django/tests/gis_tests/distapp/tests.py

import unittest

from django.contrib.gis.db.models.functions import (
    Area, Distance, Length, Perimeter, Transform, Union,
)
from django.contrib.gis.geos import GEOSGeometry, LineString, Point
from django.contrib.gis.measure import D  # alias for Distance
from django.db import NotSupportedError, connection
from django.db.models import Exists, F, OuterRef, Q
from django.test import TestCase, skipIfDBFeature, skipUnlessDBFeature

from ..utils import FuncTestMixin, mysql, oracle, postgis, spatialite
from .models import (
    AustraliaCity, CensusZipcode, Interstate, SouthTexasCity, SouthTexasCityFt,
    SouthTexasInterstate, SouthTexasZipcode,
)


class DistanceTest(TestCase):
    fixtures = ['initial']

    def setUp(self):
        # A point we are testing distances with -- using a WGS84
        # coordinate that'll be implicitly transformed to that to
        # the coordinate system of the field, EPSG:32140 (Texas South Central
        # w/units in meters)
        self.stx_pnt = GEOSGeometry('POINT (-95.370401017314293 29.704867409475465)', 4326)
        # Another one for Australia
        self.au_pnt = GEOSGeometry('POINT (150.791 -34.4919)', 4326)

    def get_names(self, qs):
        cities = [c.name for c in qs]
        cities.sort()
        return cities

    def test_init(self):
        """
        Test initialization of distance models.
        """
        self.assertEqual(9, SouthTexasCity.objects.count())
        self.assertEqual(9, SouthTexasCityFt.objects.count())
        self.assertEqual(11, AustraliaCity.objects.count())
        self.assertEqual(4, SouthTexasZipcode.objects.count())
        self.assertEqual(4, CensusZipcode.objects.count())
        self.assertEqual(1, Interstate.objects.count())
        self.assertEqual(1, SouthTexasInterstate.objects.count())

    @skipUnlessDBFeature("supports_dwithin_lookup")
    def test_dwithin(self):
        """
        Test the `dwithin` lookup type.
        """
        # Distances -- all should be equal (except for the
        # degree/meter pair in au_cities, that's somewhat
        # approximate).
        tx_dists = [(7000, 22965.83), D(km=7), D(mi=4.349)]
        au_dists = [(0.5, 32000), D(km=32), D(mi=19.884)]

        # Expected cities for Australia and Texas.
        tx_cities = ['Downtown Houston', 'Southside Place']
        au_cities = ['Mittagong', 'Shellharbour', 'Thirroul', 'Wollongong']

        # Performing distance queries on two projected coordinate systems one
        # with units in meters and the other in units of U.S. survey feet.
        for dist in tx_dists:
            if isinstance(dist, tuple):
                dist1, dist2 = dist
            else:
                dist1 = dist2 = dist
            qs1 = SouthTexasCity.objects.filter(point__dwithin=(self.stx_pnt, dist1))
            qs2 = SouthTexasCityFt.objects.filter(point__dwithin=(self.stx_pnt, dist2))
            for qs in qs1, qs2:
                with self.subTest(dist=dist, qs=qs):
                    self.assertEqual(tx_cities, self.get_names(qs))

        # With a complex geometry expression
        self.assertFalse(SouthTexasCity.objects.exclude(point__dwithin=(Union('point', 'point'), 0)))

        # Now performing the `dwithin` queries on a geodetic coordinate system.
        for dist in au_dists:
            with self.subTest(dist=dist):
                type_error = isinstance(dist, D) and not oracle
                if isinstance(dist, tuple):
                    if oracle or spatialite:
                        # Result in meters
                        dist = dist[1]
                    else:
                        # Result in units of the field
                        dist = dist[0]

                # Creating the query set.
                qs = AustraliaCity.objects.order_by('name')
                if type_error:
                    # A ValueError should be raised on PostGIS when trying to
                    # pass Distance objects into a DWithin query using a
                    # geodetic field.
                    with self.assertRaises(ValueError):
                        AustraliaCity.objects.filter(point__dwithin=(self.au_pnt, dist)).count()
                else:
                    self.assertEqual(au_cities, self.get_names(qs.filter(point__dwithin=(self.au_pnt, dist))))

