Removed the subdir.

pyrate/tests/plan/geometry/helpers/test_difference.py

@@ -0,0 +1,171 @@
+"""This module asserts correct runtime behaviour of the :mod:`pyrate.plan.geometry.helpers` functions
+for calculating differences.
+"""
+
+# Python standard
+from abc import ABC
+from abc import abstractmethod
+from math import isfinite
+from math import isnan
+import warnings
+
+# Typing
+from typing import Callable
+from typing import Sequence
+from typing import Tuple
+
+# Generic testing
+from unittest import TestCase
+
+# Numeric testing
+from numpy import allclose
+from numpy import array
+
+# Hypothesis testing
+from hypothesis import given
+import hypothesis.strategies as st
+
+# Test helpers
+from pyrate.plan.geometry.helpers import difference_direction
+from pyrate.plan.geometry.helpers import difference_latitude
+from pyrate.plan.geometry.helpers import difference_longitude
+from pyrate.plan.geometry.helpers import ScalarOrArray
+
+
+class TestDifference(TestCase, ABC):
+    """Makes sure the distance measure is well-behaved.
+
+    Keep in mind that it is formally not a metric since the triangle inequality does not hold.
+    """
+
+    @abstractmethod
+    def _get_difference_function(self) -> Callable[[ScalarOrArray, ScalarOrArray], ScalarOrArray]:
+        """Get the function to be tested."""
+
+    @abstractmethod
+    def _get_max(self) -> float:
+        """Get the desired maximum value (inclusive)."""
+
+    @abstractmethod
+    def _get_concrete_examples(self) -> Sequence[Tuple[float, float, float]]:
+        """Get some concrete values to be tested as a sequence of ``(value a, value b, distance between)``."""
+
+    @given(st.floats(), st.floats())
+    def test_distance_measuring_commutes_and_is_in_bounds(self, first: float, second: float) -> None:
+        """Assures flipping the sides when calculating distances does not make a significant difference."""
+
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            distance_1 = self._get_difference_function()(first, second)
+            distance_2 = self._get_difference_function()(second, first)
+
+        if isfinite(distance_1) and isfinite(distance_1):
+            # make sure it commutes
+            self.assertAlmostEqual(distance_1, distance_2)
+
+            # make sure the distance is always positive
+            self.assertGreaterEqual(distance_1, 0.0)
+            self.assertGreaterEqual(distance_2, 0.0)
+
+            # make sure the distance is within bounds
+            self.assertLessEqual(distance_1, self._get_max())
+            self.assertLessEqual(distance_2, self._get_max())
+
+        else:
+            self.assertTrue(isnan(distance_1))
+            self.assertTrue(isnan(distance_2))
+
+    @given(st.floats())
+    def test_distance_measuring_to_itself_is_zero(self, thing: float) -> None:
+        """Assures flipping the sides when calculating distances does not make a significant difference."""
+
+        with warnings.catch_warnings():
+            warnings.simplefilter("ignore")
+            distance = self._get_difference_function()(thing, thing)
+
+        # make sure the distance is always positive and very close to zero
+        if isfinite(distance):
+            self.assertGreaterEqual(distance, 0.0)
+            self.assertAlmostEqual(distance, 0.0)
+        else:
+            self.assertTrue(isnan(distance))
+
+    def test_concrete_examples(self) -> None:
+        """Checks the result for the concrete examples given in :meth:`~_get_concrete_examples`."""
+        function = self._get_difference_function()
+
+        for index, (value_a, value_b, expected_result) in enumerate(self._get_concrete_examples()):
+            with self.subTest(f"example triple #{index}"):
+                self.assertAlmostEqual(function(value_a, value_b), expected_result, delta=1e-12)
+
+    def test_concrete_examples_as_array(self) -> None:
+        """Checks the result for the concrete examples given in :meth:`~_get_concrete_examples`."""
+        function = self._get_difference_function()
+        data = array(self._get_concrete_examples()).T
+        self.assertTrue(allclose(function(data[0, :], data[1, :]), data[2, :]))
+
+
+class TestDifferenceLatitude(TestDifference):
+    """Tests :func:`pyrate.plan.geometry.helpers.difference_latitude`."""
+
+    def _get_difference_function(self) -> Callable[[ScalarOrArray, ScalarOrArray], ScalarOrArray]:
+        return difference_latitude
+
+    def _get_max(self) -> float:
+        return 180.0
+
+    def _get_concrete_examples(self) -> Sequence[Tuple[float, float, float]]:
+        return [
+            (0, 0, 0),
+            (-90, 90, 180),
+            (-89.5, 0, 89.5),
+            (-89.5, 0.5, 90),
+            (-89.5, -0.5, 89),
+            (-45, 45, 90),
+        ]
+
+
+class TestDifferenceLongitude(TestDifference):
+    """Tests :func:`pyrate.plan.geometry.helpers.difference_longitude`."""
+
+    def _get_difference_function(self) -> Callable[[ScalarOrArray, ScalarOrArray], ScalarOrArray]:
+        return difference_longitude
+
+    def _get_max(self) -> float:
+        return 180.0
+
+    def _get_concrete_examples(self) -> Sequence[Tuple[float, float, float]]:
+        return [
+            (0, 0, 0),
+            (-90, 90, 180),
+            (-89.5, 0, 89.5),
+            (-89.5, 0.5, 90),
+            (-89.5, -0.5, 89),
+            (180, -180, 0),
+            (100, -100, 160),
+            (-45, 45, 90),
+        ]
+
+
+class TestDifferenceDirection(TestDifference):
+    """Tests :func:`pyrate.plan.geometry.helpers.difference_direction`."""
+
+    def _get_difference_function(self) -> Callable[[ScalarOrArray, ScalarOrArray], ScalarOrArray]:
+        return difference_direction
+
+    def _get_max(self) -> float:
+        return 180.0
+
+    def _get_concrete_examples(self) -> Sequence[Tuple[float, float, float]]:
+        return [
+            (0, 0, 0),
+            (-90, 90, 180),
+            (0, 360, 0),
+            (10, -10, 20),
+            (10, 350, 20),
+            (370, 20, 10),
+        ]
+
+
+# Do not execute the base class as a test, see https://stackoverflow.com/a/43353680/3753684
+del TestDifference

pyrate/tests/plan/geometry/helpers/test_distance.py

@@ -0,0 +1,62 @@
+"""This module asserts correct runtime behaviour of the :mod:`pyrate.plan.geometry.helpers` functions
+for calculating distances.
+"""
+
+# Python standard library
+from datetime import timedelta
+from math import radians
+
+# Testing
+from unittest import TestCase
+
+# Hypothesis testing
+from hypothesis import given
+from hypothesis import settings
+import hypothesis.strategies as st
+
+# Scientific (testing)
+import numpy.testing
+
+# Module under test
+from pyrate.plan.geometry.helpers import fast_distance_geo
+from pyrate.plan.geometry.helpers import haversine_numpy
+
+# Own geometry
+from pyrate.plan.geometry.geospatial import MEAN_EARTH_CIRCUMFERENCE
+from pyrate.plan.geometry import PolarLocation
+
+# Test helpers
+from pyrate.common.testing.strategies.geometry import geo_bearings
+from pyrate.common.testing.strategies.geometry import polar_locations
+
+
+class TestDistanceCalculation(TestCase):
+    """Tests the geographic helper methods."""
+
+    @given(polar_locations(), polar_locations())
+    def test_haversine_formula(self, location_1: PolarLocation, location_2: PolarLocation) -> None:
+        """Test the correctness of the haversine formula."""
+        dist = haversine_numpy(
+            radians(location_1.latitude),
+            radians(location_1.longitude),
+            radians(location_2.latitude),
+            radians(location_2.longitude),
+        )
+        self.assertLessEqual(dist, MEAN_EARTH_CIRCUMFERENCE / 2)
+        numpy.testing.assert_allclose(location_1.distance(location_2), dist, atol=5.0, rtol=0.01)
+
+    @given(polar_locations(), geo_bearings(), st.floats(min_value=0.0, max_value=250_000.0))
+    @settings(deadline=timedelta(seconds=1.0))
+    # pylint: disable=no-self-use
+    def test_fast_distance_geo(self, center: PolarLocation, direction: float, distance: float) -> None:
+        """Test the correctness of the fast great-circle approximation."""
+
+        other, _ = center.translate(direction, distance)
+
+        distance_calculated = fast_distance_geo(
+            radians(other.latitude),
+            radians(other.longitude),
+            radians(center.latitude),
+            radians(center.longitude),
+        )
+        numpy.testing.assert_allclose(distance, distance_calculated, atol=0.5, rtol=0.05)

