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() >>> wkb = bytes.fromhex("010100000000000000000045400000000000001440") >>> g.fromWkb(wkb) >>> g.exportToWkt() 'Point (42 5)'

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 performing 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.

```
d = QgsDistanceArea()
d.setEllipsoid('WGS84')
d.setEllipsoidalMode(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.

Additional information can be found in following sources:

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