    @skipUnlessDBFeature("supports_distances_lookups")
    def test_distance_lookups(self):
        """
        Test the `distance_lt`, `distance_gt`, `distance_lte`, and `distance_gte` lookup types.
        """
        # Retrieving the cities within a 20km 'donut' w/a 7km radius 'hole'
        # (thus, Houston and Southside place will be excluded as tested in
        # the `test02_dwithin` above).
        for model in [SouthTexasCity, SouthTexasCityFt]:
            stx_pnt = self.stx_pnt.transform(model._meta.get_field('point').srid, clone=True)
            qs = model.objects.filter(point__distance_gte=(stx_pnt, D(km=7))).filter(
                point__distance_lte=(stx_pnt, D(km=20)),
            )
            cities = self.get_names(qs)
            self.assertEqual(cities, ['Bellaire', 'Pearland', 'West University Place'])

        # Doing a distance query using Polygons instead of a Point.
        z = SouthTexasZipcode.objects.get(name='77005')
        qs = SouthTexasZipcode.objects.exclude(name='77005').filter(poly__distance_lte=(z.poly, D(m=275)))
        self.assertEqual(['77025', '77401'], self.get_names(qs))
        # If we add a little more distance 77002 should be included.
        qs = SouthTexasZipcode.objects.exclude(name='77005').filter(poly__distance_lte=(z.poly, D(m=300)))
        self.assertEqual(['77002', '77025', '77401'], self.get_names(qs))

    @skipUnlessDBFeature("supports_distances_lookups", "supports_distance_geodetic")
    def test_geodetic_distance_lookups(self):
        """
        Test distance lookups on geodetic coordinate systems.
        """
        # Line is from Canberra to Sydney.  Query is for all other cities within
        # a 100km of that line (which should exclude only Hobart & Adelaide).
        line = GEOSGeometry('LINESTRING(144.9630 -37.8143,151.2607 -33.8870)', 4326)
        dist_qs = AustraliaCity.objects.filter(point__distance_lte=(line, D(km=100)))
        expected_cities = [
            'Batemans Bay', 'Canberra', 'Hillsdale',
            'Melbourne', 'Mittagong', 'Shellharbour',
            'Sydney', 'Thirroul', 'Wollongong',
        ]
        if spatialite:
            # SpatiaLite is less accurate and returns 102.8km for Batemans Bay.
            expected_cities.pop(0)
        self.assertEqual(expected_cities, self.get_names(dist_qs))

        msg = "2, 3, or 4-element tuple required for 'distance_lte' lookup."
        with self.assertRaisesMessage(ValueError, msg):  # Too many params.
            len(AustraliaCity.objects.filter(point__distance_lte=('POINT(5 23)', D(km=100), 'spheroid', '4', None)))

        with self.assertRaisesMessage(ValueError, msg):  # Too few params.
            len(AustraliaCity.objects.filter(point__distance_lte=('POINT(5 23)',)))

        msg = "For 4-element tuples the last argument must be the 'spheroid' directive."
        with self.assertRaisesMessage(ValueError, msg):
            len(AustraliaCity.objects.filter(point__distance_lte=('POINT(5 23)', D(km=100), 'spheroid', '4')))

        # Getting all cities w/in 550 miles of Hobart.
        hobart = AustraliaCity.objects.get(name='Hobart')
        qs = AustraliaCity.objects.exclude(name='Hobart').filter(point__distance_lte=(hobart.point, D(mi=550)))
        cities = self.get_names(qs)
        self.assertEqual(cities, ['Batemans Bay', 'Canberra', 'Melbourne'])

        # Cities that are either really close or really far from Wollongong --
        # and using different units of distance.
        wollongong = AustraliaCity.objects.get(name='Wollongong')
        d1, d2 = D(yd=19500), D(nm=400)  # Yards (~17km) & Nautical miles.