pyrate/tests/plan/geometry/helpers/test_normalize.py

@@ -0,0 +1,182 @@
+"""This module asserts correct runtime behaviour of the :mod:`pyrate.plan.geometry.helpers` functions
+for normalization.
+"""
+
+# Python standard
+from abc import ABC
+from abc import abstractmethod
+
+# Typing
+from typing import Callable
+from typing import Sequence
+from typing import Tuple
+
+# Generic testing
+from unittest import TestCase
+
+# Numeric testing
+from numpy import allclose
+from numpy import array
+
+# Hypothesis testing
+from hypothesis import given
+import hypothesis.strategies as st
+
+# Test helpers
+from pyrate.plan.geometry.helpers import normalize_direction
+from pyrate.plan.geometry.helpers import normalize_latitude
+from pyrate.plan.geometry.helpers import normalize_longitude
+from pyrate.plan.geometry.helpers import ScalarOrArray
+
+
+class TestNormalize(TestCase, ABC):
+    """Makes sure the normalizations are well-behaved."""
+
+    @abstractmethod
+    def _get_normalization_function(self) -> Callable[[ScalarOrArray], ScalarOrArray]:
+        """Get the function to be tested."""
+
+    @abstractmethod
+    def _get_min(self) -> float:
+        """Get the desired minimum value (inclusive)."""
+
+    @abstractmethod
+    def _get_max(self) -> float:
+        """Get the desired maximum value, see :meth:`TestNormalize._max_is_inclusive`."""
+
+    def _max_is_inclusive(self) -> bool:  # pylint: disable=no-self-use
+        """If :meth:`TestNormalize._get_max` is to be seen as inclusive or exclusive"""
+        return False
+
+    @abstractmethod
+    def _get_concrete_examples(self) -> Sequence[Tuple[float, float]]:
+        """Get some concrete values to be tested as a sequence of ``(non-normalized, normalized)``."""
+
+    @given(st.floats(allow_infinity=False, allow_nan=False))
+    def test_bounds(self, value: float) -> None:
+        """Assures that the normalized value is within its bounds."""
+
+        normalized = self._get_normalization_function()(value)
+
+        # make sure the normalized value is within bounds
+        self.assertGreaterEqual(normalized, self._get_min())
+
+        if self._max_is_inclusive():
+            self.assertLessEqual(normalized, self._get_max())
+        else:
+            self.assertLess(normalized, self._get_max())
+
+    @given(st.floats(allow_infinity=False, allow_nan=False))
+    def test_normalizing_twice(self, value: float) -> None:
+        """Assures that normalizing twice does not really change the value."""
+
+        normalized = self._get_normalization_function()(value)
+        normalized_twice = self._get_normalization_function()(normalized)
+
+        self.assertAlmostEqual(normalized, normalized_twice, places=10)
+
+    @given(st.floats(min_value=-400, max_value=+400))
+    def test_already_normalized_values(self, value: float) -> None:
+        """Assures that values stay unchanged if and only if are already normalized (i.e. within bounds)."""
+        below_max = value < self._get_max() or (self._max_is_inclusive() and value == self._get_max())
+        if self._get_min() <= value and below_max:
+            self.assertAlmostEqual(self._get_normalization_function()(value), value, delta=1e-12)
+        else:
+            self.assertNotEqual(self._get_normalization_function()(value), value)
+
+    def test_concrete_examples(self) -> None:
+        """Checks the result for the concrete examples given in :meth:`~_get_concrete_examples`."""
+        function = self._get_normalization_function()
+
+        for index, (non_normalized, normalized) in enumerate(self._get_concrete_examples()):
+            with self.subTest(f"example triple #{index}"):
+                self.assertAlmostEqual(function(non_normalized), normalized, delta=1e-12)
+
+    def test_concrete_examples_as_array(self) -> None:
+        """Checks the result for the concrete examples given in :meth:`~_get_concrete_examples`."""
+        function = self._get_normalization_function()
+        data = array(self._get_concrete_examples()).T
+        self.assertTrue(allclose(function(data[0, :]), data[1, :]))
+
+
+class TestNormalizeLatitude(TestNormalize):
+    """Tests :func:`pyrate.plan.geometry.helpers.normalize_latitude`."""
+
+    def _get_normalization_function(self) -> Callable[[ScalarOrArray], ScalarOrArray]:
+        return normalize_latitude
+
+    def _get_min(self) -> float:
+        return -90.0
+
+    def _get_max(self) -> float:
+        return 90.0
+
+    def _max_is_inclusive(self) -> bool:
+        return True
+
+    def _get_concrete_examples(self) -> Sequence[Tuple[float, float]]:
+        return [
+            (0, 0),
+            (90, 90),
+            (-90, -90),
+            (100, 80),
+            (180, 0),
+            (270, -90),
+            (-180, 0),
+            (-270, 90),
+            (-10, -10),
+        ]
+
+
+class TestNormalizeLongitude(TestNormalize):
+    """Tests :func:`pyrate.plan.geometry.helpers.normalize_longitude`."""
+
+    def _get_normalization_function(self) -> Callable[[ScalarOrArray], ScalarOrArray]:
+        return normalize_longitude
+
+    def _get_min(self) -> float:
+        return -180.0
+
+    def _get_max(self) -> float:
+        return 180.0
+
+    def _get_concrete_examples(self) -> Sequence[Tuple[float, float]]:
+        return [
+            (0, 0),
+            (90, 90),
+            (-90, -90),
+            (100, 100),
+            (180, -180),
+            (-180, -180),
+            (270, -90),
+            (-10, -10),
+        ]
+
+
+class TestNormalizeDirection(TestNormalize):
+    """Tests :func:`pyrate.plan.geometry.helpers.normalize_direction`."""
+
+    def _get_normalization_function(self) -> Callable[[ScalarOrArray], ScalarOrArray]:
+        return normalize_direction
+
+    def _get_min(self) -> float:
+        return 0.0
+
+    def _get_max(self) -> float:
+        return 360.0
+
+    def _get_concrete_examples(self) -> Sequence[Tuple[float, float]]:
+        return [
+            (0, 0),
+            (90, 90),
+            (-90, 270),
+            (100, 100),
+            (180, 180),
+            (-180, 180),
+            (270, 270),
+            (-10, 350),
+        ]
+
+
+# Do not execute the base class as a test, see https://stackoverflow.com/a/43353680/3753684
+del TestNormalize

