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-
-  OpenGIS <http://www.opengis.org> support in MySQL
-
-------------------------------------------------------------------------
-Note: Blue colored lines among the text is features not implemented yet.
-They are:
-
-    * Spatial Reference Systems and their IDs (SRIDs) related things:
-          o Functions like Length() and Area() assume planar coordinate
-            system.
-          o All objects are currently considered to be in the same
-      planar coordinate system.
-    * Function Length() on LineString and MultiLineString currently
-      should be called as GLength().
-* No binary constructors like GeomFromWKB().
-
-We also have to add "PostGIS compatibility" sections.
-
-
-  1 Introduction
-
-MySQL implements a subset of *SQL2 with Geometry Types* environment
-proposed by OpenGIS consortium's *Simple Features Specification For
-SQL*. In this environment a geometry-valued column is implemented as a
-column whose SQL type is drawn from the set of Geometry Types. SQL
-server supports both textual and binary access to geometry.
-
-
-  2 OpenGIS Geometry Model in MySQL
-
-MySQL supports the Open GIS Geometry Model based hierarcy of spatial
-objects classes, which consists of:
-
-    * Geometry
-          o *Point*
-          o Curve
-          + *LineString*
-          o Surface
-          + *Polygon*
-          o *GeometryCollection*
-                + *MultiPoint*
-                + MultiCurve
-                # *MultiLineString*
-                + MultiSurface
-                # *MultiPolygon*
-
-The base *Geometry* class has subclasses for Point, Curve, Surface and
-GeometryCollection.
-
-Geometry, Curve, Surface, MultiCurve and MultiSurface are defined to be
-non-instantiable classes, it is not possible to create an object of
-these classes.
-
-Point, LineString, Polygon, GeometryCollection, MultiPoint,
-MultiLineString, MultiPolygon are instantiable classes (bolded on the
-hierarcy tree). MySQL provides a number of functions to construct
-instances of these classes.
-
-TODO: Each spatial object is associated with a Spatial Reference System,
-which describes the coordinate space in which the geometric object is
-defined.
-
-
-    2.1 Geometry
-
-Geometry is the root class of the hierarchy. Geometry is an abstract
-(non-instantiable) class. The instantiable subclasses of Geometry
-defined in this specification are restricted to 0, 1 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 (i.e. all defined geometries
-include their boundary).
-
-
-    2.2 Point
-
-A *Point* is a 0-dimensional geometry and represents a single location
-in coordinate space. A Point in the case of 2D has a x-coordinate value
-and a y-coordinate value. In the case of more dimensions, a Point has a
-coordinate value for each dimension. The boundary of a Point is the
-empty set.
-
-
-    2.3 Curve
-
-A *Curve* is a one-dimensional geometric object usually stored as a
-sequence of points, with the subclass of Curve specifying the form of
-the interpolation between points. MySQL implementation defines only one
-subclass of Curve, LineString, which uses linear interpolation between
-points.
-
-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 end point. The
-boundary of a closed Curve is empty. A Curve that is simple and closed
-is a Ring. The boundary of a non-closed Curve consists of its two end
-points. A Curve is defined as topologically closed.
-
-
-    2.4 LineString, Line, LinearRing
-
-A LineString is a Curve with linear interpolation between points. Each
-consecutive pair of points defines a line segment. A Line is a
-LineString with exactly 2 points. A LinearRing is a LineString that is
-both closed and simple.
-
-
-    2.5 Surface
-
-A *Surface* is a two-dimensional geometric object. The OpenGIS Abstract
-Specification defines a simple Surface as consisting of a single 'patch'
-that is associated with one 'exterior boundary' and 0 or more 'interior'
-boundaries. Simple surfaces in three-dimensional space are isomorphic to
-planar surfaces. Polyhedral surfaces are formed by 'stitching' together
-simple surfaces along their boundaries, polyhedral surfaces in
-three-dimensional space may not be planar as a whole.
-
-The boundary of a simple Surface is the set of closed curves
-corresponding to its exterior and interior boundaries.
-
-The only instantiable subclass of Surface defined in this specification,
-Polygon, is a simple Surface that is planar.
