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16.5.2.7 GeometryCollection Functions »
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16.5.2.6. MultiPolygon Functions

These functions return properties of MultiPolygon values.

  • 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.


User Comments

Posted by Mircea LUTIC on February 1 2005 12:05pm[Delete] [Edit]

The result of Area() depends on the type of Spatial Reference (SRID).

The value above is based on euclidian geometry.

The area of a triangle (and hence of a Polygon and MultiPolygon) is given by Heron's formula
SQRT ( s * (s-a) * (s-b) * (s-c) )
only in planar (euclidian) geometry.

Here a, b and c are the lengths of the sides of a triangle as given by GLength() (see also comment on MultiLineString functions) and s=(a+b+c)/2.

On a sphere where coordinates are lattitude and longitude and the lengths of the sides are measured in radians the formula to use for the area is

AreaInSteradians = 4*atan(sqrt( tan(s/2) * tan((s-a)/2) * tan((s-b)/2) * tan((s-c)/2) ))

AreaInSqMeters = AreaInSteradians * RadiusOfSphere^2

See also my comment on 19.5.2.4 MultiLineString Functions

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