pyrate/tests/plan/geometry/helpers/test_other.py

@@ -0,0 +1,120 @@
+"""This module asserts correct runtime behaviour of various additional helpers."""
+
+# Python Standard Library
+from math import tau
+
+# Generic testing
+from unittest import TestCase
+
+# Hypothesis testing
+import hypothesis.extra.numpy as st_numpy
+from hypothesis import given
+import hypothesis.strategies as st
+
+# Scientific
+import numpy as np
+from numpy.testing import assert_almost_equal
+
+# Module under test
+from pyrate.plan.geometry.helpers import cartesian_to_spherical
+from pyrate.plan.geometry.helpers import difference_latitude
+from pyrate.plan.geometry.helpers import difference_longitude
+from pyrate.plan.geometry.helpers import mean_angle
+from pyrate.plan.geometry.helpers import mean_coordinate
+from pyrate.plan.geometry.helpers import meters2rad
+from pyrate.plan.geometry.helpers import rad2meters
+
+# Own strategies
+from pyrate.common.testing.strategies.geometry import geo_bearings
+
+
+_POSITIVE_FLOATS = st.floats(min_value=0.0, max_value=1e9, allow_infinity=False, allow_nan=False)
+
+
+class TestRadiansAndMeterConversion(TestCase):
+    """Makes sure the conversion between meters and radians works."""
+
+    @given(_POSITIVE_FLOATS)
+    def test_is_reversible_float(self, meters: float) -> None:
+        """Tests that the two functions are the reverse of each other."""
+        self.assertAlmostEqual(meters, rad2meters(meters2rad(meters)), places=5)
+
+    @given(st_numpy.arrays(dtype=float, shape=st_numpy.array_shapes(), elements=_POSITIVE_FLOATS))
+    def test_is_reversible_numpy(self, meters: np.ndarray) -> None:  # pylint: disable=no-self-use
+        """Tests that the two functions are the reverse of each other."""
+        assert_almost_equal(meters, rad2meters(meters2rad(meters)), decimal=5)
+
+
+class TestCartesianToSpherical(TestCase):
+    """Makes sure the conversion from cartesian to spherical coordinates works."""
+
+    def test_raises_if_not_on_unit_sphere(self) -> None:
+        """Asserts that an exception is raised if values are not on the unit sphere."""
+        with self.assertRaises(AssertionError):
+            cartesian_to_spherical(np.array([(10, 20, 30)]))
+
+    def test_specific_values(self) -> None:  # pylint: disable=no-self-use
+        """Asserts that an exception is raised if values are not on the unit sphere."""
+        data_in = np.array([(1, 0, 0), (0, 1, 0), (0, 0, 1), (0.5, 0.5, np.sqrt(1 - 0.5**2 - 0.5**2))])
+        expected_data_out = np.array([(0, 0), (0, np.pi / 2), (-np.pi / 2, 0), (-np.pi / 4, np.pi / 4)]).T
+
+        assert_almost_equal(cartesian_to_spherical(data_in), expected_data_out)
+
+
+class TestAngleAndCoordinateMean(TestCase):
+    """Makes sure the mean computation and angles and coordinates works correctly."""
+
+    @given(geo_bearings(), st.floats(min_value=0.0, max_value=1e-9))
+    def test_raises_if_ambiguous(self, angle: float, noise: float) -> None:
+        """Asserts that an exception is raised if no sensible mean can be calculated."""
+
+        ambiguous_pair = np.array([angle, (angle + 180 + noise) % 360])
+        with self.assertRaises(ValueError):
+            mean_angle(np.radians(ambiguous_pair))
+        with self.assertRaises(ValueError):
+            mean_coordinate(np.array([0.0, 67.2]), ambiguous_pair)
+
+        # But the methods should recover from an exception on the latitude mean computation
+        latitude, _ = mean_coordinate(ambiguous_pair, np.array([0.0, 67.2]))
+        self.assertAlmostEqual(latitude, 0.0)
+
+    @given(
+        st_numpy.arrays(
+            elements=st.floats(min_value=0.0, max_value=np.pi), dtype=float, shape=st_numpy.array_shapes()
+        )
+    )
+    def test_mean_angle_is_in_valid_range(self, data: np.ndarray) -> None:
+        """Asserts that means are never negative and always between ``0°`` and ``360°``."""
+
+        try:
+            mean = mean_angle(data)
+            self.assertGreaterEqual(mean, 0.0)
+            self.assertLessEqual(mean, np.pi)
+
+        except ValueError:
+            pass  # this might happen with the generated values and is okay
+
+    @given(geo_bearings(), st.floats(min_value=0.0, max_value=170))
+    def test_obvious_values_angle(self, angle: float, difference: float) -> None:
+        """Asserts that the result is sensible for known values."""
+
+        mean = mean_angle(np.radians(np.array([angle, (angle + difference) % 360])))
+        self.assertAlmostEqual(mean, np.radians((angle + difference / 2)) % tau, delta=1e-6)
+
+    @given(
+        st.floats(min_value=-80.0, max_value=+80.0),
+        st.floats(min_value=-170.0, max_value=+170.0),
+        st.floats(min_value=-9.0, max_value=9.0),
+        st.floats(min_value=-9.0, max_value=9.0),
+    )
+    def test_obvious_values_coordinate(
+        self, latitude: float, longitude: float, lat_delta: float, lon_delta: float
+    ) -> None:
+        """Asserts that the result is sensible for known values."""
+
+        lat_mean, lon_mean = mean_coordinate(
+            latitudes=np.array([latitude, latitude + lat_delta]),
+            longitudes=np.array([longitude, longitude + lon_delta]),
+        )
+        self.assertLessEqual(difference_latitude(lat_mean, (latitude + lat_delta / 2)), 1e-6)
+        self.assertLessEqual(difference_longitude(lon_mean, (longitude + lon_delta / 2)), 1e-6)

pyrate/tests/plan/geometry/helpers/test_translate.py

@@ -0,0 +1,34 @@
+"""This module asserts correct runtime behaviour of the :mod:`pyrate.plan.geometry.helpers` functions
+for translation.
+
+Note that most of the correctness is asserted by the use in
+:meth:`pyrate.plan.geometry.PolarPolygon.translate` and :meth:`pyrate.plan.geometry.PolarRoute.translate`.
+Also, no extensive tests are needed since we trust the underlying library due to its widespread adoption and
+maturity.
+We only need to check that the conversion of parameters and results works as expcted.
+"""
+
+# Testing
+from unittest import TestCase
+
+# Scientific (testing)
+from numpy import array
+
+# Module under test
+from pyrate.plan.geometry.helpers import translate_numpy
+
+
+class TestTranslate(TestCase):
+    """Tests the translation helpers."""
+
+    COORDINATES = array([[1.0, 2.0], [3.0, -4.0], [-5.0, 6.0]])
+    DIRECTIONS = array([0.0, 90.0, -90.0])
+    DISTANCES = array([1.0, 100.0, 10000.0])
+
+    def test_translate_numpy(self) -> None:  # pylint: disable=no-self-use
+        """Test that any combination of types of input are accepted."""
+
+        translate_numpy(TestTranslate.COORDINATES, TestTranslate.DIRECTIONS, TestTranslate.DISTANCES)
+        translate_numpy(TestTranslate.COORDINATES, 90, TestTranslate.DISTANCES)
+        translate_numpy(TestTranslate.COORDINATES, TestTranslate.DIRECTIONS, 100)
+        translate_numpy(TestTranslate.COORDINATES, 90, 100)

pyrate/tests/plan/geometry/primitives/__init__.py

@@ -0,0 +1,53 @@
+"""This module asserts correct runtime behaviour of the :mod:`pyrate.plan.geometry` primitives for
+locations, polygons and trajectories.
+
+Quite a few tests are marked with ``@settings(max_examples=<some small count>)`` since this test suite makes
+up a very large part of the total testing time and some tests just don't justify wasting many resources on
+them due to very simple code being tested.
+"""
+
+# Python standard math
+from math import isclose
+
+# Typing
+from typing import Union
+
+# Hypothesis testing
+from hypothesis import HealthCheck
+from hypothesis import settings
+
+# Package under test
+from pyrate.plan.geometry import PolarLocation
+from pyrate.plan.geometry import PolarPolygon
+from pyrate.plan.geometry import PolarRoute
+
+
+#: Tests that require the generation of cartesian routes are slow since the generation of examples is slow.
+#: As polar routes, cartesian polygons and polar polygons depend on this, they are also run at reduced rate.
+slow_route_max_examples = settings(
+    max_examples=int(settings().max_examples * 0.1), suppress_health_check=(HealthCheck.too_slow,)
+)
+
+
+#: A test that only tests very few examples since the property to be tested is rather trivial and we do not
+#: want to invest significant amounts of time into it.
+simple_property_only_few_examples = settings(
+    max_examples=int(max(5, settings().max_examples * 0.001)), suppress_health_check=(HealthCheck.too_slow,)
+)
+
+
+def is_near_special_point(polar_location: PolarLocation, tolerance: float = 1e-6) -> bool:
+    """Checks if the given ``polar_location`` is within ``tolerance`` of the poles or +/- 180° longitude."""
+    return (
+        isclose(polar_location.latitude, -90, abs_tol=tolerance)
+        or isclose(polar_location.latitude, +90, abs_tol=tolerance)
+        or isclose(polar_location.longitude, -180, abs_tol=tolerance)
+        or isclose(polar_location.longitude, +180, abs_tol=tolerance)
+    )
+
+
+def is_any_near_special_point(
+    polar_line_object: Union[PolarPolygon, PolarRoute], tolerance: float = 1e-6
+) -> bool:
+    """Checks if any point in in the given geometry ``is_near_special_point`` within the ``tolerance``."""
+    return any(is_near_special_point(location, tolerance) for location in polar_line_object.locations)

pyrate/tests/plan/geometry/primitives/test_common.py

@@ -0,0 +1,44 @@
+"""Tests some general properties of geometries."""
+
+# Generic testing
+from unittest import TestCase
+
+# Scientific testing
+from numpy.testing import assert_array_almost_equal
+
+# Hypothesis testing
+from hypothesis import given
+import hypothesis.strategies as st
+
+# Package under test
+from pyrate.plan.geometry import CartesianGeometry
+
+# Test helpers
+from pyrate.common.testing.strategies.geometry import cartesian_objects
+from pyrate.common.testing.strategies.geometry import geo_bearings
+
+
+class TestCartesianGeometries(TestCase):
+    """Asserts general properties of the cartesian geometries."""
+
+    @given(
+        cartesian_objects(),
+        geo_bearings(),
+        st.floats(min_value=1.0, max_value=100_000.0),
+    )
+    def test_translation_is_invertible(
+        self,
+        original: CartesianGeometry,
+        direction: float,
+        distance: float,
+    ) -> None:
+        """Tests that translation is invertible and a valid backwards vector is returned."""
+
+        # translate & translate back
+        translated, back_vector = original.translate(direction, distance)
+        back_direction = (direction + 180) % 360
+        translated_translated, back_back_vector = translated.translate(back_direction, distance)
+
+        # check the result
+        assert_array_almost_equal(back_vector, -back_back_vector, decimal=9)
+        self.assertTrue(original.equals_exact(translated_translated, tolerance=1e-9))

