"""
Created on 18. des. 2015

@author: pab
"""
import pytest
import numpy as np
from numpy.testing import assert_array_almost_equal  # @UnresolvedImport
from nvector import FrameB, FrameE, FrameN, FrameL, GeoPoint, GeoPath, unit, delta_L

EARTH_RADIUS_M = 6371009.0

@pytest.mark.parametrize("lat_a,lat_b,method", [(81, 80, 'ellipsoid'),
                                                (79, 80, 'ellipsoid'),
                                                (81, 80, 'greatcircle'),
                                                (79, 80, 'greatcircle')])
def test_geo_path_on_path(lat_a, lat_b, method):
    wgs84 = FrameE(name='WGS84')
    point_a = wgs84.GeoPoint(latitude=lat_a, longitude=0, degrees=True)
    point_b = wgs84.GeoPoint(latitude=lat_b, longitude=0, degrees=True)
    point_c = wgs84.GeoPoint(latitude=0.5*(lat_a+lat_b), longitude=0, degrees=True)

    path = GeoPath(point_a, point_b)
    for point in [point_a, point_b, point_c]:
        assert path.on_path(point, method=method)

    point_a1 = wgs84.GeoPoint(latitude=lat_a, longitude=1e-6, degrees=True)
    point_b1 = wgs84.GeoPoint(latitude=lat_b, longitude=1e-6, degrees=True)
    for point in [point_a1, point_b1]:
        assert not path.on_path(point, method=method)

    tol = 1e-10
    lat_e, lat_f = (lat_a-tol, lat_b + tol) if lat_a < lat_b else (lat_a+tol, lat_b - tol)
    point_e = wgs84.GeoPoint(latitude=lat_e, longitude=0, degrees=True)
    point_f = wgs84.GeoPoint(latitude=lat_f, longitude=0, degrees=True)
    for point in [point_e, point_f]:
        assert not path.on_path(point, method=method)

    # Test vectorized

class TestGeoPoint:

    def test_scalar_geopoint_to_nvector_to_geopoint(self):
        wgs84 = FrameE(name='WGS84')
        gp1 = wgs84.GeoPoint(10, 5, degrees=True)
        np1 = gp1.to_nvector()
        gp2 = np1.to_geo_point()
        assert gp1 == gp2
        # Check that the round trip returns a scalar GeoPoint
        assert np.ndim(gp2.z) == 0
        assert np.ndim(gp2.latitude) == 0
        assert np.ndim(gp2.longitude) == 0

    def test_scalar_geopoint_to_nvector_to_ecef_to_geopoint(self):
        wgs84 = FrameE(name='WGS84')
        gp1 = wgs84.GeoPoint(10, 5, degrees=True)
        np1 = gp1.to_nvector()
        ep1 = np1.to_ecef_vector()
        gp2 = ep1.to_geo_point()
        assert gp1 == gp2
        # Check that the round trip returns a scalar GeoPoint
        assert np.ndim(gp2.z) == 0
        assert np.ndim(gp2.latitude) == 0
        assert np.ndim(gp2.longitude) == 0

        assert np.ndim(ep1.length) == 0
        assert np.ndim(ep1.azimuth) == 0
        assert np.ndim(ep1.elevation) == 0


    def test_vector_geopoint_to_nvector_to_geopoint(self):
        wgs84 = FrameE(name='WGS84')
        gp1 = wgs84.GeoPoint(10, [5, 7], degrees=True)
        np1 = gp1.to_nvector()
        gp2 = np1.to_geo_point()
        assert gp1 == gp2
        # Check that the round trip returns a vector GeoPoint
        assert np.ndim(gp2.z) == 1
        assert np.ndim(gp2.latitude) == 1
        assert np.ndim(gp2.longitude) == 1

    def test_vector_geopoint_to_nvector_to_ecef_to_geopoint(self):
        wgs84 = FrameE(name='WGS84')
        gp1 = wgs84.GeoPoint([10, 15], 5, degrees=True)
        np1 = gp1.to_nvector()
        ep1 = np1.to_ecef_vector()
        gp2 = ep1.to_geo_point()
        assert gp1 == gp2
        # Check that the round trip returns a vector GeoPoint
        assert np.ndim(gp2.z) == 1
        assert np.ndim(gp2.latitude) == 1
        assert np.ndim(gp2.longitude) == 1

