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# 7. Geometriebearbeitung

Hinweis

Die Codefragmente auf dieser Seite müssen wie folgt importiert werden, wenn Sie sich außerhalb der pyqgis-Konsole befinden:

``` 1from qgis.core import (
2  QgsGeometry,
3  QgsGeometryCollection,
4  QgsPoint,
5  QgsPointXY,
6  QgsWkbTypes,
7  QgsProject,
8  QgsFeatureRequest,
9  QgsVectorLayer,
10  QgsDistanceArea,
11  QgsUnitTypes,
12  QgsCoordinateTransform,
13  QgsCoordinateReferenceSystem
14)
```

Points, linestrings and polygons that represent a spatial feature are commonly referred to as geometries. In QGIS they are represented with the `QgsGeometry` class.

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.

Description and specifications of all possible geometries construction and relationships are available in the OGC Simple Feature Access Standards for advanced details.

## 7.1. Geometrieaufbau

PyQGIS provides several options for creating a geometry:

• from coordinates

```1gPnt = QgsGeometry.fromPointXY(QgsPointXY(1,1))
2print(gPnt)
3gLine = QgsGeometry.fromPolyline([QgsPoint(1, 1), QgsPoint(2, 2)])
4print(gLine)
5gPolygon = QgsGeometry.fromPolygonXY([[QgsPointXY(1, 1),
6    QgsPointXY(2, 2), QgsPointXY(2, 1)]])
7print(gPolygon)
```

Coordinates are given using `QgsPoint` class or `QgsPointXY` class. The difference between these classes is that `QgsPoint` supports M and Z dimensions.

A Polyline (Linestring) is represented by a list of points.

A Polygon is represented by a list of linear rings (i.e. closed linestrings). The first ring is the outer ring (boundary), optional subsequent rings are holes in the polygon. Note that unlike some programs, QGIS will close the ring for you so there is no need to duplicate the first point as the last.

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)

```geom = QgsGeometry.fromWkt("POINT(3 4)")
print(geom)
```
• from well-known binary (WKB)

```1g = QgsGeometry()
2wkb = bytes.fromhex("010100000000000000000045400000000000001440")
3g.fromWkb(wkb)
4
5# print WKT representation of the geometry
6print(g.asWkt())
```

## 7.2. Zugriff auf die Geometrie

First, you should find out the geometry type. The `wkbType()` method is the one to use. It returns a value from the `QgsWkbTypes.Type` enumeration.

```1print(gPnt.wkbType())
2# output: 'WkbType.Point'
3print(gLine.wkbType())
4# output: 'WkbType.LineString'
5print(gPolygon.wkbType())
6# output: 'WkbType.Polygon'
```

As an alternative, one can use the `type()` method which returns a value from the `QgsWkbTypes.GeometryType` enumeration.

```print(gLine.type())
# output: 'GeometryType.Line'
```

You can use the `displayString()` function to get a human readable geometry type.

```1print(QgsWkbTypes.displayString(gPnt.wkbType()))
2# output: 'Point'
3print(QgsWkbTypes.displayString(gLine.wkbType()))
4# output: 'LineString'
5print(QgsWkbTypes.displayString(gPolygon.wkbType()))
6# output: 'Polygon'
```

There is also a helper function `isMultipart()` to find out whether a geometry is multipart or not.

To extract information from a geometry there are accessor functions for every vector type. Here’s an example on how to use these accessors:

```1print(gPnt.asPoint())
2# output: <QgsPointXY: POINT(1 1)>
3print(gLine.asPolyline())
4# output: [<QgsPointXY: POINT(1 1)>, <QgsPointXY: POINT(2 2)>]
5print(gPolygon.asPolygon())
6# output: [[<QgsPointXY: POINT(1 1)>, <QgsPointXY: POINT(2 2)>, <QgsPointXY: POINT(2 1)>, <QgsPointXY: POINT(1 1)>]]
```

Bemerkung

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()` and `asMultiPolygon()`.