pyrate/tests/plan/geometry/primitives/test_geospatial.py

@@ -0,0 +1,217 @@
+"""Tests that the geometry base classes in :mod:`pyrate.plan.geometry.geospatial` work correctly."""
+
+# Python standard
+from copy import copy
+from copy import deepcopy
+from json import loads
+
+# Typing
+from typing import Any
+from typing import Sequence
+from typing import Tuple
+
+# Generic testing
+from unittest import TestCase
+
+# Hypothesis testing
+from hypothesis import given
+from hypothesis import HealthCheck
+from hypothesis import Phase
+from hypothesis import settings
+import hypothesis.strategies as st
+
+# Package under test
+from pyrate.plan.geometry import CartesianLocation
+from pyrate.plan.geometry import CartesianPolygon
+from pyrate.plan.geometry import CartesianRoute
+from pyrate.plan.geometry import Direction
+from pyrate.plan.geometry import Geospatial
+from pyrate.plan.geometry import PolarLocation
+from pyrate.plan.geometry import PolarPolygon
+from pyrate.plan.geometry import PolarRoute
+
+# Hypothesis testing
+from pyrate.common.testing.strategies.geometry import geospatial_objects
+
+
+_CARTESIAN_LOCATION_1 = CartesianLocation(5003.0, 139.231)
+_CARTESIAN_LOCATION_2 = CartesianLocation(600.1, 139.231)
+_POLAR_LOCATION_1 = PolarLocation(65.01, -180.0)
+_POLAR_LOCATION_2 = PolarLocation(-80.3, -180.0)
+
+
+class TestStringRepresentations(TestCase):
+    """Makes sure that the string conversion with ``__str__`` and ``__repr__`` works."""
+
+    _GROUND_TRUTH: Sequence[Tuple[Geospatial, str]] = [
+        (
+            _CARTESIAN_LOCATION_1,
+            "CartesianLocation(east=5003.0, north=139.231)",
+        ),
+        (
+            PolarLocation(65.01, -180.0),
+            "PolarLocation(latitude=65.00999999999999, longitude=-180.0)",
+        ),
+        (
+            CartesianPolygon([_CARTESIAN_LOCATION_1, _CARTESIAN_LOCATION_1, _CARTESIAN_LOCATION_1]),
+            "CartesianPolygon(locations=[(5003.0, 139.231), (5003.0, 139.231), (5003.0, 139.231), "
+            "(5003.0, 139.231)])",
+        ),
+        (
+            PolarPolygon([_POLAR_LOCATION_1, _POLAR_LOCATION_1, _POLAR_LOCATION_1]),
+            "PolarPolygon(locations=[PolarLocation(latitude=65.00999999999999, longitude=-180.0), "
+            "PolarLocation(latitude=65.00999999999999, longitude=-180.0), "
+            "PolarLocation(latitude=65.00999999999999, longitude=-180.0)])",
+        ),
+        (
+            CartesianRoute([_CARTESIAN_LOCATION_1, _CARTESIAN_LOCATION_2, _CARTESIAN_LOCATION_1]),
+            "CartesianRoute(locations=[(5003.0, 139.231), (600.1, 139.231), (5003.0, 139.231)])",
+        ),
+        (
+            PolarRoute([_POLAR_LOCATION_1, _POLAR_LOCATION_2, _POLAR_LOCATION_1, _POLAR_LOCATION_1]),
+            "PolarRoute(locations=[PolarLocation(latitude=65.00999999999999, longitude=-180.0), "
+            "PolarLocation(latitude=-80.3, longitude=-180.0), "
+            "PolarLocation(latitude=65.00999999999999, longitude=-180.0), "
+            "PolarLocation(latitude=65.00999999999999, longitude=-180.0)])",
+        ),
+    ]
+
+    def test_conversions(self) -> None:
+        """Makes sure that all given geospatial objects can be converted."""
+
+        for geospatial, desired_str in TestStringRepresentations._GROUND_TRUTH:
+
+            with self.subTest(f"{type(geospatial)}.__str__"):
+                self.assertEqual(str(geospatial), desired_str)
+
+            with self.subTest(f"{type(geospatial)}.__repr__"):
+                self.assertEqual(repr(geospatial), desired_str)
+
+
+class TestGeoJsonRepresentations(TestCase):
+    """Makes sure that the conversion to GeoJSON via the common property ``__geo_interface__`` works."""
+
+    _GROUND_TRUTH: Sequence[Tuple[Geospatial, str]] = [
+        (
+            _CARTESIAN_LOCATION_1,
+            '{"type": "Feature", "geometry": {"type": "Point", '
+            '"coordinates": [5003.0, 139.231]}, "properties": {}}',
+        ),
+        (
+            PolarLocation(65.01, -180.0),
+            '{"type": "Feature", "geometry": {"type": "Point", "coordinates": [-180.0, 65.01]}, '
+            '"properties": {}}',
+        ),
+        (
+            CartesianPolygon([_CARTESIAN_LOCATION_1, _CARTESIAN_LOCATION_1, _CARTESIAN_LOCATION_1]),
+            '{"type": "Feature", "geometry": {"type": "Polygon", "coordinates": '
+            "[[[5003.0, 139.231], [5003.0, 139.231], [5003.0, 139.231], [5003.0, 139.231]]]}, "
+            '"properties": {}}',
+        ),
+        (
+            PolarPolygon([_POLAR_LOCATION_1, _POLAR_LOCATION_1, _POLAR_LOCATION_1]),
+            '{"type": "Feature", "geometry": {"type": "Polygon", '
+            '"coordinates": [[[-180.0, 65.01], [-180.0, 65.01], [-180.0, 65.01]]]}, "properties": {}}',
+        ),
+        (
+            CartesianRoute([_CARTESIAN_LOCATION_1, _CARTESIAN_LOCATION_2, _CARTESIAN_LOCATION_1]),
+            '{"type": "Feature", "geometry": {"type": "LineString", "coordinates": '
+            '[[5003.0, 139.231], [600.1, 139.231], [5003.0, 139.231]]}, "properties": {}}',
+        ),
+        (
+            PolarRoute([_POLAR_LOCATION_1, _POLAR_LOCATION_2, _POLAR_LOCATION_1]),
+            '{"type": "Feature", "geometry": {"type": "LineString", "coordinates": '
+            '[[-180.0, 65.01], [-180.0, -80.3], [-180.0, 65.01]]}, "properties": {}}',
+        ),
+    ]
+
+    def test_conversions(self) -> None:
+        """Makes sure that all given geospatial objects can be converted."""
+
+        for geospatial, desired_geojson in TestGeoJsonRepresentations._GROUND_TRUTH:
+            for indent in (None, 1, 8):
+                with self.subTest(f"{type(geospatial)} with indent={indent}"):
+                    geojson = geospatial.to_geo_json(indent=indent)
+                    # load as JSON get get better error messages and become whitespace independent
+                    self.assertDictEqual(loads(geojson), loads(desired_geojson))
+
+
+class TestIdentifiers(TestCase):
+    """Makes sure that identifiers are validated correctly.
+
+    The test is only performed on polar locations for simplicity and because validation is handled in the
+    abstract common parent class :class:`pyrate.plan.geometry.Geospatial` anyway.
+    """
+
+    @given(st.integers(min_value=0, max_value=(2**63) - 1))
+    def test_on_locations_success(self, integer: int) -> None:  # pylint: disable=no-self-use
+        """Tests that valid identifiers are accepted."""
+        PolarLocation(latitude=0.0, longitude=0.0, identifier=integer)
+
+    @given(
+        st.one_of(
+            st.integers(max_value=-1),  # negative numbers
+            st.integers(min_value=2**63),  # very large numbers
+        )
+    )
+    def test_on_locations_rejected(self, integer: int) -> None:
+        """Tests that invalid identifiers are rejected."""
+        with self.assertRaises(AssertionError):
+            PolarLocation(latitude=0.0, longitude=0.0, identifier=integer)
+
+
+class TestEqualityMethods(TestCase):
+    """Test the various equality methods."""
+
+    @given(geospatial_objects(stable=True))
+    @settings(
+        max_examples=200,
+        suppress_health_check=(HealthCheck.data_too_large,),
+        phases=(Phase.explicit, Phase.reuse, Phase.generate, Phase.target),  # Do not shrink as it takes long
+    )
+    def test_equality_after_translation(self, geospatial: Any) -> None:
+        """Tests that translated objects are only equal under sufficient tolerance."""
+
+        # We discard the second output since it differs between cartesian and polar objects
+        translated, _ = geospatial.translate(direction=Direction.North, distance=0.5)
+
+        # Try since generated primitives might cause an exception to be thrown
+        # e.g. if projected routes become length 0
+        try:
+            # They should not be equal
+            self.assertNotEqual(geospatial, translated)
+            self.assertFalse(geospatial.equals(translated))
+            self.assertFalse(geospatial.equals_exact(translated, tolerance=0.0))
+            if hasattr(geospatial, "equals_almost_congruent"):
+                self.assertFalse(
+                    geospatial.equals_almost_congruent(translated, abs_tolerance=0.0, rel_tolerance=0.0)
+                )
+
+            # They should be equal within some tolerance (the tolerance needs to be large for the polar
+            # variants)
+            # TODO(Someone): re-enable; see #114
+            # self.assertTrue(geospatial.equals_exact(translated, tolerance=5))
+            # self.assertTrue(geospatial.almost_equals(translated, decimal=-1))
+
+            # We do not use `equals_almost_congruent` as it is not a per-coordinate difference and might cause
+            # a very large symmetric difference on very large objects
+
+        except ValueError:
+            pass
+
+
+class TestCopyAndDeepcopy(TestCase):
+    """Tests that all geometric objects can be deep-copied."""
+
+    @given(geospatial_objects())
+    @settings(max_examples=500)
+    def test_is_copyable(self, geospatial: Any) -> None:
+        """Tests that copies can be made and are equal to the original."""
+
+        # Check copy
+        copied = copy(geospatial)
+        self.assertEqual(geospatial, copied)
+
+        # Check deepcopy
+        deep_copied = deepcopy(geospatial)
+        self.assertEqual(geospatial, deep_copied)