        assert np.ndim(ep1.length) == 1
        assert np.ndim(ep1.azimuth) == 1
        assert np.ndim(ep1.elevation) == 1


class TestFrames:
    def test_compare_E_frames(self):
        E = FrameE(name='WGS84')
        E2 = FrameE(a=E.a, f=E.f)
        assert E == E2
        assert E == E
        E3 = FrameE(a=E.a, f=0)
        assert E != E3

    def test_compare_B_frames(self):
        E = FrameE(name='WGS84')
        E2 = FrameE(name='WGS72')

        n_EB_E = E.Nvector(unit([[1], [2], [3]]), z=-400)
        B = FrameB(n_EB_E, yaw=10, pitch=20, roll=30, degrees=True)
        assert B == B
        assert B != E

        B2 = FrameB(n_EB_E, yaw=1, pitch=20, roll=30, degrees=True)
        assert B != B2

        B3 = FrameB(n_EB_E, yaw=10, pitch=20, roll=30, degrees=True)
        assert B == B3

        n_EC_E = E.Nvector(unit([[1], [2], [2]]), z=-400)
        B4 = FrameB(n_EC_E, yaw=10, pitch=20, roll=30, degrees=True)
        assert B != B4

        n_ED_E = E2.Nvector(unit([[1], [2], [3]]), z=-400)
        B5 = FrameB(n_ED_E, yaw=10, pitch=20, roll=30, degrees=True)
        assert B != B5

    def test_compare_N_frames(self):
        wgs84 = FrameE(name='WGS84')
        wgs72 = FrameE(name='WGS72')
        pointA = wgs84.GeoPoint(latitude=1, longitude=2, z=3, degrees=True)
        pointB = wgs72.GeoPoint(latitude=1, longitude=2, z=6, degrees=True)

        frame_N = FrameN(pointA)
        frame_L1 = FrameL(pointA, wander_azimuth=0)
        frame_L2 = FrameL(pointA, wander_azimuth=0)
        frame_L3 = FrameL(pointB, wander_azimuth=0)

        assert frame_N == frame_N

        assert frame_N == frame_L1
        assert not (frame_N != frame_L1)

        assert frame_N == frame_L2

        assert frame_N != frame_L3
        assert frame_L1 != frame_L3

    def test_compare_L_frames(self):
        wgs84 = FrameE(name='WGS84')
        wgs72 = FrameE(name='WGS72')
        pointA = wgs84.GeoPoint(latitude=1, longitude=2, z=3, degrees=True)
        pointB = wgs72.GeoPoint(latitude=1, longitude=2, z=6, degrees=True)

        frame_N = FrameL(pointA)
        frame_N1 = FrameL(pointA, wander_azimuth=10)
        frame_N2 = FrameL(pointB, wander_azimuth=10)

        assert frame_N == frame_N
        assert frame_N != frame_N1
        assert frame_N != frame_N2
        assert frame_N1 != frame_N2


class TestExamples:
    @staticmethod
    def test_compute_delta_L_in_moving_frame_east():
        wgs84 = FrameE(name='WGS84')
        point_a = wgs84.GeoPoint(latitude=1, longitude=2, z=0, degrees=True)
        point_b = wgs84.GeoPoint(latitude=1, longitude=2.005, z=0, degrees=True)
        sensor_position = wgs84.GeoPoint(latitude=1.000090437, longitude=2.0025, z=0, degrees=True)
        path = GeoPath(point_a, point_b)
        ti = np.linspace(0, 1.0, 8)
        ship_positions0 = path.interpolate(ti[:-1])
        ship_positions1 = path.interpolate(ti[1:])
        headings = ship_positions0.delta_to(ship_positions1).azimuth_deg
        assert_array_almost_equal(headings, 90, decimal=4)

        ship_positions = path.interpolate(ti)

        delta = delta_L(ship_positions, sensor_position, wander_azimuth=np.pi / 2)

        x, y, z = delta.pvector
        azimuth = np.round(delta.azimuth_deg)
        # positive angle about down-axis

        print('Ex1, delta L = {0}'.format(delta.pvector.T))
        print('Ex1, azimuth = {0} deg'.format(azimuth))

        true_x = [278.2566243359911, 198.7547317612817, 119.25283909376164,
                  39.750946370747656, -39.75094637085409, -119.25283909387079,
                  -198.75473176137066, -278.2566243360949]
        assert_array_almost_equal(x, true_x, decimal=3)
        assert_array_almost_equal(y, -10, decimal=3)
        assert_array_almost_equal(z, 0, decimal=2)
        assert_array_almost_equal(azimuth,
                                  [-2., -3., -5., -14., -166., -175., -177., -178.])