        # Normal geodetic distance lookup (uses `distance_sphere` on PostGIS.
        gq1 = Q(point__distance_lte=(wollongong.point, d1))
        gq2 = Q(point__distance_gte=(wollongong.point, d2))
        qs1 = AustraliaCity.objects.exclude(name='Wollongong').filter(gq1 | gq2)

        # Geodetic distance lookup but telling GeoDjango to use `distance_spheroid`
        # instead (we should get the same results b/c accuracy variance won't matter
        # in this test case).
        querysets = [qs1]
        if connection.features.has_DistanceSpheroid_function:
            gq3 = Q(point__distance_lte=(wollongong.point, d1, 'spheroid'))
            gq4 = Q(point__distance_gte=(wollongong.point, d2, 'spheroid'))
            qs2 = AustraliaCity.objects.exclude(name='Wollongong').filter(gq3 | gq4)
            querysets.append(qs2)

        for qs in querysets:
            cities = self.get_names(qs)
            self.assertEqual(cities, ['Adelaide', 'Hobart', 'Shellharbour', 'Thirroul'])

    @skipUnlessDBFeature("supports_distances_lookups")
    def test_distance_lookups_with_expression_rhs(self):
        stx_pnt = self.stx_pnt.transform(SouthTexasCity._meta.get_field('point').srid, clone=True)
        qs = SouthTexasCity.objects.filter(
            point__distance_lte=(stx_pnt, F('radius')),
        ).order_by('name')
        self.assertEqual(
            self.get_names(qs),
            ['Bellaire', 'Downtown Houston', 'Southside Place', 'West University Place']
        )

        # With a combined expression
        qs = SouthTexasCity.objects.filter(
            point__distance_lte=(stx_pnt, F('radius') * 2),
        ).order_by('name')
        self.assertEqual(len(qs), 5)
        self.assertIn('Pearland', self.get_names(qs))

        # With spheroid param
        if connection.features.supports_distance_geodetic:
            hobart = AustraliaCity.objects.get(name='Hobart')
            qs = AustraliaCity.objects.filter(
                point__distance_lte=(hobart.point, F('radius') * 70, 'spheroid'),
            ).order_by('name')
            self.assertEqual(self.get_names(qs), ['Canberra', 'Hobart', 'Melbourne'])

        # With a complex geometry expression
        self.assertFalse(SouthTexasCity.objects.filter(point__distance_gt=(Union('point', 'point'), 0)))
        self.assertEqual(
            SouthTexasCity.objects.filter(point__distance_lte=(Union('point', 'point'), 0)).count(),
            SouthTexasCity.objects.count(),
        )

    @unittest.skipUnless(mysql, 'This is a MySQL-specific test')
    def test_mysql_geodetic_distance_error(self):
        msg = 'Only numeric values of degree units are allowed on geodetic distance queries.'
        with self.assertRaisesMessage(ValueError, msg):
            AustraliaCity.objects.filter(point__distance_lte=(Point(0, 0), D(m=100))).exists()

    @skipUnlessDBFeature('supports_dwithin_lookup')
    def test_dwithin_subquery(self):
        """dwithin lookup in a subquery using OuterRef as a parameter."""
        qs = CensusZipcode.objects.annotate(
            annotated_value=Exists(SouthTexasCity.objects.filter(
                point__dwithin=(OuterRef('poly'), D(m=10)),
            ))
        ).filter(annotated_value=True)
        self.assertEqual(self.get_names(qs), ['77002', '77025', '77401'])

    @skipUnlessDBFeature('supports_dwithin_lookup', 'supports_dwithin_distance_expr')
    def test_dwithin_with_expression_rhs(self):
        # LineString of Wollongong and Adelaide coords.
        ls = LineString(((150.902, -34.4245), (138.6, -34.9258)), srid=4326)
        qs = AustraliaCity.objects.filter(
            point__dwithin=(ls, F('allowed_distance')),
        ).order_by('name')
        self.assertEqual(
            self.get_names(qs),
            ['Adelaide', 'Mittagong', 'Shellharbour', 'Thirroul', 'Wollongong'],
        )