pyrate/tests/plan/geometry/primitives/test_locations.py

@@ -0,0 +1,173 @@
+"""Tests that the location classes in :mod:`pyrate.plan.geometry.location` work correctly."""
+
+# Python standard math
+from math import isclose
+
+# Typing
+from typing import cast
+
+# Generic testing
+from unittest import TestCase
+
+# Geometry
+from shapely.geometry import Point
+
+# Hypothesis testing
+from hypothesis import given
+from hypothesis import HealthCheck
+from hypothesis import settings
+import hypothesis.strategies as st
+
+# Package under test
+from pyrate.plan.geometry import CartesianLocation
+from pyrate.plan.geometry import PolarLocation
+
+# Test helpers
+from pyrate.common.testing.strategies.geometry import cartesian_locations
+from pyrate.common.testing.strategies.geometry import geo_bearings
+from pyrate.common.testing.strategies.geometry import polar_locations
+
+# Local test helpers
+from . import is_near_special_point
+from . import simple_property_only_few_examples
+
+
+class TestLocationConversion(TestCase):
+    """Test for correct runtime behaviour in :mod:`pyrate.plan` location and shape primitives."""
+
+    @given(cartesian_locations(origin=polar_locations()))
+    @settings(max_examples=20, suppress_health_check=(HealthCheck.data_too_large,))  # this is a slow test
+    def test_projection_and_back_projection_origin_in_route(
+        self, cartesian_location: CartesianLocation
+    ) -> None:
+        """Test the projection with an origin already being present in the geometry."""
+        recreated = cartesian_location.to_polar().to_cartesian(cast(PolarLocation, cartesian_location.origin))
+        self.assertTrue(recreated.equals_exact(recreated, tolerance=1e-6))
+
+    @given(cartesian_locations(origin=st.none()), polar_locations())
+    @simple_property_only_few_examples  # this only checks very simple additional logic
+    def test_projection_and_back_projection_origin_given_extra(
+        self, cartesian_location: CartesianLocation, origin: PolarLocation
+    ) -> None:
+        """Test the projection with an origin being provided."""
+        recreated = cartesian_location.to_polar(origin).to_cartesian(origin)
+        self.assertTrue(recreated.equals_exact(recreated, tolerance=1e-6))
+
+    @given(cartesian_locations(origin=st.none()))
+    @simple_property_only_few_examples  # this only checks very simple additional logic
+    def test_projection_and_back_projection_origin_not_given(
+        self, cartesian_location: CartesianLocation
+    ) -> None:
+        """Test the projection with no origin being given."""
+        with self.assertRaises(ValueError):
+            cartesian_location.to_polar()
+
+    @given(cartesian_locations(origin=polar_locations()), polar_locations())
+    @simple_property_only_few_examples  # this only checks very simple additional logic
+    def test_projection_and_back_projection_origin_given_twice(
+        self, cartesian_location: CartesianLocation, origin: PolarLocation
+    ) -> None:
+        """Test the projection with ambiguous origin being provided."""
+        with self.assertRaises(ValueError):
+            cartesian_location.to_polar(origin)
+
+    def test_distance_measuring_specific(self) -> None:
+        """Tests a specific input/output pair."""
+
+        location_a = PolarLocation(latitude=55.6544, longitude=139.74477)
+        location_b = PolarLocation(latitude=21.4225, longitude=39.8261)
+        distance = location_a.distance(location_b, approximate=False)
+        self.assertAlmostEqual(distance, 8_665_850.116876071)
+
+    @given(
+        polar_locations(),
+        geo_bearings(),
+        st.floats(min_value=1.0, max_value=100_000.0, allow_nan=False, allow_infinity=False),
+    )
+    def test_translation_is_invertible(
+        self, original: PolarLocation, direction: float, distance: float
+    ) -> None:
+        """Tests that translation is invertible and a valid bearing is returned.
+
+        Warning:
+            Only tests in-depth in the case where latitudes and longitudes are not near the poles.
+        """
+
+        # translate
+        translated, back_direction = original.translate(direction, distance)
+        self.assertGreaterEqual(back_direction, 0.0)
+        self.assertLess(back_direction, 360.0)
+
+        # translate back
+        translated_translated, back_back_direction = translated.translate(back_direction, distance)
+        self.assertGreaterEqual(back_back_direction, 0.0)
+        self.assertLess(back_back_direction, 360.0)
+
+        # the method seems to have problems at poles
+        if not is_near_special_point(original) and not is_near_special_point(translated):
+            # the method is rather rough, so we want to add larger tolerances than usual while checking
+            self.assertTrue(isclose(direction, back_back_direction, abs_tol=1e-6))
+            self.assertTrue(original.equals_exact(translated_translated, 1e-6))
+
+    @given(cartesian_locations())
+    def test_from_shapely_conversion(self, cartesian_location: CartesianLocation) -> None:
+        """Test that :meth:`pyrate.plan.geometry.location.CartesianLocation.from_shapely` works."""
+
+        # we only want to compare the coordinates, so create a new instance without the identifier, name, etc.
+        bare = CartesianLocation(cartesian_location.x, cartesian_location.y)
+        bare_shapely = Point(cartesian_location.x, cartesian_location.y)
+        recreated = CartesianLocation.from_shapely(bare_shapely)
+        self.assertEqual(recreated, bare)
+
+
+class TestPolarLocationDistanceIsAMetric(TestCase):
+    """Makes sure that :meth:`~pyrate.plan.geometry.location.PolarLocation.distance` is a metric.
+
+    This should always succeed since we use a very stable external library for this.
+
+    See `Wikipedia <https://en.wikipedia.org/wiki/Metric_(mathematics)#Definition>`__ for the axioms.
+    """
+
+    @given(polar_locations(), polar_locations(), st.booleans())
+    def test_distance_measuring_commutes_and_sanity_checks(
+        self, location_a: PolarLocation, location_b: PolarLocation, approximate: bool
+    ) -> None:
+        """Assures flipping the sides when calculating distances does not make a significant difference."""
+
+        distance_1 = location_a.distance(location_b, approximate)
+        distance_2 = location_b.distance(location_a, approximate)
+
+        # make sure it commutes
+        self.assertAlmostEqual(distance_1, distance_2)
+
+        # make sure the distance is always positive
+        self.assertGreaterEqual(distance_1, 0.0)
+        self.assertGreaterEqual(distance_2, 0.0)
+
+    @given(polar_locations(), polar_locations(), polar_locations(), st.booleans())
+    def test_distance_measuring_triangle_inequality(
+        self,
+        location_a: PolarLocation,
+        location_b: PolarLocation,
+        location_c: PolarLocation,
+        approximate: bool,
+    ) -> None:
+        """Assures flipping the sides when calculating distances does not make a significant difference."""
+
+        distance_a_b = location_a.distance(location_b, approximate)
+        distance_b_c = location_b.distance(location_c, approximate)
+        distance_a_c = location_a.distance(location_c, approximate)
+
+        # allow for floating point errors
+        abs_tolerance = 1e-6  # 1 micro meter
+        self.assertGreaterEqual(distance_a_b + distance_b_c + abs_tolerance, distance_a_c)
+
+    @given(polar_locations(), st.booleans())
+    def test_distance_measuring_to_itself_is_zero(self, location: PolarLocation, approximate: bool) -> None:
+        """Assures flipping the sides when calculating distances does not make a significant difference."""
+
+        distance = location.distance(location, approximate)
+
+        # make sure the distance is always positive and very close to zero
+        self.assertGreaterEqual(distance, 0.0)
+        self.assertAlmostEqual(distance, 0.0)