    @staticmethod
    def test_compute_delta_N_in_moving_frame_east():
        wgs84 = FrameE(name='WGS84')
        point_a = wgs84.GeoPoint(latitude=1, longitude=2, z=0, degrees=True)
        point_b = wgs84.GeoPoint(latitude=1, longitude=2.005, z=0, degrees=True)
        sensor_position = wgs84.GeoPoint(latitude=1.0, longitude=2.0025, z=0, degrees=True)
        path = GeoPath(point_a, point_b)
        ti = np.linspace(0, 1.0, 8)
        ship_positions0 = path.interpolate(ti[:-1])
        ship_positions1 = path.interpolate(ti[1:])
        headings = ship_positions0.delta_to(ship_positions1).azimuth_deg
        assert_array_almost_equal(headings, 90, decimal=4)

        ship_positions = path.interpolate(ti)

        delta = ship_positions.delta_to(sensor_position)

        x, y, z = delta.pvector
        azimuth = np.round(delta.azimuth_deg)
        # positive angle about down-axis

        print('Ex1, delta north, east, down = {0}'.format(delta.pvector.T))
        print('Ex1, azimuth = {0} deg'.format(azimuth))

        true_y = [278.2566243359911, 198.7547317612817, 119.25283909376164,
                  39.750946370747656, -39.75094637085409, -119.25283909387079,
                  -198.75473176137066, -278.2566243360949]
        assert_array_almost_equal(x, 0, decimal=3)
        assert_array_almost_equal(y, true_y)
        assert_array_almost_equal(z, 0, decimal=2)
        n2 = len(azimuth) // 2
        assert_array_almost_equal(azimuth[:n2], 90)
        assert_array_almost_equal(azimuth[n2:], -90)

    @staticmethod
    def test_compute_delta_L_in_moving_frame_north():
        wgs84 = FrameE(name='WGS84')
        point_a = wgs84.GeoPoint(latitude=1, longitude=2, z=0, degrees=True)
        point_b = wgs84.GeoPoint(latitude=1.005, longitude=2.0, z=0,
                                 degrees=True)
        sensor_position = wgs84.GeoPoint(latitude=1.0025, longitude=2.0, z=0,
                                         degrees=True)
        path = GeoPath(point_a, point_b)
        ti = np.linspace(0, 1.0, 8)
        ship_positions0 = path.interpolate(ti[:-1])
        ship_positions1 = path.interpolate(ti[1:])
        headings = ship_positions0.delta_to(ship_positions1).azimuth_deg
        assert_array_almost_equal(headings, 0, decimal=8)

        ship_positions = path.interpolate(ti)

        delta0 = delta_L(ship_positions, sensor_position, wander_azimuth=0)
        delta = ship_positions.delta_to(sensor_position)
        assert_array_almost_equal(delta0.pvector, delta.pvector)

        x, y, z = delta.pvector
        azimuth = np.round(np.abs(delta.azimuth_deg))
        # positive angle about down-axis

        print('Ex1, delta north, east, down = {0}'.format(delta.pvector.T))
        print('Ex1, azimuth = {0} deg'.format(azimuth))

        true_x = [276.436537069603, 197.45466985931083, 118.47280221160541,
                  39.49093416312986, -39.490934249581684, -118.47280298990226,
                  -197.454672021303, -276.4365413071498]
        assert_array_almost_equal(x, true_x)
        assert_array_almost_equal(y, 0, decimal=8)
        assert_array_almost_equal(z, 0, decimal=2)
        n2 = len(azimuth) // 2
        assert_array_almost_equal(azimuth[:n2], 0)
        assert_array_almost_equal(azimuth[n2:], 180)

    @staticmethod
    def test_Ex1_A_and_B_to_delta_in_frame_N():
        wgs84 = FrameE(name='WGS84')
        point_a = wgs84.GeoPoint(latitude=1, longitude=2, z=3, degrees=True)
        point_b = wgs84.GeoPoint(latitude=4, longitude=5, z=6, degrees=True)