-
-
-    2.6 Polygon
-
-A Polygon is a planar Surface, defined by 1 exterior boundary and 0 or
-more interior boundaries. Each interior boundary defines a hole in the
-Polygon. The assertions for polygons (the rules that define valid
-polygons) are:
-
-    * Polygons are topologically closed.
-    * The boundary of a Polygon consists of a set of LinearRings (i.e.
-      LineStrings which are both simple and closed) that make up its
-      exterior and interior boundaries.
-    * No two rings in the boundary cross, the rings in the boundary of a
-      Polygon may intersect at a Point but only as a tangent.
-    * A Polygon may not have cut lines, spikes or punctures.
-    * The Interior of every Polygon is a connected point set.
-    * The Exterior of a Polygon with 1 or more holes is not connected.
-Each hole defines a connected component of the Exterior.
-
-In the above assertions, Interior, Closure and Exterior have the
-standard topological definitions. The combination of 1 and 3 make a
-Polygon a Regular Closed point set. Polygons are simple geometries.
-
-
-    2.6 GeometryCollection
-
-A *GeometryCollection* is a geometry that is a collection of 1 or more
-geometries of any class. All the elements in a GeometryCollection must
-be in the same Spatial Reference (i.e. in the same coordinate system).
-GeometryCollection places no other constraints on its elements. However
-subclasses of GeometryCollection described below may restrict membership
-based on dimension and may also place other constraints on the degree of
-spatial overlap between elements.
-
-
-    2.7 MultiPoint
-
-A *MultiPoint* is a 0 dimensional geometric collection. The elements of
-a MultiPoint are restricted to Points. The points are not connected or
-ordered. A MultiPoint is simple if no two Points in the MultiPoint are
-equal (have identical coordinate values). The boundary of a MultiPoint
-is the empty set.
-
-
-    2.8 MultiCurve
-
-A MultiCurve is a one-dimensional geometry collection whose elements are
-Curves. MultiCurve is a non-instantiable class, it defines a set of
-methods for its subclasses and is included for reasons of extensibility.
-
-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.
-
-The boundary of a MultiCurve is obtained by applying the "mod 2 union
-rule": A point is in the boundary of a MultiCurve if it is in the
-boundaries of an odd number of elements of the MultiCurve.
-
-A MultiCurve is closed if all of its elements are closed. The boundary
-of a closed MultiCurve is always empty. A MultiCurve is defined as
-topologically closed.
-
-
-    2.9 MultiLineString
-
-A *MultiLineString* is a MultiCurve whose elements are LineStrings.
-
-
-    2.10 MultiSurface
-
-A MultiSurface is a two-dimensional geometric collection whose elements
-are surfaces. The interiors of any two surfaces in a MultiSurface may
-not intersect. The boundaries of any two elements in a MultiSurface may
-intersect at most at a finite number of points.
-
-MultiSurface is a non-instantiable class in this specification, it
-defines a set of methods for its subclasses and is included for reasons
-of extensibility. The instantiable subclass of MultiSurface is
-MultiPolygon, corresponding to a collection of Polygons.
-
-
-    2.11 MultiPolygon
-
-A MultiPolygon is a MultiSurface whose elements are Polygons.
-
-The assertions for MultiPolygons are :
-
-    * The interiors of 2 Polygons that are elements of a MultiPolygon
-      may not intersect.
-    * The Boundaries of any 2 Polygons that are elements of a
-      MultiPolygon may not cross and may touch at only a finite number
-      of points. (Note that crossing is prevented by assertion 1 above).
-    * A MultiPolygon is defined as topologically closed.
-    * A MultiPolygon may not have cut lines, spikes or punctures, a
-      MultiPolygon is a Regular, Closed point set.
-    * The interior of a MultiPolygon with more than 1 Polygon is not
-      connected, the number of connected components of the interior of a
-MultiPolygon is equal to the number of Polygons in the MultiPolygon.
-
-The boundary of a MultiPolygon is a set of closed curves (LineStrings)
-corresponding to the boundaries of its element Polygons. Each Curve in
-the boundary of the MultiPolygon is in the boundary of exactly 1 element
-Polygon, and every Curve in the boundary of an element Polygon is in the
-boundary of the MultiPolygon.