    @skipIfDBFeature('supports_dwithin_distance_expr')
    def test_dwithin_with_expression_rhs_not_supported(self):
        ls = LineString(((150.902, -34.4245), (138.6, -34.9258)), srid=4326)
        msg = (
            'This backend does not support expressions for specifying '
            'distance in the dwithin lookup.'
        )
        with self.assertRaisesMessage(NotSupportedError, msg):
            list(AustraliaCity.objects.filter(
                point__dwithin=(ls, F('allowed_distance')),
            ))


'''
=============================
Distance functions on PostGIS
=============================

                                              | Projected Geometry | Lon/lat Geometry | Geography (4326)

ST_Distance(geom1, geom2)                     |    OK (meters)     |   :-( (degrees)  |    OK (meters)

ST_Distance(geom1, geom2, use_spheroid=False) |    N/A             |   N/A            |    OK (meters), less accurate, quick

Distance_Sphere(geom1, geom2)                 |    N/A             |   OK (meters)    |    N/A

Distance_Spheroid(geom1, geom2, spheroid)     |    N/A             |   OK (meters)    |    N/A

ST_Perimeter(geom1)                           |    OK              |   :-( (degrees)  |    OK


================================
Distance functions on SpatiaLite
================================

                                                | Projected Geometry | Lon/lat Geometry

ST_Distance(geom1, geom2)                       |    OK (meters)     |      N/A

ST_Distance(geom1, geom2, use_ellipsoid=True)   |    N/A             |      OK (meters)

ST_Distance(geom1, geom2, use_ellipsoid=False)  |    N/A             |      OK (meters), less accurate, quick

Perimeter(geom1)                                |    OK              |      :-( (degrees)

'''  # NOQA


class DistanceFunctionsTests(FuncTestMixin, TestCase):
    fixtures = ['initial']

    @skipUnlessDBFeature("has_Area_function")
    def test_area(self):
        # Reference queries:
        # SELECT ST_Area(poly) FROM distapp_southtexaszipcode;
        area_sq_m = [5437908.90234375, 10183031.4389648, 11254471.0073242, 9881708.91772461]
        # Tolerance has to be lower for Oracle
        tol = 2
        for i, z in enumerate(SouthTexasZipcode.objects.annotate(area=Area('poly')).order_by('name')):
            self.assertAlmostEqual(area_sq_m[i], z.area.sq_m, tol)

    @skipUnlessDBFeature("has_Distance_function")
    def test_distance_simple(self):
        """
        Test a simple distance query, with projected coordinates and without
        transformation.
        """
        lagrange = GEOSGeometry('POINT(805066.295722839 4231496.29461335)', 32140)
        houston = SouthTexasCity.objects.annotate(dist=Distance('point', lagrange)).order_by('id').first()
        tol = 2 if oracle else 5
        self.assertAlmostEqual(
            houston.dist.m,
            147075.069813,
            tol
        )

    @skipUnlessDBFeature("has_Distance_function", "has_Transform_function")
    def test_distance_projected(self):
        """
        Test the `Distance` function on projected coordinate systems.
        """
        # The point for La Grange, TX
        lagrange = GEOSGeometry('POINT(-96.876369 29.905320)', 4326)
        # Reference distances in feet and in meters. Got these values from
        # using the provided raw SQL statements.
        #  SELECT ST_Distance(point, ST_Transform(ST_GeomFromText('POINT(-96.876369 29.905320)', 4326), 32140))
        #  FROM distapp_southtexascity;
        m_distances = [147075.069813, 139630.198056, 140888.552826,
                       138809.684197, 158309.246259, 212183.594374,
                       70870.188967, 165337.758878, 139196.085105]
        #  SELECT ST_Distance(point, ST_Transform(ST_GeomFromText('POINT(-96.876369 29.905320)', 4326), 2278))
        #  FROM distapp_southtexascityft;
        ft_distances = [482528.79154625, 458103.408123001, 462231.860397575,
                        455411.438904354, 519386.252102563, 696139.009211594,
                        232513.278304279, 542445.630586414, 456679.155883207]