It is possible to iterate over all the parts of a geometry, regardless of the geometry’s type. E.g.

```geom = QgsGeometry.fromWkt( 'MultiPoint( 0 0, 1 1, 2 2)' )
for part in geom.parts():
print(part.asWkt())
```
```Point (0 0)
Point (1 1)
Point (2 2)
```
```geom = QgsGeometry.fromWkt( 'LineString( 0 0, 10 10 )' )
for part in geom.parts():
print(part.asWkt())
```
```LineString (0 0, 10 10)
```
```gc = QgsGeometryCollection()
gc.fromWkt('GeometryCollection( Point(1 2), Point(11 12), LineString(33 34, 44 45))')
print(gc[1].asWkt())
```
```Point (11 12)
```

It’s also possible to modify each part of the geometry using `QgsGeometry.parts()` method.

```1geom = QgsGeometry.fromWkt( 'MultiPoint( 0 0, 1 1, 2 2)' )
2for part in geom.parts():
3  part.transform(QgsCoordinateTransform(
4    QgsCoordinateReferenceSystem("EPSG:4326"),
5    QgsCoordinateReferenceSystem("EPSG:3111"),
6    QgsProject.instance())
7  )
8
9print(geom.asWkt())
```
```MultiPoint ((-10334728.12541878595948219 -5360106.25905461423099041),(-10462135.16126426123082638 -5217485.4735023295506835),(-10589399.84444035589694977 -5072021.45942386891692877))
```

## 7.3. Geometry Predicates and Operations

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

Let’s see an example that combines iterating over the features in a given layer and performing some geometric computations based on their geometries. The below code will compute and print the area and perimeter of each country in the `countries` layer within our tutorial QGIS project.

The following code assumes `layer` is a `QgsVectorLayer` object that has Polygon feature type.

``` 1# let's access the 'countries' layer
2layer = QgsProject.instance().mapLayersByName('countries')[0]
3
4# let's filter for countries that begin with Z, then get their features
5query = '"name" LIKE \'Z%\''
6features = layer.getFeatures(QgsFeatureRequest().setFilterExpression(query))
7
8# now loop through the features, perform geometry computation and print the results
9for f in features:
10  geom = f.geometry()
11  name = f.attribute('NAME')
12  print(name)
13  print('Area: ', geom.area())
14  print('Perimeter: ', geom.length())
```
```1Zambia
2Area:  62.82279065343119
3Perimeter:  50.65232014052552
4Zimbabwe
5Area:  33.41113559136517
6Perimeter:  26.608288555013935
```

Now you have calculated and printed the areas and perimeters of the geometries. You may however quickly notice that the values are strange. That is because areas and perimeters don’t take CRS into account when computed using the `area()` and `length()` methods from the `QgsGeometry` class. For a more powerful area and distance calculation, the `QgsDistanceArea` class can be used, which can perform ellipsoid based calculations:

The following code assumes `layer` is a `QgsVectorLayer` object that has Polygon feature type.

``` 1d = QgsDistanceArea()
2d.setEllipsoid('WGS84')
3
4layer = QgsProject.instance().mapLayersByName('countries')[0]
5
6# let's filter for countries that begin with Z, then get their features
7query = '"name" LIKE \'Z%\''
8features = layer.getFeatures(QgsFeatureRequest().setFilterExpression(query))
9
10for f in features:
11  geom = f.geometry()
12  name = f.attribute('NAME')
13  print(name)
14  print("Perimeter (m):", d.measurePerimeter(geom))
15  print("Area (m2):", d.measureArea(geom))
16
17  # let's calculate and print the area again, but this time in square kilometers
18  print("Area (km2):", d.convertAreaMeasurement(d.measureArea(geom), QgsUnitTypes.AreaSquareKilometers))
```
```1Zambia
2Perimeter (m): 5539361.250294601
3Area (m2): 751989035032.9031
4Area (km2): 751989.0350329031
5Zimbabwe
6Perimeter (m): 2865021.3325076113
7Area (m2): 389267821381.6008
8Area (km2): 389267.8213816008
```

Alternatively, you may want to know the distance between two points.

``` 1d = QgsDistanceArea()
2d.setEllipsoid('WGS84')
3
4# Let's create two points.
5# Santa claus is a workaholic and needs a summer break,
6# lets see how far is Tenerife from his home
7santa = QgsPointXY(25.847899, 66.543456)
8tenerife = QgsPointXY(-16.5735, 28.0443)
9
10print("Distance in meters: ", d.measureLine(santa, tenerife))
```

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.