-
-
-  3 Exchange of spatial data
-
-MySQL provides binary and textual mechanismes to exchange spatial data.
-Exchange is provided via so called Well Known Binary (WKB) and Well
-Known Textual (WKT) representations of spatial data proposed by OpenGIS
-specifications.
-
-
-    3.1 Well-known Text representation (WKT)
-
-The Well-known Text (WKT) representation of Geometry is designed to
-exchange geometry data in textual format.
-
-WKT is defined below in Bechus-Naur forms:
-
-    * the notation {}* denotes 0 or more repetitions of the tokens
-      within the braces;
-* the braces do not appear in the output token list.
-
-The text representation of the implemented instantiable geometric types
-conforms to this grammar:
-
-<Geometry Tagged Text> :=
-            <Point Tagged Text>
-          | <LineString Tagged Text>
-          | <Polygon Tagged Text>
-          | <MultiPoint Tagged Text>
-          | <MultiLineString Tagged Text>
-          | <MultiPolygon Tagged Text>
-          | <GeometryCollection Tagged Text>
-
-<Point Tagged Text> :=
-
-            POINT <Point Text>
-
-<LineString Tagged Text> :=
-
-            LINESTRING <LineString Text>
-
-<Polygon Tagged Text> :=
-
-            POLYGON <Polygon Text>
-
-<MultiPoint Tagged Text> :=
-
-            MULTIPOINT <Multipoint Text>
-
-<MultiLineString Tagged Text> :=
-
-            MULTILINESTRING <MultiLineString Text>
-
-<MultiPolygon Tagged Text> :=
-
-            MULTIPOLYGON <MultiPolygon Text>
-
-<GeometryCollection Tagged Text> :=
-
-            GEOMETRYCOLLECTION <GeometryCollection Text>
-
-<Point Text> := EMPTY | ( <Point> )
-
-<Point> := <x> <y>
-
-<x> := double precision literal
-
-<y> := double precision literal
-
-<LineString Text> := EMPTY
-
-          | ( <Point >  {, <Point > }* )
-
-<Polygon Text> := EMPTY
-
-          | ( <LineString Text >  {, < LineString Text > }*)
-
-<Multipoint Text> := EMPTY
-
-          | ( <Point Text >  {, <Point Text > }* )
-
-<MultiLineString Text> := EMPTY
-
-          | ( <LineString Text >  {, < LineString Text > }* )
-
-<MultiPolygon Text> := EMPTY
-
-          | ( < Polygon Text >  {, < Polygon Text > }* )
-
-<GeometryCollection Text> := EMPTY
-
-          | ( <Geometry Tagged Text> {, <Geometry Tagged Text> }* )
-
-
-      WKT examples
-
-Examples of textual representations of Geometry objects are shown below:
-
-    * |POINT(10 10)| - a Point
-    * |LINESTRING( 10 10, 20 20, 30 40)| - a LineString with three points
-    * |POLYGON((10 10, 10 20, 20 20,20 15, 10 10))| - a Polygon with one
-      exterior ring and 0 interior rings
-    * |MULTIPOINT(10 10, 20 20)| - a MultiPoint with two Points
-    * |MULTILINESTRING((10 10, 20 20), (15 15, 30 15))| - a
-      MultiLineString with two LineStrings
-    * |MULTIPOLYGON(((10 10, 10 20, 20 20, 20 15, 10 10)), ((60 60, 70
-      70, 80 60, 60 60 ) ))| - a MultiPolygon with two Polygons
-    * |GEOMETRYCOLLECTION( POINT (10 10),POINT (30 30), LINESTRING (15
-      15, 20 20))| - a GeometryCollection consisting of two Points and
-one LineString
-
-
-    3.2 Well-known Binary representation (WKB)
-
-Well Known Binary Representations is proposed by OpenGIS specifications
-to exchange geometry data in binary format. This is WKB description:
-
-// Basic Type definitions
-// byte : 1 byte
-// uint32 : 32 bit unsigned integer (4 bytes)
-// double : double precision number (8 bytes)
-// Building Blocks : Point, LinearRing
-
-Point {
-	double [numDimentions];