pyrate/tests/plan/geometry/primitives/test_polygons.py

@@ -0,0 +1,266 @@
+"""Tests that the polygon classes in :mod:`pyrate.plan.geometry.polygon` work correctly."""
+
+# Python standard math
+from math import sqrt
+
+# Typing
+from typing import cast
+
+# Generic testing
+from unittest import TestCase
+
+# Geometry
+from shapely.geometry import Polygon
+
+# Scientific
+from numpy import array
+
+# Scientific testing
+from numpy.testing import assert_array_less
+
+# Hypothesis testing
+from hypothesis import given
+import hypothesis.strategies as st
+
+# Package under test
+from pyrate.plan.geometry import CartesianPolygon
+from pyrate.plan.geometry import LocationType
+from pyrate.plan.geometry import PolarLocation
+from pyrate.plan.geometry import PolarPolygon
+
+# Test helpers
+from pyrate.common.testing.strategies.geometry import cartesian_polygons
+from pyrate.common.testing.strategies.geometry import geo_bearings
+from pyrate.common.testing.strategies.geometry import polar_locations
+from pyrate.common.testing.strategies.geometry import polar_polygons
+
+# Local test helpers
+from . import is_any_near_special_point
+from . import simple_property_only_few_examples
+from . import slow_route_max_examples
+
+
+class TestPolarPolygons(TestCase):
+    """Asserts general properties of the polar polygons."""
+
+    @given(polar_polygons())
+    @slow_route_max_examples
+    def test_area_is_non_negative(self, polar_polygon: PolarPolygon) -> None:
+        """Tests that all areas are non-negative."""
+        self.assertGreaterEqual(polar_polygon.area, 0, "areas must be non-negative")
+
+    @given(polar_polygons())
+    @slow_route_max_examples
+    def test_is_valid(self, polygon: PolarPolygon) -> None:
+        """Test that the generated polygons are valid."""
+
+        self.assertTrue(polygon.is_valid)
+
+    def test_is_not_valid(self) -> None:
+        """Test that a known invalid polygon is detected as such."""
+
+        location = PolarLocation(12, 23.999)
+        polygon = PolarPolygon([location, location, location])
+        self.assertFalse(polygon.is_valid)
+
+    @given(polar_polygons(), polar_locations(), st.booleans())
+    @slow_route_max_examples
+    def test_distance_to_vertices_is_non_negative(
+        self, polar_polygon: PolarPolygon, polar_location: PolarLocation, approximate: bool
+    ) -> None:
+        """Tests that all distances to vertices are non-negative."""
+        distance = polar_polygon.distance_to_vertices(polar_location, approximate)
+        self.assertGreaterEqual(distance, 0, "distances must be non-negative")
+
+    @given(polar_polygons(max_vertices=50))
+    @slow_route_max_examples
+    def test_simplification(self, original: PolarPolygon) -> None:
+        """Checks the the area change is valid and the rough position is preserved."""
+
+        simplified = original.simplify(tolerance=sqrt(original.area) / 10)
+
+        self.assertLessEqual(len(simplified.locations), len(original.locations))
+        self.assertTrue(original.almost_congruent(simplified, rel_tolerance=0.3))
+
+    @given(polar_polygons())
+    @slow_route_max_examples
+    def test_simplification_artificial(self, original: PolarPolygon) -> None:
+        """This duplicates the first point and looks whether it is removed."""
+
+        locations = original.locations
+        original.locations = [locations[0]] + locations
+
+        simplified = original.simplify(tolerance=sqrt(original.area) / 1000)
+
+        # strictly less, as opposed to test_simplification()
+        self.assertLess(len(simplified.locations), len(original.locations))
+        self.assertTrue(original.almost_congruent(simplified, rel_tolerance=0.05))
+
+    @given(polar_polygons())
+    @simple_property_only_few_examples  # this only checks the call signatures so no need for many examples
+    def test_numpy_conversion_invertible(self, polar_polygon: PolarPolygon) -> None:
+        """Tests that the polygon conversion can be inverted."""
+        recreated = PolarPolygon.from_numpy(
+            polar_polygon.to_numpy(),
+            name=polar_polygon.name,
+            location_type=polar_polygon.location_type,
+            identifier=polar_polygon.identifier,
+        )
+        self.assertEqual(polar_polygon, recreated)
+
+    @given(
+        st.sampled_from(
+            [
+                PolarPolygon(
+                    locations=[
+                        PolarLocation(latitude=-76.40057132099628, longitude=-171.92454675519284),
+                        PolarLocation(latitude=-76.40057132099628, longitude=-171.92454675519284),
+                        PolarLocation(latitude=-76.40057132099628, longitude=-171.92454675519284),
+                    ],
+                    name="K",
+                ),
+                PolarPolygon(
+                    locations=[
+                        PolarLocation(latitude=-33.68964326163993, longitude=89.95053943144632),
+                        PolarLocation(latitude=-33.68964326163993, longitude=89.95053943144632),
+                        PolarLocation(latitude=-33.68964326163993, longitude=89.95053943144632),
+                        PolarLocation(latitude=-33.68964326163993, longitude=89.95053943144632),
+                        PolarLocation(latitude=-33.68964326163993, longitude=89.95053943144632),
+                        PolarLocation(latitude=-33.68964326163993, longitude=89.95053943144632),
+                        PolarLocation(latitude=-33.68964326163993, longitude=89.95053943144632),
+                    ],
+                    location_type=LocationType.TESTING,
+                    name="_1",
+                ),
+                PolarPolygon(
+                    locations=[
+                        PolarLocation(latitude=0.0, longitude=0.029771743643124182),
+                        PolarLocation(latitude=0.0, longitude=0.029771743643124182),
+                        PolarLocation(latitude=0.0, longitude=0.029771743643124182),
+                        PolarLocation(latitude=0.0, longitude=0.029771743643124182),
+                    ],
+                    name="",
+                ),
+            ]
+        ),
+        geo_bearings(),
+        st.floats(min_value=1.0, max_value=100_000.0, allow_nan=False, allow_infinity=False),
+    )
+    def test_translation_is_invertible(
