

- `MBRDisjoint(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether the Minimum Bounding Rectangles of the two geometries `g1` and `g2` are disjoint (do not intersect).

- `MBREqual(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether the Minimum Bounding Rectangles of the two geometries `g1` and `g2` are the same.

- `MBRIntersects(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether the Minimum Bounding Rectangles of the two geometries `g1` and `g2` intersect.

- `MBROverlaps(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether the Minimum Bounding Rectangles of the two geometries `g1` and `g2` overlap. The term spatially overlaps is used if two geometries intersect and their intersection results in a geometry of the same dimension but not equal to either of the given geometries.

- `MBRTouches(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether the Minimum Bounding Rectangles of the two geometries `g1` and `g2` touch. Two geometries spatially touch if the interiors of the geometries do not intersect, but the boundary of one of the geometries intersects either the boundary or the interior of the other.

- `MBRWithin(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether the Minimum Bounding Rectangle of `g1` is within the Minimum Bounding Rectangle of `g2`. This tests the opposite relationship as `MBRContains()`.

      mysql> SET @g1 = GeomFromText('Polygon((0 0,0 3,3 3,3 0,0 0))');
      mysql> SET @g2 = GeomFromText('Polygon((0 0,0 5,5 5,5 0,0 0))');
      mysql> SELECT MBRWithin(@g1,@g2), MBRWithin(@g2,@g1);
      +--------------------+--------------------+
      | MBRWithin(@g1,@g2) | MBRWithin(@g2,@g1) |
      +--------------------+--------------------+
      |                  1 |                  0 |
      +--------------------+--------------------+

### 15.5.6. Functions That Test Spatial Relationships Between Geometries

The OpenGIS specification defines the following functions. They test the relationship between two geometry values `g1` and `g2`.

The return values 1 and 0 indicate true and false, respectively.

### Note

Currently, MySQL does not implement these functions according to the specification. Those that are implemented return the same result as the corresponding MBR-based functions. This includes functions in the following list other than `Distance()` and `Related()`.

These functions may be implemented in future releases with full support for spatial analysis, not just MBR-based support.

- `Contains(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether `g1` completely contains `g2`. This tests the opposite relationship as `Within()`.

- `Crosses(`g1`,`g2`)`

  Returns 1 if `g1` spatially crosses `g2`. Returns `NULL` if `g1` is a `Polygon` or a `MultiPolygon`, or if `g2` is a `Point` or a `MultiPoint`. Otherwise, returns 0.

  The term spatially crosses denotes a spatial relation between two given geometries that has the following properties:

  - The two geometries intersect

  - Their intersection results in a geometry that has a dimension that is one less than the maximum dimension of the two given geometries

  - Their intersection is not equal to either of the two given geometries

- `Disjoint(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether `g1` is spatially disjoint from (does not intersect) `g2`.

- `Distance(`g1`,`g2`)`

  Returns as a double-precision number the shortest distance between any two points in the two geometries.

- `Equals(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether `g1` is spatially equal to `g2`.

- `Intersects(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether `g1` spatially intersects `g2`.

- `Overlaps(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether `g1` spatially overlaps `g2`. The term spatially overlaps is used if two geometries intersect and their intersection results in a geometry of the same dimension but not equal to either of the given geometries.

- `Related(`g1`,`g2`,`pattern_matrix`)`

  Returns 1 or 0 to indicate whether the spatial relationship specified by `pattern_matrix` exists between `g1` and `g2`. Returns –1 if the arguments are `NULL`. The pattern matrix is a string. Its specification will be noted here if this function is implemented.

- `Touches(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether `g1` spatially touches `g2`. Two geometries spatially touch if the interiors of the geometries do not intersect, but the boundary of one of the geometries intersects either the boundary or the interior of the other.

- `Within(`g1`,`g2`)`

  Returns 1 or 0 to indicate whether `g1` is spatially within `g2`. This tests the opposite relationship as `Contains()`.

## 15.6. Optimizing Spatial Analysis

Search operations in non-spatial databases can be optimized using `SPATIAL` indexes. This is true for spatial databases as well. With the help of a great variety of multi-dimensional indexing methods that have previously been designed, it is possible to optimize spatial searches. The most typical of these are:

- Point queries that search for all objects that contain a given point

- Region queries that search for all objects that overlap a given region

MySQL uses R-Trees with quadratic splitting for `SPATIAL` indexes on spatial columns. A `SPATIAL` index is built using the MBR of a geometry. For most geometries, the MBR is a minimum rectangle that surrounds the geometries. For a horizontal or a vertical linestring, the MBR is a rectangle degenerated into the linestring. For a point, the MBR is a rectangle degenerated into the point.