-};
-
-LinearRing  {
-	uint32 numPoints;
-	Point    points[numPoints];
-}
-
-enum wkbGeometryType {
-	wkbPoint = 1,
-	wkbLineString = 2,
-	wkbPolygon = 3,
-	wkbMultiPoint = 4,
-	wkbMultiLineString = 5,
-	wkbMultiPolygon = 6,
-	wkbGeometryCollection = 7
-};
-
-enum wkbByteOrder {
-	wkbXDR = 0,    // Big Endian
-	wkbNDR = 1    // Little Endian
-};
-
-WKBPoint {
-	byte    byteOrder;
-	uint32    wkbType;     // 1
-	Point    point;
-}
-
-WKBLineString {
-	byte    byteOrder;
-	uint32    wkbType;    // 2
-	uint32    numPoints;
-	Point    points[numPoints];
-}
-
-WKBPolygon {
-	byte    byteOrder;
-	uint32    wkbType;    // 3
-	uint32    numRings;
-	LinearRing    rings[numRings];
-}
-
-WKBMultiPoint {
-	byte    byteOrder;
-	uint32    wkbType;       // 4
-	uint32    num_wkbPoints;
-	WKBPoint    WKBPoints[num_wkbPoints];
-}
-
-WKBMultiLineString {
-	byte    byteOrder;
-	uint32    wkbType;    // 5
-	uint32    num_wkbLineStrings;
-	WKBLineString WKBLineStrings[num_wkbLineStrings];
-}
-
-wkbMultiPolygon {
-	byte    byteOrder;
-	uint32    wkbType;    // 6
-	uint32    num_wkbPolygons;
-	WKBPolygon    wkbPolygons[num_wkbPolygons];
-}
-
-WKBGeometry {
-	union {
-		WKBPoint    point;
-		WKBLineString    linestring;
-		WKBPolygon    polygon;
-		WKBGeometryCollection    collection;
-		WKBMultiPoint    mpoint;
-		WKBMultiLineString    mlinestring;
-		WKBMultiPolygon    mpolygon;
-	}
-
-};
-
-WKBGeometryCollection {
-	byte    byte_order;
-	uint32    wkbType;    // 7
-	uint32    num_wkbGeometries;
-	WKBGeometry    wkbGeometries[num_wkbGeometries];
-}
-
-
-    3.3 MySQL data types for spatial objects
-
-MySQL implementation of OpenGIS provides the *GEOMETRY* data type to be
-used in CREATE TABLE statements. For example, this statement creates a
-table *geom* with spatial field *g*:
-
-CREATE TABLE geom (
-	g Geometry;
-);
-
-A field of *GEOMETRY* type can store a spatial objects of any OpenGIS
-geometry class described above.
-
-
-    3.4 Internal spatial data representation
-
-Internally (in *.MYD* files) spatial objects are stored in *WKB*,
-combined with object's *SRID* (a numeric ID of Spatial Reference System
-object associated with). During spatial analysis, for example,
-calculating the fact that one object crosses another one, only those
-with the same *SRID* are accepted.
-
-*SRID* may affect a way in which various spatial characteristics are
-calculated. For example, in different coordinate systems distance
-between two objects may differ even objects have the same coordinates,
-like distance on plane coordinate system and distance on geocentric
-(coordinates on Earth surface) systems are different things.
-
-There is a plan to provide a number of commonly used coordinate systems
-in MySQL OpenGIS implementation.
-
-
-    3.5 INSERTing spatial objects
-
-Spatial data can be INSERTed using a spatial constructor. The term
-*spatial constructor* is used in this manual to refer to any function
-which can construct a value of GEOMETRY type, i.e. an internal MySQL
-representation of spatial data.
-
-
-      3.5.1 Textual spatial constructors
-
-Textual spatial constructors take a gemometry description in WKT and
-built GEOMETRY value.
-
-    * |*GeomFromText(geometryTaggedText String [, SRID
-      Integer]):Geometry *| - constructs a Geometry value from its
-      well-known textual representation.
-
-      |*GeomFromText()*| function accepts a WKT of any Geometry class as
-      it's first argument.