        # Testing using different variations of parameters and using models
        # with different projected coordinate systems.
        dist1 = SouthTexasCity.objects.annotate(distance=Distance('point', lagrange)).order_by('id')
        dist2 = SouthTexasCityFt.objects.annotate(distance=Distance('point', lagrange)).order_by('id')
        dist_qs = [dist1, dist2]

        # Original query done on PostGIS, have to adjust AlmostEqual tolerance
        # for Oracle.
        tol = 2 if oracle else 5

        # Ensuring expected distances are returned for each distance queryset.
        for qs in dist_qs:
            for i, c in enumerate(qs):
                with self.subTest(c=c):
                    self.assertAlmostEqual(m_distances[i], c.distance.m, tol)
                    self.assertAlmostEqual(ft_distances[i], c.distance.survey_ft, tol)

    @skipUnlessDBFeature("has_Distance_function", "supports_distance_geodetic")
    def test_distance_geodetic(self):
        """
        Test the `Distance` function on geodetic coordinate systems.
        """
        # Testing geodetic distance calculation with a non-point geometry
        # (a LineString of Wollongong and Shellharbour coords).
        ls = LineString(((150.902, -34.4245), (150.87, -34.5789)), srid=4326)

        # Reference query:
        #  SELECT ST_distance_sphere(point, ST_GeomFromText('LINESTRING(150.9020 -34.4245,150.8700 -34.5789)', 4326))
        #  FROM distapp_australiacity ORDER BY name;
        distances = [1120954.92533513, 140575.720018241, 640396.662906304,
                     60580.9693849269, 972807.955955075, 568451.8357838,
                     40435.4335201384, 0, 68272.3896586844, 12375.0643697706, 0]
        qs = AustraliaCity.objects.annotate(distance=Distance('point', ls)).order_by('name')
        for city, distance in zip(qs, distances):
            with self.subTest(city=city, distance=distance):
                # Testing equivalence to within a meter (kilometer on SpatiaLite).
                tol = -3 if spatialite else 0
                self.assertAlmostEqual(distance, city.distance.m, tol)

    @skipUnlessDBFeature("has_Distance_function", "supports_distance_geodetic")
    def test_distance_geodetic_spheroid(self):
        tol = 2 if oracle else 4

        # Got the reference distances using the raw SQL statements:
        #  SELECT ST_distance_spheroid(point, ST_GeomFromText('POINT(151.231341 -33.952685)', 4326),
        #    'SPHEROID["WGS 84",6378137.0,298.257223563]') FROM distapp_australiacity WHERE (NOT (id = 11));
        #  SELECT ST_distance_sphere(point, ST_GeomFromText('POINT(151.231341 -33.952685)', 4326))
        #  FROM distapp_australiacity WHERE (NOT (id = 11));  st_distance_sphere
        spheroid_distances = [
            60504.0628957201, 77023.9489850262, 49154.8867574404,
            90847.4358768573, 217402.811919332, 709599.234564757,
            640011.483550888, 7772.00667991925, 1047861.78619339,
            1165126.55236034,
        ]
        sphere_distances = [
            60580.9693849267, 77144.0435286473, 49199.4415344719,
            90804.7533823494, 217713.384600405, 709134.127242793,
            639828.157159169, 7786.82949717788, 1049204.06569028,
            1162623.7238134,
        ]
        # Testing with spheroid distances first.
        hillsdale = AustraliaCity.objects.get(name='Hillsdale')
        qs = AustraliaCity.objects.exclude(id=hillsdale.id).annotate(
            distance=Distance('point', hillsdale.point, spheroid=True)
        ).order_by('id')
        for i, c in enumerate(qs):
            with self.subTest(c=c):
                self.assertAlmostEqual(spheroid_distances[i], c.distance.m, tol)
        if postgis or spatialite:
            # PostGIS uses sphere-only distances by default, testing these as well.
            qs = AustraliaCity.objects.exclude(id=hillsdale.id).annotate(
                distance=Distance('point', hillsdale.point)
            ).order_by('id')
            for i, c in enumerate(qs):
                with self.subTest(c=c):
                    self.assertAlmostEqual(sphere_distances[i], c.distance.m, tol)