### 15.6.1. Creating Spatial Indexes

MySQL can create spatial indexes using syntax similar to that for creating regular indexes, but extended with the `SPATIAL` keyword. Currently, columns in spatial indexes must be declared `NOT NULL`. The following examples demonstrate how to create spatial indexes:

- With `CREATE TABLE`:

      CREATE TABLE geom (g GEOMETRY NOT NULL, SPATIAL INDEX(g));

- With `ALTER TABLE`:

      ALTER TABLE geom ADD SPATIAL INDEX(g);

- With `CREATE INDEX`:

      CREATE SPATIAL INDEX sp_index ON geom (g);

For `MyISAM` tables, `SPATIAL INDEX` creates an R-tree index. For non-spatial indexing of spatial columns, `MyISAM` tables creates a B-tree index. A B-tree index on spatial values will be useful for exact-value lookups, but not for range scans.

For more information on indexing spatial columns, see Section 12.1.4, “`CREATE INDEX` Syntax”.

To drop spatial indexes, use `ALTER TABLE` or `DROP INDEX`:

- With `ALTER TABLE`:

      ALTER TABLE geom DROP INDEX g;

- With `DROP INDEX`:

      DROP INDEX sp_index ON geom;

Example: Suppose that a table `geom` contains more than 32,000 geometries, which are stored in the column `g` of type `GEOMETRY`. The table also has an `AUTO_INCREMENT` column `fid` for storing object ID values.

    mysql> DESCRIBE geom;
    +-------+----------+------+-----+---------+----------------+
    | Field | Type     | Null | Key | Default | Extra          |
    +-------+----------+------+-----+---------+----------------+
    | fid   | int(11)  |      | PRI | NULL    | auto_increment |
    | g     | geometry |      |     |         |                |
    +-------+----------+------+-----+---------+----------------+
    2 rows in set (0.00 sec)

    mysql> SELECT COUNT(*) FROM geom;
    +----------+
    | count(*) |
    +----------+
    |    32376 |
    +----------+
    1 row in set (0.00 sec)

To add a spatial index on the column `g`, use this statement:

    mysql> ALTER TABLE geom ADD SPATIAL INDEX(g);
    Query OK, 32376 rows affected (4.05 sec)
    Records: 32376  Duplicates: 0  Warnings: 0

### 15.6.2. Using a Spatial Index

The optimizer investigates whether available spatial indexes can be involved in the search for queries that use a function such as `MBRContains()` or `MBRWithin()` in the `WHERE` clause. The following query finds all objects that are in the given rectangle:

    mysql> SET @poly =
        -> 'Polygon((30000 15000,31000 15000,31000 16000,30000 16000,30000 15000))';
    mysql> SELECT fid,AsText(g) FROM geom WHERE
        -> MBRContains(GeomFromText(@poly),g);
    +-----+---------------------------------------------------------------+
    | fid | AsText(g)                                                     |
    +-----+---------------------------------------------------------------+
    |  21 | LINESTRING(30350.4 15828.8,30350.6 15845,30333.8 15845,30 ... |
    |  22 | LINESTRING(30350.6 15871.4,30350.6 15887.8,30334 15887.8, ... |
    |  23 | LINESTRING(30350.6 15914.2,30350.6 15930.4,30334 15930.4, ... |
    |  24 | LINESTRING(30290.2 15823,30290.2 15839.4,30273.4 15839.4, ... |
    |  25 | LINESTRING(30291.4 15866.2,30291.6 15882.4,30274.8 15882. ... |
    |  26 | LINESTRING(30291.6 15918.2,30291.6 15934.4,30275 15934.4, ... |
    | 249 | LINESTRING(30337.8 15938.6,30337.8 15946.8,30320.4 15946. ... |
    |   1 | LINESTRING(30250.4 15129.2,30248.8 15138.4,30238.2 15136. ... |
    |   2 | LINESTRING(30220.2 15122.8,30217.2 15137.8,30207.6 15136, ... |
    |   3 | LINESTRING(30179 15114.4,30176.6 15129.4,30167 15128,3016 ... |
    |   4 | LINESTRING(30155.2 15121.4,30140.4 15118.6,30142 15109,30 ... |
    |   5 | LINESTRING(30192.4 15085,30177.6 15082.2,30179.2 15072.4, ... |
    |   6 | LINESTRING(30244 15087,30229 15086.2,30229.4 15076.4,3024 ... |
    |   7 | LINESTRING(30200.6 15059.4,30185.6 15058.6,30186 15048.8, ... |
    |  10 | LINESTRING(30179.6 15017.8,30181 15002.8,30190.8 15003.6, ... |
    |  11 | LINESTRING(30154.2 15000.4,30168.6 15004.8,30166 15014.2, ... |
    |  13 | LINESTRING(30105 15065.8,30108.4 15050.8,30118 15053,3011 ... |
    | 154 | LINESTRING(30276.2 15143.8,30261.4 15141,30263 15131.4,30 ... |
    | 155 | LINESTRING(30269.8 15084,30269.4 15093.4,30258.6 15093,30 ... |
    | 157 | LINESTRING(30128.2 15011,30113.2 15010.2,30113.6 15000.4, ... |
    +-----+---------------------------------------------------------------+
    20 rows in set (0.00 sec)