-
-      For construction of Geometry values restricted to a particular
-      subclass, an implementation also provides a class-specific
-      construction function for each instantiable subtype as described
-      in the list below:
-
-    * |*PointFromText(pointTaggedText String [,SRID Integer]):Point *| -
-      constructs a Point
-
-    * |*LineFromText(lineStringTaggedText String [,SRID
-      Integer]):LineString *| - constructs a LineString
-
-      . |*LineStringFromText()*| - synonym for LineFromText().
-
-    * |*PolyFromText(polygonTaggedText String [,SRID Integer]):Polygon
-      *|- constructs a Polygon
-
-      |*PolygonFromText()*| - synonym for PolyFromText().
-
-    * |*MPointFromText(multiPointTaggedText String [,SRID
-      Integer]):MultiPoint *| - constructs a MultiPoint
-
-      |*MultiPointFromText()*| - synonym for MPointFromText().
-
-    * |*MLineFromText(multiLineStringTaggedText String [,SRID
-      Integer]):MultiLineString *| - constructs a MultiLineString
-
-      |*MultiLineStringFromText()*| - synonym for MLineFromText().
-
-    * |*MPolyFromText(multiPolygonTaggedText String [,SRID
-      Integer]):MultiPolygon *| - constructs a MultiPolygon
-
-      |*MultiPolygonFromText()*| - synonym for MPolyFromText().
-
-    * |*GeomCollFromText(geometryCollectionTaggedText String [,SRID
-      Integer]):GeomCollection *| - constructs a GeometryCollection
-
-Usage examples:
-
-INSERT INTO geom VALUES (GeomFromText('POINT(1 1)'))
-INSERT INTO geom VALUES (GeomFromText('LINESTRING(0 0,1 1,2 2)'))
-INSERT INTO geom VALUES (GeomFromText('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('GEOMETRYCOLLECTION(POINT(1 1),LINESTRING(0 0,1 1,2 2,3 3,4 4))'))
-
-The second argument of spatial constructirs, described above, is
-currently ignored, It will be used to specify SRID in the future.
-Nowdays, it is added for reasons of compatibility with OpenGIS
-specifications and PostGIS implementation.
-
-As an optional feature, an implementation may also support building of
-Polygon or MultiPolygon values given an arbitrary collection of possibly
-intersecting rings or closed LineString values. Implementations that
-support this feature should include the following functions:
-
-    * |*BdPolyFromText(multiLineStringTaggedText String, SRID
-      Integer):Polygon *| - constructs a Polygon given an arbitrary
-      collection of closed linestrings as a MultiLineString text
-      representation.
-    * |*BdMPolyFromText(multiLineStringTaggedText String, SRID
-      Integer):MultiPolygon *| - constructs a MultiPolygon given an
-      arbitrary collection of closed linestrings as a MultiLineString
-text representation.
-
-
-      3.5.2 Binary spatial constructors
-
-    * |*GeomFromWKB(WKBGeometry Binary, SRID Integer):Geometry *| -
-      constructs a Geometry value given its well-known binary
-      representation.
-
-      |*GeomFromWKB()*| function can accept in it's first argument a WKB
-      of Geometry of any class. For construction of Geometry values
-      restricted to a particular subclass, an implementation also
-      provides a class-specific construction function for each
-      instantiable subclass as described in the list below:
-
-    * |*PointFromWKB(WKBPoint Binary, SRID Integer):Point - *|constructs
-      a Point
-    * |* LineFromWKB(WKBLineString Binary, SRID Integer):LineString *| -
-      constructs a LineString
-    * |* PolyFromWKB(WKBPolygon Binary, SRID Integer):Polygon *| -
-      constructs a Polygon
-    * |* MPointFromWKB(WKBMultiPoint Binary, SRID Integer):MultiPoint *|
-      - constructs a MultiPoint
-    * |* MLineFromWKB(WKBMultiLineString Binary, SRID
-      Integer):MultiLineString *| - constructs a MultiLineString
-    * |* MPolyFromWKB(WKBMultiPolygon Binary, SRID Integer):
-      MultiPolygon *| - constructs a MultiPolygon
-    * |* GeomCollFromWKB(WKBGeometryCollection Binary, SRID Integer):
-GeomCollection *| - constructs a GeometryCollection
-
-As an optional feature, an implementation may also support the uilding'
-of Polygon or MultiPolygon values given an arbitrary collection of
-possibly intersecting rings or closed LineString values. Implementations
-that support this feature should include the following functions:
-
-    * |* BdPolyFromWKB (WKBMultiLineString Binary,SRID Integer): Polygon
-      *| - constructs a Polygon given an arbitrary collection of closed
-      linestrings as a MultiLineString binary representation.