    @skipIfDBFeature("supports_distance_geodetic")
    @skipUnlessDBFeature("has_Distance_function")
    def test_distance_function_raw_result(self):
        distance = Interstate.objects.annotate(
            d=Distance(Point(0, 0, srid=4326), Point(0, 1, srid=4326)),
        ).first().d
        self.assertEqual(distance, 1)

    @skipUnlessDBFeature("has_Distance_function")
    def test_distance_function_d_lookup(self):
        qs = Interstate.objects.annotate(
            d=Distance(Point(0, 0, srid=3857), Point(0, 1, srid=3857)),
        ).filter(d=D(m=1))
        self.assertTrue(qs.exists())

    @skipUnlessDBFeature('supports_tolerance_parameter')
    def test_distance_function_tolerance_escaping(self):
        qs = Interstate.objects.annotate(
            d=Distance(
                Point(500, 500, srid=3857),
                Point(0, 0, srid=3857),
                tolerance='0.05) = 1 OR 1=1 OR (1+1',
            ),
        ).filter(d=D(m=1)).values('pk')
        msg = 'The tolerance parameter has the wrong type'
        with self.assertRaisesMessage(TypeError, msg):
            qs.exists()

    @skipUnlessDBFeature('supports_tolerance_parameter')
    def test_distance_function_tolerance(self):
        # Tolerance is greater than distance.
        qs = Interstate.objects.annotate(
            d=Distance(
                Point(0, 0, srid=3857),
                Point(1, 1, srid=3857),
                tolerance=1.5,
            ),
        ).filter(d=0).values('pk')
        self.assertIs(qs.exists(), True)

    @skipIfDBFeature("supports_distance_geodetic")
    @skipUnlessDBFeature("has_Distance_function")
    def test_distance_function_raw_result_d_lookup(self):
        qs = Interstate.objects.annotate(
            d=Distance(Point(0, 0, srid=4326), Point(0, 1, srid=4326)),
        ).filter(d=D(m=1))
        msg = 'Distance measure is supplied, but units are unknown for result.'
        with self.assertRaisesMessage(ValueError, msg):
            list(qs)

    @skipUnlessDBFeature("has_Distance_function", 'has_Transform_function')
    def test_distance_transform(self):
        """
        Test the `Distance` function used with `Transform` on a geographic field.
        """
        # We'll be using a Polygon (created by buffering the centroid
        # of 77005 to 100m) -- which aren't allowed in geographic distance
        # queries normally, however our field has been transformed to
        # a non-geographic system.
        z = SouthTexasZipcode.objects.get(name='77005')

        # Reference query:
        # SELECT ST_Distance(ST_Transform("distapp_censuszipcode"."poly", 32140),
        #   ST_GeomFromText('<buffer_wkt>', 32140))
        # FROM "distapp_censuszipcode";
        dists_m = [3553.30384972258, 1243.18391525602, 2186.15439472242]

        # Having our buffer in the SRID of the transformation and of the field
        # -- should get the same results. The first buffer has no need for
        # transformation SQL because it is the same SRID as what was given
        # to `transform()`.  The second buffer will need to be transformed,
        # however.
        buf1 = z.poly.centroid.buffer(100)
        buf2 = buf1.transform(4269, clone=True)
        ref_zips = ['77002', '77025', '77401']

        for buf in [buf1, buf2]:
            qs = CensusZipcode.objects.exclude(name='77005').annotate(
                distance=Distance(Transform('poly', 32140), buf)
            ).order_by('name')
            self.assertEqual(ref_zips, sorted(c.name for c in qs))
            for i, z in enumerate(qs):
                self.assertAlmostEqual(z.distance.m, dists_m[i], 5)