        # Find the exact vector between the two positions, given in meters
        # north, east, and down, i.e. find delta_N.

        # SOLUTION:
        delta = point_a.delta_to(point_b)
        x, y, z = delta.pvector
        azimuth = delta.azimuth_deg
        elevation = delta.elevation_deg
        print('Ex1, delta north, east, down = {0}, {1}, {2}'.format(x, y, z))
        print('Ex1, azimuth = {0} deg'.format(azimuth))

        assert_array_almost_equal(x, 331730.23478089)
        assert_array_almost_equal(y, 332997.87498927)
        assert_array_almost_equal(z, 17404.27136194)
        assert_array_almost_equal(azimuth, 45.10926324)
        assert_array_almost_equal(elevation, 2.12055861)

    @staticmethod
    def test_Ex2_B_and_delta_in_frame_B_to_C_in_frame_E():
        # delta vector from B to C, decomposed in B is given:

        # A custom reference ellipsoid is given (replacing WGS-84):
        wgs72 = FrameE(name='WGS72')

        # Position and orientation of B is given 400m above E:
        n_EB_E = wgs72.Nvector(unit([[1], [2], [3]]), z=-400)

        frame_B = FrameB(n_EB_E, yaw=10, pitch=20, roll=30, degrees=True)
        p_BC_B = frame_B.Pvector(np.r_[3000, 2000, 100].reshape((-1, 1)))

        p_BC_E = p_BC_B.to_ecef_vector()
        p_EB_E = n_EB_E.to_ecef_vector()
        p_EC_E = p_EB_E + p_BC_E

        pointC = p_EC_E.to_geo_point()

        lat, lon, z = pointC.latlon_deg
        # Here we also assume that the user wants output height (= - depth):
        msg = 'Ex2, Pos C: lat, lon = {},{} deg,  height = {} m'
        print(msg.format(lat, lon, -z))

        assert_array_almost_equal(lat, 53.32637826)
        assert_array_almost_equal(lon, 63.46812344)
        assert_array_almost_equal(z, -406.00719607)

    @staticmethod
    def test_Ex3_ECEF_vector_to_geodetic_latitude():

        wgs84 = FrameE(name='WGS84')
        # Position B is given as p_EB_E ("ECEF-vector")
        position_B = 6371e3 * np.vstack((0.9, -1, 1.1))  # m
        p_EB_E = wgs84.ECEFvector(position_B)

        # Find position B as geodetic latitude, longitude and height
        pointB = p_EB_E.to_geo_point()
        lat, lon, h = pointB.latitude_deg, pointB.longitude_deg, -pointB.z

        msg = 'Ex3, Pos B: lat, lon = {} {} deg, height = {} m'
        print(msg.format(lat, lon, h))
        assert_array_almost_equal(lat, 39.37874867)
        assert_array_almost_equal(lon, -48.0127875)
        assert_array_almost_equal(h, 4702059.83429485)

    @staticmethod
    def test_Ex4_geodetic_latitude_to_ECEF_vector():
        wgs84 = FrameE(name='WGS84')
        pointB = wgs84.GeoPoint(latitude=1, longitude=2, z=-3, degrees=True)

        p_EB_E = pointB.to_ecef_vector()
        print('Ex4: p_EB_E = {0} m'.format(p_EB_E.pvector.ravel()))

        assert_array_almost_equal(p_EB_E.pvector.ravel(),
                                  [6373290.27721828, 222560.20067474,
                                   110568.82718179])

    @staticmethod
    def test_Ex5_great_circle_distance():
        frame_E = FrameE(a=6371e3, f=0)
        positionA = frame_E.GeoPoint(latitude=88, longitude=0, degrees=True)
        positionB = frame_E.GeoPoint(latitude=89, longitude=-170, degrees=True)
        s_AB, _azia, _azib = positionA.distance_and_azimuth(positionB)

        p_AB_E = positionB.to_ecef_vector() - positionA.to_ecef_vector()
        # The Euclidean distance is given by:
        d_AB = p_AB_E.length

        msg = 'Ex5, Great circle distance = {} km, Euclidean distance = {} km'
        print(msg.format(s_AB / 1000, d_AB / 1000))

        assert_array_almost_equal(s_AB / 1000, 332.45644411)
        assert_array_almost_equal(d_AB / 1000, 332.41872486)