-    * |*BdMPolyFromWKB(WKBMultiLineString Binary, SRID
-      Integer):MultiPolygon *| - constructs a MultiPolygon given an
-      arbitrary collection of closed linestrings as a MultiLineString
-binary representation.
-
-Inserting in *WKB* assumes that |GeomFromWKB()| function argument
-contains a buffer with a correctly formed spatial object in WKB. In ODBC
-applications it can be done using binding of argument. One also can
-insert object in *WKB* using |mysql_escape_string()| in |libmysqlclient|
-applications.
-
-For example:
-
-INSERT INTO geom VALUES (GeomFromWKB(buf,SRID));
-
-where |buf| is a binary buffer with a spatial object in *WKB*
-representation.
-
-
-    3.5 SELECTing spatial objects
-
-Spatial objects are selected either in *WKT* or *WKB* representation by
-use of AsText() and AsBinary() functions correspondently.
-
-
-mysql> select AsText(g) as g from geom;
-+-------------------------+
-| g                       |
-+-------------------------+
-| POINT(1 1)              |
-| LINESTRING(0 0,1 1,2 2) |
-+-------------------------+
-2 rows in set (0.00 sec)
-
-mysql> 
-
-The query:
-
-SELECT AsBinary(g) FROM geom
-
-returns a BLOB which contains *WKB* representation of object.
-
-
-  4 Functions for spatial analysis
-
-
-    4.1 Basic functions on Geometry
-
-    * |*AsText(g:Geometry):String*| - Exports this Geometry to a
-      specific well-known text representation of Geometry.
-    * |*AsBinary(g:Geometry):Binary*| - Exports this Geometry to a
-      specific well-known binary representation of Geometry.
-    * |*GeometryType(g:Geometry):String*| - Returns the name of the
-      instantiable subtype of Geometry of which this Geometry instance
-      is a member. The name of the instantiable subtype of Geometry is
-      returned as a string.
-    * |*Dimension(g:Geometry):Integer*| - The inherent dimension of this
-      Geometry object, which must be less than or equal to the
-      coordinate dimension. This specification is restricted to
-      geometries in two-dimensional coordinate space.
-    * |*IsEmpty(g:Geometry):Integer*| - Returns 1 (TRUE) if this
-      Geometry is the empty geometry . If true, then this Geometry
-      represents the empty point set, , for the coordinate space.
-    * |*IsSimple(g:Geometry):Integer *| - Returns 1 (TRUE) if this
-      Geometry has no anomalous geometric points, such as self
-      intersection or self tangency. The description of each
-      instantiable geometric class includes the specific conditions that
-      cause an instance of that class to be classified as not simple.
-    * |*SRID(g:Geometry):Integer*| - Returns the Spatial Reference
-      System ID for this Geometry.
-    * |*Distance(g1:Geometry,g2:Geometry):Double*| - the shortest
-distance between any two points in the two geometries.
-
-
-    4.2 Functions for specific geometry type
-
-
-      GeometryCollection functions
-
-    * *NumGeometries(g:GeometryCollection ):Integer * -Returns the
-      number of geometries in this GeometryCollection.
-    * *GeometryN(g:GeometryCollection,N:integer):Geometry * -Returns the
-Nth geometry in this GeometryCollection.
-
-
-      Point functions
-
-    * *X(p:Point):Double* -The x-coordinate value for this Point.
-* *Y(p:Point):Double* -The y-coordinate value for this Point.
-
-
-      LineString functions
-
-    * *StartPoint(l:LineString):Point* The start point of this LineString.
-    * *EndPoint(l:LineString):Point* The end point of this LineString.
-    * *PointN(l:LineString,N:Integer):Point* Returns the specified point
-      N in this Linestring.
-    * *Length(l:LineString):Double* The length of this LineString in its
-      associated spatial reference.
