Points, linestrings and polygons that represent a spatial feature are commonly
referred to as geometries. In QGIS they are represented with the `QgsGeometry`
class. All possible geometry types are nicely shown in JTS discussion page.

Sometimes one geometry is actually a collection of simple (single-part) geometries. Such a geometry is called a multi-part geometry. If it contains just one type of simple geometry, we call it multi-point, multi-linestring or multi-polygon. For example, a country consisting of multiple islands can be represented as a multi-polygon.

The coordinates of geometries can be in any coordinate reference system (CRS). When fetching features from a layer, associated geometries will have coordinates in CRS of the layer.

There are several options for creating a geometry:

from coordinates:

gPnt = QgsGeometry.fromPoint(QgsPoint(1,1)) gLine = QgsGeometry.fromPolyline( [ QgsPoint(1,1), QgsPoint(2,2) ] ) gPolygon = QgsGeometry.fromPolygon( [ [ QgsPoint(1,1), QgsPoint(2,2), \ QgsPoint(2,1) ] ] )

Coordinates are given using

`QgsPoint`class.Polyline (Linestring) is represented by a list of points. Polygon is represented by a list of linear rings (i.e. closed linestrings). First ring is outer ring (boundary), optional subsequent rings are holes in the polygon.

Multi-part geometries go one level further: multi-point is a list of points, multi-linestring is a list of linestrings and multi-polygon is a list of polygons.

from well-known text (WKT):

gem = QgsGeometry.fromWkt("POINT (3 4)")

from well-known binary (WKB):

g = QgsGeometry() g.setWkbAndOwnership(wkb, len(wkb))

First, you should find out geometry type, `wkbType()` method is the one to
use — it returns a value from QGis.WkbType enumeration:

```
>>> gPnt.wkbType() == QGis.WKBPoint
True
>>> gLine.wkbType() == QGis.WKBLineString
True
>>> gPolygon.wkbType() == QGis.WKBPolygon
True
>>> gPolygon.wkbType() == QGis.WKBMultiPolygon
False
```

As an alternative, one can use `type()` method which returns a value from
QGis.GeometryType enumeration. There is also a helper function `isMultipart()`
to find out whether a geometry is multipart or not.

To extract information from geometry there are accessor functions for every vector type. How to use accessors:

```
>>> gPnt.asPoint()
(1,1)
>>> gLine.asPolyline()
[(1,1), (2,2)]
>>> gPolygon.asPolygon()
[[(1,1), (2,2), (2,1), (1,1)]]
```

Note: the tuples (x,y) are not real tuples, they are `QgsPoint` objects,
the values are accessible with `x()` and `y()` methods.

For multipart geometries there are similar accessor functions:
`asMultiPoint()`, `asMultiPolyline()`, `asMultiPolygon()`.

QGIS uses GEOS library for advanced geometry operations such as geometry
predicates (`contains()`, `intersects()`, ...) and set operations
(`union()`, `difference()`, ...). It can also compute geometric properties of geometries, such as area (in the case of polygons) or lengths (for polygons and lines)

Here you have a small example that combines iterating over the features in a given layer and perfoming some geometric computations based on their geometries.

```
#we assume that 'layer' is a polygon layer
features = layer.getFeatures()
for f in features:
geom = f.geometry()
print "Area:", geom.area()
print "Perimeter:", geom.length()
```

Areas and perimeters don’t take CRS into account when computed using these methods from the `QgsGeometry` class. For a more powerful area and distance calculation, the `QgsDistanceArea` class can be used. If projections are turned off, calculations will be planar, otherwise they’ll be done on the ellipsoid. When an ellipsoid is not set explicitly, WGS84 parameters are used for calculations.

```
d = QgsDistanceArea()
d.setProjectionsEnabled(True)
print "distance in meters: ", d.measureLine(QgsPoint(10,10),QgsPoint(11,11))
```

You can find many example of algorithms that are included in QGIS and use these methods to analyze and transform vector data. Here are some links to the code of a few of them.

- Geometry transformation: Reproject algorithm
- Distance and area using the
`QgsDistanceArea`class: Distance matrix algorithm - Multi-part to single-part algorithm