    @staticmethod
    def test_alternative_great_circle_distance():
        frame_E = FrameE(a=6371e3, f=0)
        point_a = frame_E.GeoPoint(latitude=88, longitude=0, degrees=True)
        point_b = frame_E.GeoPoint(latitude=89, longitude=-170, degrees=True)
        path = GeoPath(point_a, point_b)

        s_AB = path.track_distance(method='greatcircle')
        d_AB = path.track_distance(method='euclidean')
        s1_AB = path.track_distance(method='exact')

        msg = 'Ex5, Great circle distance = {} km, Euclidean distance = {} km'
        print(msg.format(s_AB / 1000, d_AB / 1000))

        assert_array_almost_equal(s_AB / 1000, 332.45644411)
        assert_array_almost_equal(s1_AB / 1000, 332.45644411)
        assert_array_almost_equal(d_AB / 1000, 332.41872486)

    @staticmethod
    def test_exact_ellipsoidal_distance():
        wgs84 = FrameE(name='WGS84')
        pointA = wgs84.GeoPoint(latitude=88, longitude=0, degrees=True)
        pointB = wgs84.GeoPoint(latitude=89, longitude=-170, degrees=True)
        s_AB, _azia, _azib = pointA.distance_and_azimuth(pointB)

        p_AB_E = pointB.to_ecef_vector() - pointA.to_ecef_vector()
        # The Euclidean distance is given by:
        d_AB = p_AB_E.length

        msg = 'Ex5, Great circle distance = {} km, Euclidean distance = {} km'
        print(msg.format(s_AB / 1000, d_AB / 1000))

        assert_array_almost_equal(s_AB / 1000, 333.94750946834665)
        assert_array_almost_equal(d_AB / 1000, 333.90962112)

    @staticmethod
    def test_Ex6_interpolated_position():

        # Position B at time t0 and t2 is given as n_EB_E_t0 and n_EB_E_t1:
        # Enter elements as lat/long in deg:
        wgs84 = FrameE(name='WGS84')
        n_EB_E_t0 = wgs84.GeoPoint(89, 0, degrees=True).to_nvector()
        n_EB_E_t1 = wgs84.GeoPoint(89, 180, degrees=True).to_nvector()

        # The times are given as:
        t0 = 10.
        t1 = 20.
        ti = 16.  # time of interpolation

        # Find the interpolated position at time ti, n_EB_E_ti

        # SOLUTION:
        # Using standard interpolation:
        ti_n = (ti - t0) / (t1 - t0)
        n_EB_E_ti = n_EB_E_t0 + ti_n * (n_EB_E_t1 - n_EB_E_t0)

        # When displaying the resulting position for humans, it is more
        # convenient to see lat, long:
        g_EB_E_ti = n_EB_E_ti.to_geo_point()
        lat_ti, lon_ti = g_EB_E_ti.latitude_deg, g_EB_E_ti.longitude_deg
        msg = 'Ex6, Interpolated position: lat, long = {} deg, {} deg'
        print(msg.format(lat_ti, lon_ti))

        assert_array_almost_equal(lat_ti, 89.7999805)
        assert_array_almost_equal(lon_ti, 180.)

        # Alternative solution
        path = GeoPath(n_EB_E_t0, n_EB_E_t1)

        g_EB_E_ti = path.interpolate(ti_n).to_geo_point()
        lat_ti, lon_ti = g_EB_E_ti.latitude_deg, g_EB_E_ti.longitude_deg
        msg = 'Ex6, Interpolated position: lat, long = {} deg, {} deg'
        print(msg.format(lat_ti, lon_ti))

        assert_array_almost_equal(lat_ti, 89.7999805)
        assert_array_almost_equal(lon_ti, 180.)