    @skipUnlessDBFeature("has_Distance_function")
    def test_distance_order_by(self):
        qs = SouthTexasCity.objects.annotate(distance=Distance('point', Point(3, 3, srid=32140))).order_by(
            'distance'
        ).values_list('name', flat=True).filter(name__in=('San Antonio', 'Pearland'))
        self.assertSequenceEqual(qs, ['San Antonio', 'Pearland'])

    @skipUnlessDBFeature("has_Length_function")
    def test_length(self):
        """
        Test the `Length` function.
        """
        # Reference query (should use `length_spheroid`).
        # SELECT ST_length_spheroid(ST_GeomFromText('<wkt>', 4326) 'SPHEROID["WGS 84",6378137,298.257223563,
        #   AUTHORITY["EPSG","7030"]]');
        len_m1 = 473504.769553813
        len_m2 = 4617.668

        if connection.features.supports_length_geodetic:
            qs = Interstate.objects.annotate(length=Length('path'))
            tol = 2 if oracle else 3
            self.assertAlmostEqual(len_m1, qs[0].length.m, tol)
            # TODO: test with spheroid argument (True and False)
        else:
            # Does not support geodetic coordinate systems.
            with self.assertRaises(NotSupportedError):
                list(Interstate.objects.annotate(length=Length('path')))

        # Now doing length on a projected coordinate system.
        i10 = SouthTexasInterstate.objects.annotate(length=Length('path')).get(name='I-10')
        self.assertAlmostEqual(len_m2, i10.length.m, 2)
        self.assertTrue(
            SouthTexasInterstate.objects.annotate(length=Length('path')).filter(length__gt=4000).exists()
        )
        # Length with an explicit geometry value.
        qs = Interstate.objects.annotate(length=Length(i10.path))
        self.assertAlmostEqual(qs.first().length.m, len_m2, 2)

    @skipUnlessDBFeature("has_Perimeter_function")
    def test_perimeter(self):
        """
        Test the `Perimeter` function.
        """
        # Reference query:
        # SELECT ST_Perimeter(distapp_southtexaszipcode.poly) FROM distapp_southtexaszipcode;
        perim_m = [18404.3550889361, 15627.2108551001, 20632.5588368978, 17094.5996143697]
        tol = 2 if oracle else 7
        qs = SouthTexasZipcode.objects.annotate(perimeter=Perimeter('poly')).order_by('name')
        for i, z in enumerate(qs):
            self.assertAlmostEqual(perim_m[i], z.perimeter.m, tol)

        # Running on points; should return 0.
        qs = SouthTexasCity.objects.annotate(perim=Perimeter('point'))
        for city in qs:
            self.assertEqual(0, city.perim.m)

    @skipUnlessDBFeature("has_Perimeter_function")
    def test_perimeter_geodetic(self):
        # Currently only Oracle supports calculating the perimeter on geodetic
        # geometries (without being transformed).
        qs1 = CensusZipcode.objects.annotate(perim=Perimeter('poly'))
        if connection.features.supports_perimeter_geodetic:
            self.assertAlmostEqual(qs1[0].perim.m, 18406.3818954314, 3)
        else:
            with self.assertRaises(NotSupportedError):
                list(qs1)
        # But should work fine when transformed to projected coordinates
        qs2 = CensusZipcode.objects.annotate(perim=Perimeter(Transform('poly', 32140))).filter(name='77002')
        self.assertAlmostEqual(qs2[0].perim.m, 18404.355, 3)

    @skipUnlessDBFeature("supports_null_geometries", "has_Area_function", "has_Distance_function")
    def test_measurement_null_fields(self):
        """
        Test the measurement functions on fields with NULL values.
        """
        # Creating SouthTexasZipcode w/NULL value.
        SouthTexasZipcode.objects.create(name='78212')
        # Performing distance/area queries against the NULL PolygonField,
        # and ensuring the result of the operations is None.
        htown = SouthTexasCity.objects.get(name='Downtown Houston')
        z = SouthTexasZipcode.objects.annotate(
            distance=Distance('poly', htown.point), area=Area('poly')
        ).get(name='78212')
        self.assertIsNone(z.distance)
        self.assertIsNone(z.area)