-    * *IsRing(l:LineString):Integer* Returns 1 (TRUE) if this LineString
-      is closed (StartPoint ( ) = EndPoint ( )) and this LineString is
-      simple (does not pass through the same point more than once).
-    * *IsClosed(l:LineString):Integer* Returns 1 (TRUE) if this
-      LineString is closed (StartPoint ( ) = EndPoint ( )).
-    * *NumPoints(l:LineString):Integer* The number of points in this
-LineString.
-
-
-      MultiLineString functions
-
-    * *Length(m:MultiLineString):Double* The Length of this
-      MultiLineString which is equal to the sum of the lengths of the
-      elements.
-    * *IsClosed(m:MultiLineString):Integer* Returns 1 (TRUE) if this
-      MultiLineString is closed (StartPoint() = EndPoint() for each
-LineString in this MultiLineString)
-
-
-      Polygon functions
-
-    * *Area(p:Polygon):Double* The area of this Polygon, as measured in
-      the spatial reference system of this Polygon.
-    * *Centroid(p:Polygon):Point* The mathematical centroid for this
-      Polygon as a Point. The result is not guaranteed to be on this
-      Polygon.
-    * *PointOnSurface(p:Polygon):Point* A point guaranteed to be on this
-      Polygon.
-    * *NumInteriorRing(p:Polygon):Integer* Returns the number of
-      interior rings in this Polygon.
-    * *ExteriorRing(p:Polygon):LineString* Returns the exterior ring of
-      this Polygon as a LineString.
-    * *InteriorRingN(p:Polygon,N:Integer):LineString* Returns the Nth
-interior ring for this Polygon as a LineString.
-
-
-      MultiPolygon functions
-
-    * *Area(m:MultuSurface):Double* The area of this MultiPolygon, as
-      measured in the spatial reference system of this MultiPolygon.
-    * *Centroid(m:MultyPolygon):Point* The mathematical centroid for
-      this MultiPolygon as a Point. The result is not guaranteed to be
-      on this MultiPolygon.
-    * *PointOnSurface(m:MultuPolygon):Point* A Point guaranteed to be on
-this MultiPolygon.
-
-Notes: /functions for specific geometry type retrun NULL if passed
-object type is incorrect. For example Area() returns NULL if object type
-is neither Polygon nor MultiPolygon/
-
-
-    4.3 Spatial operations (compound spatial constructors)
-
-    * |*Envelope(g:Geometry):Geometry*|The minimum bounding box for this
-      Geometry, returned as a Geometry. The polygon is defined by the
-      corner points of the bounding box
-      |POLYGON((MINX,MINY),(MAXX,MINY),(MAXX,MAXY),(MINX,MAXY),(MINX,MINY))|.
-
-    * |*Boundary(g:Geometry):Geometry*| - returns the closure of the
-      combinatorial boundary of this Geometry.
-    * |*Intersection(g1,g2:Geometry):Geometry*| - a geometry that
-      represents the point set intersection of g1 with g2.
-    * |*Union(g1,g2:Geometry):Geometry*| - a geometry that represents
-      the point set union of g1 with g2.
-    * |*Difference(g1,g2:Geometry):Geometry*| - a geometry that
-      represents the point set difference of g1 with g2.
-    * |*SymDifference(g1,g2:Geometry):Geometry*| - a geometry that
-      represents the point set symmetric difference of g1 with g2.
-    * |*Buffer(g:Geometry,distance:Double):Geometry*| - a geometry that
-      represents all points whose distance from g is less than or equal
-      to distance.
-    * |*ConvexHull(g:Geometry):Geometry*| - a geometry that represents
-the convex hull of g.
-
-
-    4.4 Functions for testing Spatial Relations between geometric objects
-
-    * |*Equals(g1,g2)*| - Returns 1 if g1 is spatially equal to g2.
-    * |*Disjoint(g1,g2)*| - Returns 1 if g1 is spatially disjoint from g2.
-    * |*Intersects(g1,g2)*| - Returns 1 if g1 spatially intersects g2.
-    * |*Touches(g1,g2)*| - Returns 1 if g1 spatially touches g2.
-    * |*Crosses(g1,g2)*| - Returns 1 if g1 spatially crosses g2.
-    * |*Within(g1,g2)*| - Returns 1 if g1 is spatially within g2.