    @staticmethod
    def test_Ex7_mean_position():

        # Three positions A, B and C are given:
        # Enter elements directly:
        # n_EA_E=unit(np.vstack((1, 0, -2)))
        # n_EB_E=unit(np.vstack((-1, -2, 0)))
        # n_EC_E=unit(np.vstack((0, -2, 3)))

        # or input as lat/long in deg:
        points = GeoPoint(latitude=[90, 60, 50], longitude=[0, 10, -20],
                          degrees=True)
        nvectors = points.to_nvector()
        nmean = nvectors.mean()
        n_EM_E = nmean.normal
        assert_array_almost_equal(n_EM_E.ravel(),
                                  [0.384117, -0.046602, 0.922107])

    @staticmethod
    def test_Ex8_position_A_and_azimuth_and_distance_to_B():
        frame = FrameE(a=EARTH_RADIUS_M, f=0)
        pointA = frame.GeoPoint(latitude=80, longitude=-90, degrees=True)
        pointB, _azimuthb = pointA.displace(distance=1000, azimuth=200,
                                            degrees=True)
        pointB2, _azimuthb = pointA.displace(distance=1000,
                                             azimuth=np.deg2rad(200))
        assert_array_almost_equal(pointB.latlon, pointB2.latlon)

        lat_B, lon_B = pointB.latitude_deg, pointB.longitude_deg

        print('Ex8, Destination: lat, long = {0} {1} deg'.format(lat_B, lon_B))
        assert_array_almost_equal(lat_B, 79.99154867)
        assert_array_almost_equal(lon_B, -90.01769837)

    @staticmethod
    def test_Ex9_intersect():

        # Two paths A and B are given by two pairs of positions:
        pointA1 = GeoPoint(10, 20, degrees=True)
        pointA2 = GeoPoint(30, 40, degrees=True)
        pointB1 = GeoPoint(50, 60, degrees=True)
        pointB2 = GeoPoint(70, 80, degrees=True)
        pathA = GeoPath(pointA1, pointA2)
        pathB = GeoPath(pointB1, pointB2)

        pointC = pathA.intersect(pathB).to_geo_point()

        lat, lon = pointC.latitude_deg, pointC.longitude_deg
        msg = 'Ex9, Intersection: lat, long = {} {} deg'
        print(msg.format(lat, lon))
        assert_array_almost_equal(lat, 40.31864307)
        assert_array_almost_equal(lon, 55.90186788)

    def test_intersect_on_parallell_paths(self):

        # Two paths A and B are given by two pairs of positions:
        pointA1 = GeoPoint(10, 20, degrees=True)
        pointA2 = GeoPoint(30, 40, degrees=True)
        pointB1 = GeoPoint(10, 20, degrees=True)
        pointB2 = GeoPoint(30, 40, degrees=True)
        pathA = GeoPath(pointA1, pointA2)
        pathB = GeoPath(pointB1, pointB2)

        pointC = pathA.intersect(pathB).to_geo_point()

        lat, lon = pointC.latitude_deg, pointC.longitude_deg
        msg = 'Ex9, Intersection: lat, long = {} {} deg'
        print(msg.format(lat, lon))
        assert np.isnan(lat)
        assert np.isnan(lon)

    def test_Ex10_cross_track_distance(self):

        frame = FrameE(a=6371e3, f=0)
        # Position A1 and A2 and B as lat/long in deg:
        pointA1 = frame.GeoPoint(0, 0, degrees=True)
        pointA2 = frame.GeoPoint(10, 0, degrees=True)
        pointB = frame.GeoPoint(1, 0.1, degrees=True)
        pointB2 = frame.GeoPoint(11, 0.1, degrees=True)
        pointB3 = frame.GeoPoint(-1, 0.1, degrees=True)

        pathA = GeoPath(pointA1, pointA2)

        # Find the cross track distance from path A to position B.
        s_xt = pathA.cross_track_distance(pointB, method='greatcircle')
        d_xt = pathA.cross_track_distance(pointB, method='euclidean')
        msg = 'Ex10, Cross track distance = {} m, Euclidean = {} m'
        print(msg.format(s_xt, d_xt))

        pointC = pathA.closest_point_on_great_circle(pointB)
        pointC2 = pathA.closest_point_on_great_circle(pointB2)
        pointC3 = pathA.closest_point_on_path(pointB2)
        pointC4 = pathA.closest_point_on_path(pointB3)
        s_xt2, _az_bc, _az_cb = pointB.distance_and_azimuth(pointC)
        assert_array_almost_equal(s_xt2, 11117.79911015)
        assert_array_almost_equal(s_xt, 11117.79911015)
        assert_array_almost_equal(d_xt, 11117.79346741)

        assert pathA.on_path(pointC)
        assert pathA.on_path(pointC, method='exact')

        assert not pathA.on_path(pointC2)
        assert not pathA.on_path(pointC2, method='exact')
        assert pointC3 == pointA2
        assert pointC4 == pointA1