+        self, original: PolarPolygon, direction: float, distance: float
+    ) -> None:
+        """Tests that translation is invertible and a valid bearing is returned.
+
+        Warning:
+            Only tests in-depth in the case where latitudes and longitudes are not near the poles.
+            Since the tests are quite flaky due to the underling library, we only test specific polygons.
+        """
+        # translate
+        translated, back_direction = original.translate(direction, distance)
+        assert_array_less(0.0 - 1e-12, back_direction)
+        assert_array_less(back_direction, 360.0 + 1e-12)
+
+        # translate back
+        translated_translated, back_back_direction = translated.translate(back_direction[0], distance)
+        assert_array_less(0.0 - 1e-12, back_back_direction)
+        assert_array_less(back_back_direction, 360.0 + 1e-12)
+
+        # the method seems to have problems at poles
+        if not is_any_near_special_point(original) and not is_any_near_special_point(translated):
+            # the method is rather rough, so we want to add larger tolerances than usual while checking
+            self.assertAlmostEqual(direction, back_back_direction[0], delta=0.1)
+            self.assertTrue(original.equals_exact(translated_translated, tolerance=0.1))
+
+    def test_non_finite_from_numpy_raises(self) -> None:
+        """Tests that invalid parameter to :meth:`~PolarPolygon.from_numpy` warn about it."""
+
+        with self.assertRaises(AssertionError):
+            PolarPolygon.from_numpy(array([(1, 2), (2, 4), (4, float("NaN"))]))
+        with self.assertRaises(AssertionError):
+            PolarPolygon.from_numpy(array([(float("Inf"), 2), (2, 4), (4, 1)]))
+        with self.assertRaises(AssertionError):
+            PolarPolygon.from_numpy(array([(1, 2), (2, float("-Inf")), (4, 4)]))
+
+
+class TestCartesianPolygons(TestCase):
+    """Asserts general properties of the cartesian polygons."""
+
+    @given(cartesian_polygons())
+    @simple_property_only_few_examples  # this only checks the call signatures so no need for many examples
+    def test_numpy_conversion_invertible(self, cartesian_polygon: CartesianPolygon) -> None:
+        """Tests that the polygon conversion can be inverted."""
+        recreated = CartesianPolygon.from_numpy(
+            cartesian_polygon.to_numpy(),
+            origin=cartesian_polygon.origin,
+            name=cartesian_polygon.name,
+            location_type=cartesian_polygon.location_type,
+            identifier=cartesian_polygon.identifier,
+        )
+
+        self.assertEqual(cartesian_polygon, recreated)
+
+    @given(cartesian_polygons(origin=polar_locations()))
+    @slow_route_max_examples
+    def test_projection_and_back_projection_origin_in_route(
+        self, cartesian_polygon: CartesianPolygon
+    ) -> None:
+        """Test the projection with an origin already being present in the geometry."""
+        recreated = cartesian_polygon.to_polar().to_cartesian(cast(PolarLocation, cartesian_polygon.origin))
+        self.assertTrue(recreated.equals_exact(recreated, tolerance=1e-6))
+
+    @given(cartesian_polygons(origin=st.none()), polar_locations())
+    @simple_property_only_few_examples  # this only checks very simple additional logic
+    def test_projection_and_back_projection_origin_given_extra(
+        self, cartesian_polygon: CartesianPolygon, origin: PolarLocation
+    ) -> None:
+        """Test the projection with an origin being provided."""
+        recreated = cartesian_polygon.to_polar(origin).to_cartesian(origin)
+        self.assertTrue(recreated.equals_exact(recreated, tolerance=1e-6))
+
+    @given(cartesian_polygons(origin=st.none()))
+    @simple_property_only_few_examples  # this only checks very simple additional logic
+    def test_projection_and_back_projection_origin_not_given(
+        self, cartesian_polygon: CartesianPolygon
+    ) -> None:
+        """Test the projection with no origin being given."""
+        with self.assertRaises(ValueError):
+            cartesian_polygon.to_polar()
+
+    @given(cartesian_polygons(origin=polar_locations()), polar_locations())
+    @simple_property_only_few_examples  # this only checks very simple additional logic
+    def test_projection_and_back_projection_origin_given_twice(
+        self, cartesian_polygon: CartesianPolygon, origin: PolarLocation
+    ) -> None:
+        """Test the projection with ambiguous origin being provided."""
+        with self.assertRaises(ValueError):
+            cartesian_polygon.to_polar(origin)
+
+    @given(cartesian_polygons())
+    @slow_route_max_examples
+    def test_locations_property_attributes(self, cartesian_polygon: CartesianPolygon) -> None:
+        """Test that all contained locations share the same attributes."""
+        for location in cartesian_polygon.locations:
+            self.assertEqual(location.location_type, cartesian_polygon.location_type)
+            self.assertEqual(location.name, cartesian_polygon.name)
+            self.assertEqual(location.identifier, cartesian_polygon.identifier)
+            self.assertEqual(location.origin, cartesian_polygon.origin)
+
+    @given(cartesian_polygons())
+    @slow_route_max_examples
+    def test_from_shapely_conversion(self, cartesian_polygon: CartesianPolygon) -> None:
+        """Test that :meth:`pyrate.plan.geometry.polygon.CartesianPolygon.from_shapely` works."""
+        # we only want to compare the coordinates, so create a new instance without the identifier, name, etc.
+        bare = CartesianPolygon.from_numpy(cartesian_polygon.to_numpy())
+        bare_shapely = Polygon(cartesian_polygon.to_numpy())
+        recreated = CartesianPolygon.from_shapely(bare_shapely)
+        self.assertEqual(recreated, bare)
+
+    def test_non_finite_from_numpy_raises(self) -> None:
+        """Tests that invalid parameter to :meth:`~CartesianPolygon.from_numpy` warn about it."""
+
+        with self.assertRaises(AssertionError):
+            CartesianPolygon.from_numpy(array([(1, 2), (2, 4), (4, float("NaN"))]))
+        with self.assertRaises(AssertionError):
+            CartesianPolygon.from_numpy(array([(float("Inf"), 2), (2, 4), (4, 1)]))
+        with self.assertRaises(AssertionError):
+            CartesianPolygon.from_numpy(array([(1, 2), (2, float("-Inf")), (4, 4)]))