-    * |*Contains(g1,g2)*| - Returns 1 if g1 spatially contains g2.
-* |*Overlaps(g1,g2)*| - Returns 1 if g1 spatially overlaps g2.
-
-
-  5 Optimizing spatial analysis
-
-
-    5.1 MBR
-
-MBR is a minimal bounding rectangle (box) for spatial object. It can be
-represented as a set of min and max values of each dimension.
-
-For example:
-
-(Xmin,Xmax,Ymin,Ymax)
-
-
-    5.2 Using SPATIAL indexes
-
-To optimize spatial object relationships analysis it is possible to
-create a spatial index on geometry field using R-tree algorythm. R-tree
-based spatial indexes store MBRs of spatial objects as a key values.
-
-CREATE SPATIAL INDEX gind ON geom (g);
-
-Or together with table definition:
-
-CREATE TABLE geom (
-  g GEOMETRY,
-  SPATIAL INDEX(g)
-);
-
-Optimizer attaches R-tree based SPATIAL index when a query with spatial
-objects relationship functions is executed in WHERE clause.
-
-For example:
-
-SELECT geom.name FROM geom 
-       WHERE Within(geom.g,GeomFromText('POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))',SRID));
-
-
-    8 OpenGIS extensions implemented in MySQL
-
-MySQL provides it's own constructors to build geometry objects:
-
-    * |*Point(double,double,SRID)*| - constructs a geometry of Point
-      class using it's coordinates and SRID.
-    * |*MultiPoint(Point,Point,...,Point)*| - constructs a MultiPoint
-      using Points. When any argument is not a geometry of Point class
-      the return value is NULL.
-    * |*LineString(Point,Point,...,Point)*| - constructs a LineString
-      from a number of Points. When any argument is not a geometry of
-      Point class the return value is NULL. When the number of Points is
-      less than two the return value is NULL.
-    * |*MultiLineString(LineString,LineString,...,LineString)*| -
-      constructs a MultiLineString using using LineStrings. When any
-      argument is not a geometry of LineStringClass return value is NULL.
-    * |*Polygon(LineString,LineString,...,LineString)*| - constructs a
-      Polygon from a number of LineStrings. When any argument is not a
-      LinearRing (i.e. not closed and simple geometry of class
-      LineString) the return value is NULL.
-    * |*MultiPolygon(Polygon,Polygon,...,Polygon)*| - constructs a
-      MultiPolygon from a set of Polygons. When any argument is not a
-      Polygon, the rerurn value is NULL.
-    * |*GeometryCollection(Geometry,Geometry,..,Geometry)*| - constucts
-      a GeometryCollection. When any argument is not a valid geometry
-object of any instantiable class, the return value is NULL.
-
-The above functions (except Point()) return NULL if arguments are not in
-the same spatial reference system (i.e. have different SRIDs).
-
-
-        Examples:
-
-INSERT INTO geom SELECT Point(x,y,SRID) FROM coords;
-SELECT AsText(g) FROM geom WHERE 
-  Contains(Polygon(LineString(Point(0,0),Point(0,1),Point(1,1),Point(1,0),Point(0,0)),SRID),geom.g);
-
-
-    9 Things that differ in MySQL implemention and OpenGIS specifications
-
-
-      9.1 Single GEOMETRY type
-
-Besides a GEOMETRY type, OpenGIS consortium specifications suggest the
-implementation of several spatial field types correspondent to every
-instansiable object subclass. For example a *Point* type is proposed to
-restrict data stored in a field of this type to only Point OpenGIS
-subclass. MySQL provides an implementation of single GEOMETRY type which
-doesn't restrict objects to certain OpenGIS subclass. Other proposed
-spatial field types are mapped into GEOMETRY type, so all these types
-can be used as a symonym for GEOMETRY: POINT, MULTIPOINT, LINESTRING,
-MULTILINESTRING, POLYGON, MULTIPOLYGON.
-
-
-      9.2 No 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.
-
-
-      9.3 No functions to add/drop spatial columns
-
-OpenGIS assumes that columns can be added/dropped using
-AddGeometryColumn() and DropGeometryColumn() functions correspondently.
-In MySQL implementation one should use ALTER TABLE instead.