Use `EXPLAIN` to check the way this query is executed:

    mysql> SET @poly =
        -> 'Polygon((30000 15000,31000 15000,31000 16000,30000 16000,30000 15000))';
    mysql> EXPLAIN SELECT fid,AsText(g) FROM geom WHERE
        -> MBRContains(GeomFromText(@poly),g)\G
    *************************** 1. row ***************************
               id: 1
      select_type: SIMPLE
            table: geom
             type: range
    possible_keys: g
              key: g
          key_len: 32
              ref: NULL
             rows: 50
            Extra: Using where
    1 row in set (0.00 sec)

Check what would happen without a spatial index:

    mysql> SET @poly =
        -> 'Polygon((30000 15000,31000 15000,31000 16000,30000 16000,30000 15000))';
    mysql> EXPLAIN SELECT fid,AsText(g) FROM g IGNORE INDEX (g) WHERE
        -> MBRContains(GeomFromText(@poly),g)\G
    *************************** 1. row ***************************
               id: 1
      select_type: SIMPLE
            table: geom
             type: ALL
    possible_keys: NULL
              key: NULL
          key_len: NULL
              ref: NULL
             rows: 32376
            Extra: Using where
    1 row in set (0.00 sec)

Executing the `SELECT` statement without the spatial index yields the same result but causes the execution time to rise from 0.00 seconds to 0.46 seconds:

    mysql> SET @poly =
        -> 'Polygon((30000 15000,31000 15000,31000 16000,30000 16000,30000 15000))';
    mysql> SELECT fid,AsText(g) FROM geom IGNORE INDEX (g) WHERE
        -> MBRContains(GeomFromText(@poly),g);
    +-----+---------------------------------------------------------------+
    | fid | AsText(g)                                                     |
    +-----+---------------------------------------------------------------+
    |   1 | LINESTRING(30250.4 15129.2,30248.8 15138.4,30238.2 15136. ... |
    |   2 | LINESTRING(30220.2 15122.8,30217.2 15137.8,30207.6 15136, ... |
    |   3 | LINESTRING(30179 15114.4,30176.6 15129.4,30167 15128,3016 ... |
    |   4 | LINESTRING(30155.2 15121.4,30140.4 15118.6,30142 15109,30 ... |
    |   5 | LINESTRING(30192.4 15085,30177.6 15082.2,30179.2 15072.4, ... |
    |   6 | LINESTRING(30244 15087,30229 15086.2,30229.4 15076.4,3024 ... |
    |   7 | LINESTRING(30200.6 15059.4,30185.6 15058.6,30186 15048.8, ... |
    |  10 | LINESTRING(30179.6 15017.8,30181 15002.8,30190.8 15003.6, ... |
    |  11 | LINESTRING(30154.2 15000.4,30168.6 15004.8,30166 15014.2, ... |
    |  13 | LINESTRING(30105 15065.8,30108.4 15050.8,30118 15053,3011 ... |
    |  21 | LINESTRING(30350.4 15828.8,30350.6 15845,30333.8 15845,30 ... |
    |  22 | LINESTRING(30350.6 15871.4,30350.6 15887.8,30334 15887.8, ... |
    |  23 | LINESTRING(30350.6 15914.2,30350.6 15930.4,30334 15930.4, ... |
    |  24 | LINESTRING(30290.2 15823,30290.2 15839.4,30273.4 15839.4, ... |
    |  25 | LINESTRING(30291.4 15866.2,30291.6 15882.4,30274.8 15882. ... |
    |  26 | LINESTRING(30291.6 15918.2,30291.6 15934.4,30275 15934.4, ... |
    | 154 | LINESTRING(30276.2 15143.8,30261.4 15141,30263 15131.4,30 ... |
    | 155 | LINESTRING(30269.8 15084,30269.4 15093.4,30258.6 15093,30 ... |
    | 157 | LINESTRING(30128.2 15011,30113.2 15010.2,30113.6 15000.4, ... |
    | 249 | LINESTRING(30337.8 15938.6,30337.8 15946.8,30320.4 15946. ... |
    +-----+---------------------------------------------------------------+
    20 rows in set (0.46 sec)

In future releases, spatial indexes may also be used for optimizing other functions. See Section 15.5.4, “Functions for Testing Spatial Relations Between Geometric Objects”.

## 15.7. MySQL Conformance and Compatibility

MySQL does not yet implement the following GIS features:

- Additional Metadata Views

  OpenGIS specifications propose several additional metadata views. For example, a system view named `GEOMETRY_COLUMNS` contains a description of geometry columns, one row for each geometry column in the database.

- The OpenGIS function `Length()` on `LineString` and `MultiLineString` currently should be called in MySQL as `GLength()`

  The problem is that there is an existing SQL function `Length()` that calculates the length of string values, and sometimes it is not possible to distinguish whether the function is called in a textual or spatial context. We need either to solve this somehow, or decide on another function name.

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