pyrate/tests/plan/geometry/primitives/test_routes.py

@@ -0,0 +1,266 @@
+"""Tests that the route classes in :mod:`pyrate.plan.geometry.route` work correctly."""
+
+# Typing
+from typing import cast
+
+# Generic testing
+from unittest import TestCase
+
+# Geometry
+from shapely.geometry import LineString
+
+# Scientific
+from numpy import array
+
+# Scientific testing
+from numpy.testing import assert_array_less
+
+# Hypothesis testing
+from hypothesis import given
+import hypothesis.strategies as st
+
+# Package under test
+from pyrate.plan.geometry import CartesianLocation
+from pyrate.plan.geometry import CartesianRoute
+from pyrate.plan.geometry import LocationType
+from pyrate.plan.geometry import PolarLocation
+from pyrate.plan.geometry import PolarRoute
+
+# Test helpers
+from pyrate.common.testing.strategies.geometry import cartesian_routes
+from pyrate.common.testing.strategies.geometry import geo_bearings
+from pyrate.common.testing.strategies.geometry import polar_locations
+from pyrate.common.testing.strategies.geometry import polar_routes
+
+# Local test helpers
+from . import is_any_near_special_point
+from . import simple_property_only_few_examples
+from . import slow_route_max_examples
+
+
+class TestPolarRoutes(TestCase):
+    """Asserts general properties of the polar routes."""
+
+    @given(polar_routes())
+    @simple_property_only_few_examples  # this only checks the call signatures so no need for many examples
+    def test_numpy_conversion_invertible(self, polar_route: PolarRoute) -> None:
+        """Tests that the route conversion can be inverted."""
+        recreated = PolarRoute.from_numpy(
+            polar_route.to_numpy(),
+            name=polar_route.name,
+            location_type=polar_route.location_type,
+            identifier=polar_route.identifier,
+        )
+        self.assertEqual(polar_route, recreated)
+
+    @given(polar_routes(), polar_locations(), st.booleans())
+    @slow_route_max_examples
+    def test_distance_to_vertices_is_non_negative(
+        self, polar_route: PolarRoute, polar_location: PolarLocation, approximate: bool
+    ) -> None:
+        """Tests that all distances to vertices are non-negative."""
+        distance = polar_route.distance_to_vertices(polar_location, approximate)
+        self.assertGreaterEqual(distance, 0, "distances must be non-negative")
+
+    @given(polar_routes())
+    @slow_route_max_examples
+    def test_length_is_non_negative(self, polar_route: PolarRoute) -> None:
+        """Tests that the length of a route is always non-negative."""
+        self.assertGreaterEqual(polar_route.length(), 0, "lengths must be non-negative")
+
+    @given(polar_routes(min_vertices=3, max_vertices=3))
+    @slow_route_max_examples
+    def test_length_values(self, polar_route: PolarRoute) -> None:
+        """Tests that the length of a route with three locations is plausible."""
+        location_a, location_b, location_c = polar_route.locations
+        distance = location_a.distance(location_b) + location_b.distance(location_c)
+        self.assertAlmostEqual(polar_route.length(), distance, msg="lengths must be non-negative")
+
+    @given(
+        st.sampled_from(
+            [
+                PolarRoute(
+                    locations=[
+                        PolarLocation(latitude=-76.40057132099628, longitude=-171.92454675519284),
+                        PolarLocation(latitude=-76, longitude=-171),
+                    ],
+                    name="K",
+                ),
+                PolarRoute(
+                    locations=[
+                        PolarLocation(latitude=-33.68964326163993, longitude=89.95053943144632),
+                        PolarLocation(latitude=-33, longitude=89),
+                        PolarLocation(latitude=-33.68964326163993, longitude=89.95053943144632),
+                        PolarLocation(latitude=-33.68964326163993, longitude=89.95053943144632),
+                        PolarLocation(latitude=-33.68964326163993, longitude=89.95053943144632),
+                    ],
+                    location_type=LocationType.TESTING,
+                    name="_1",
+                ),
+                PolarRoute(
+                    locations=[
+                        PolarLocation(latitude=0.0, longitude=0.029771743643124182),
+                        PolarLocation(latitude=0.0, longitude=0.0),
+                        PolarLocation(latitude=0.0, longitude=0.029771743643124182),
+                        PolarLocation(latitude=0.0, longitude=0.029771743643124182),
+                    ],
+                    name="",
+                ),
+            ]
+        ),
+        geo_bearings(),
+        st.floats(min_value=1.0, max_value=100_000.0),
+    )
+    def test_translation_is_invertible(self, original: PolarRoute, direction: float, distance: float) -> None:
+        """Tests that translation is invertible and a valid bearing is returned.
+
+        Warning:
+            Only tests in-depth in the case where latitudes and longitudes are not near the poles.
+            Since the tests are quite flaky due to the underling library, we only test specific routes.
+        """
+
+        # translate
+        translated, back_direction = original.translate(direction, distance)
+        assert_array_less(0.0 - 1e-12, back_direction)
+        assert_array_less(back_direction, 360.0 + 1e-12)
+
+        # translate back
+        translated_translated, back_back_direction = translated.translate(back_direction[0], distance)
+        assert_array_less(0.0 - 1e-12, back_back_direction)
+        assert_array_less(back_back_direction, 360.0 + 1e-12)
+
+        # the method seems to have problems at poles
+        if not is_any_near_special_point(original) and not is_any_near_special_point(translated):
+            # the method is rather rough, so we want to add larger tolerances than usual while checking
+            self.assertAlmostEqual(direction, back_back_direction[0], delta=0.1)
+            self.assertTrue(original.equals_exact(translated_translated, tolerance=1e-2 * distance))
+
+    def test_zero_length_route(self) -> None:
+        """Test that :meth:`pyrate.plan.geometry.route.PolarRoute.__init__` raises an exception."""
+
+        with self.assertRaises(ValueError):
+            PolarRoute(locations=[PolarLocation(0.0, 0.0)] * 2)
+
+    def test_non_finite_from_numpy_raises(self) -> None:
+        """Tests that invalid parameter to :meth:`~PolarRoute.from_numpy` warn about it."""
+
+        with self.assertRaises(AssertionError):
+            PolarRoute.from_numpy(array([(1, 2), (2, 4), (4, float("NaN"))]))
+        with self.assertRaises(AssertionError):
+            PolarRoute.from_numpy(array([(float("Inf"), 2), (2, 4), (4, 1)]))
+        with self.assertRaises(AssertionError):
+            PolarRoute.from_numpy(array([(1, 2), (2, float("-Inf")), (4, 4)]))
+
+
+class TestCartesianRoutes(TestCase):
+    """Asserts general properties of the cartesian routes."""
+
+    @given(cartesian_routes())
+    @simple_property_only_few_examples  # this only checks the call signatures so no need for many examples
+    def test_numpy_conversion_invertible(self, cartesian_route: CartesianRoute) -> None:
+        """Tests that the polygon conversion can be inverted."""
+
+        recreated = CartesianRoute.from_numpy(
+            cartesian_route.to_numpy(),
+            origin=cartesian_route.origin,
+            name=cartesian_route.name,
+            location_type=cartesian_route.location_type,
+            identifier=cartesian_route.identifier,
+        )
+
+        self.assertEqual(cartesian_route, recreated)
+
+    @given(cartesian_routes(origin=polar_locations()))
+    @slow_route_max_examples
+    def test_projection_and_back_projection_origin_in_route(self, cartesian_route: CartesianRoute) -> None:
+        """Test the projection with an origin already being present in the geometry."""
+
+        # Try since generated primitives might cause an exception to be thrown
+        # e.g. if projected routes become length 0
+        try:
+            recreated = cartesian_route.to_polar().to_cartesian(cast(PolarLocation, cartesian_route.origin))
+            self.assertTrue(recreated.equals_exact(recreated, tolerance=1e-6))
+        except ValueError:
+            pass
+
+    @given(cartesian_routes(origin=st.none()), polar_locations())
+    @simple_property_only_few_examples  # this only checks very simple additional logic
+    def test_projection_and_back_projection_origin_given_extra(
+        self, cartesian_route: CartesianRoute, origin: PolarLocation
+    ) -> None:
+        """Test the projection with an origin being provided."""
+
+        # Try since generated primitives might cause an exception to be thrown
+        # e.g. if projected routes become length 0
+        try:
+            recreated = cartesian_route.to_polar(origin).to_cartesian(origin)
+            self.assertTrue(recreated.equals_exact(recreated, tolerance=1e-6))
+        except ValueError:
+            pass
+
+    @given(cartesian_routes(origin=st.none()))
+    @simple_property_only_few_examples  # this only checks very simple additional logic
+    def test_projection_and_back_projection_origin_not_given(self, cartesian_route: CartesianRoute) -> None:
+        """Test the projection with no origin being given."""
+
+        with self.assertRaises(ValueError):
+            cartesian_route.to_polar()
+
+    @given(cartesian_routes(origin=polar_locations()), polar_locations())
+    @simple_property_only_few_examples  # this only checks very simple additional logic
+    def test_projection_and_back_projection_origin_given_twice(
+        self, cartesian_route: CartesianRoute, origin: PolarLocation
+    ) -> None:
+        """Test the projection with ambiguous origin being provided."""
+
+        with self.assertRaises(ValueError):
+            cartesian_route.to_polar(origin)
+
+    @given(cartesian_routes())
+    @slow_route_max_examples
+    def test_locations_property_attributes(self, cartesian_route: CartesianRoute) -> None:
+        """Test that all contained locations share the same attributes."""
+
+        for location in cartesian_route.locations:
+            self.assertEqual(location.location_type, cartesian_route.location_type)
+            self.assertEqual(location.name, cartesian_route.name)
+            self.assertEqual(location.identifier, cartesian_route.identifier)
+            self.assertEqual(location.origin, cartesian_route.origin)
+
+    @given(cartesian_routes())
+    @slow_route_max_examples
+    def test_from_shapely_conversion(self, cartesian_route: CartesianRoute) -> None:
+        """Test that :meth:`pyrate.plan.geometry.route.CartesianRoute.from_shapely` works."""
+
+        # we only want to compare the coordinates, so create a new instance without the identifier, name, etc.
+        bare = CartesianRoute.from_numpy(cartesian_route.to_numpy())
+        bare_shapely = LineString(cartesian_route.to_numpy())
+        recreated = CartesianRoute.from_shapely(bare_shapely)
+        self.assertEqual(recreated, bare)
+
+    @given(cartesian_routes())
+    @simple_property_only_few_examples  # this only checks very simple additional logic
+    def test_locations_property(self, cartesian_route: CartesianRoute) -> None:
+        """Test that :meth:`pyrate.plan.geometry.route.CartesianRoute.locations` works."""
+
+        locations = cartesian_route.locations
+        self.assertEqual(len(cartesian_route.coords), len(locations))
+        for i, (x, y) in enumerate(cartesian_route.coords):
+            self.assertEqual(x, locations[i].x)
+            self.assertEqual(y, locations[i].y)
+
+    def test_zero_length_route(self) -> None:
+        """Test that :meth:`pyrate.plan.geometry.route.CartesianRoute.__init__` raises an exception."""
+
+        with self.assertRaises(ValueError):
+            CartesianRoute(locations=[CartesianLocation(0.0, 0.0)] * 2)
+
+    def test_non_finite_from_numpy_raises(self) -> None:
+        """Tests that invalid parameter to :meth:`~CartesianRoute.from_numpy` warn about it."""
+
+        with self.assertRaises(AssertionError):
+            CartesianRoute.from_numpy(array([(1, 2), (2, 4), (4, float("NaN"))]))
+        with self.assertRaises(AssertionError):
+            CartesianRoute.from_numpy(array([(float("Inf"), 2), (2, 4), (4, 1)]))
+        with self.assertRaises(AssertionError):
+            CartesianRoute.from_numpy(array([(1, 2), (2, float("-Inf")), (4, 4)]))