xref: /dports/science/py-pygeodesy/PyGeodesy-21.9.16/test/testRoutes.py

# -*- coding: utf-8 -*-

# Test data for the simplify functions.

# <https://GitHub.com/milkbread/Visvalingam-Wyatt>  not Whyatt!
# <https://GitHub.com/milkbread/Visvalingam-Wyatt/blob/master/route.json>
# <https://GitHub.com/milkbread/Visvalingam-Wyatt/blob/master/out.json>
# <https://milkbread.GitHub.io/Visvalingam-Wyatt>

from base import TestsBase

from pygeodesy import LatLon_, R_KM, R_M, \
                      ellipsoidalVincenty, sphericalTrigonometry, \
                      areaOf, isclockwise, perimeterOf, unstr
try:
    from geographiclib.geodesic import Geodesic
except ImportError:
    Geodesic = None

__all__ = ('Antarctica', 'Pts', 'PtsFFI', 'RdpFFI',
           'PtsJS', 'PtsJS5', 'VwPts')
__version__ = '21.02.11'  # '18.10.12'

# <https://GeographicLib.SourceForge.io/html/python/examples.html>
Antarctica = [LatLon_(_lat, _lon) for _lat, _lon in (
    (-63.1, -58),
    (-72.9, -74),
    (-71.9,-102),
    (-74.9,-102),
    (-74.3,-131),
    (-77.5,-163),
    (-77.4, 163),
    (-71.7, 172),
    (-65.9, 140),
    (-65.7, 113),
    (-66.6,  88),
    (-66.9,  59),
    (-69.8,  25),
    (-70.0,  -4),
    (-71.0, -14),
    (-77.3, -33),
    (-77.9, -46),
    (-74.7, -61))]  # open

# <https://GitHub.com/urschrei/rdp>
PtsFFI = [LatLon_(_lat, _lon) for _lon, _lat in (
    (-0.701206, 52.220489),  # lon, lat
    (-0.701418, 52.220485),
    (-0.703903, 52.220596),
    (-0.705340, 52.220565),
    (-0.705434, 52.220821),
    (-0.705471, 52.221374),
    (-0.705456, 52.221916),
    (-0.705337, 52.222507),
    (-0.705456, 52.222827),
    (-0.705973, 52.223213),
    (-0.707747, 52.224006),
    (-0.708401, 52.224445),
    (-0.710000, 52.225944),
    (-0.710947, 52.226829),
    (-0.713120, 52.228862),
    (-0.713550, 52.229431),
    (-0.713990, 52.231090),
    (-0.714404, 52.232280),
    (-0.714460, 52.232448),
    (-0.714533, 52.232585),
    (-0.714608, 52.232688),
    (-0.714780, 52.232826),
    (-0.714839, 52.232887),
    (-0.714862, 52.232940),
    (-0.714860, 52.233013),
    (-0.714852, 52.233074),
    (-0.714808, 52.233158),
    (-0.714582, 52.233543),
    (-0.714474, 52.233818),
    (-0.714422, 52.234100),
    (-0.714348, 52.234375),
    (-0.714232, 52.234745),
    (-0.714111, 52.234989),
    (-0.714026, 52.235092),
    (-0.713913, 52.235191),
    (-0.713690, 52.235431),
    (-0.713572, 52.235607),
    (-0.713169, 52.236484),
    (-0.713114, 52.236579),
    (-0.712968, 52.236747),
    (-0.712557, 52.237239),
    (-0.712412, 52.237400),
    (-0.712330, 52.237495),
    (-0.711926, 52.238056),
    (-0.711604, 52.238529),
    (-0.711409, 52.238750),
    (-0.711181, 52.238952),
    (-0.711001, 52.239093),
    (-0.710784, 52.239315),
    (-0.710603, 52.239521),
    (-0.709919, 52.240230),
    (-0.709518, 52.240646),
    (-0.709263, 52.240825),
    (-0.708887, 52.240669),
    (-0.708684, 52.240627),
    (-0.708565, 52.240600),
    (-0.708298, 52.240573),
    (-0.707846, 52.240577),
    (-0.707594, 52.240596),
    (-0.707289, 52.240673),
    (-0.707042, 52.240745),
    (-0.706827, 52.240795),
    (-0.706592, 52.240829),
    (-0.706265, 52.240852),
    (-0.705551, 52.240890),
    (-0.705282, 52.240890),
    (-0.704945, 52.240863),
    (-0.704327, 52.240795),
    (-0.703726, 52.240756))]

RdpFFI = [LatLon_(_lat, _lon) for _lon, _lat in (
    (-0.701206, 52.220489),  # lon, lat
    (-0.705340, 52.220565),
    (-0.705456, 52.222827),
    (-0.713120, 52.228862),
    (-0.714862, 52.232940),
    (-0.709263, 52.240825),
    (-0.703726, 52.240756))]

# <https://GitHub.com/mourner/simplify-js/tree/master/test>
PtsJS = [LatLon_(_y, _x) for _x, _y in (
    (224.55, 250.15), (226.91, 244.19), (233.31, 241.45), (234.98, 236.06),
    (244.21, 232.76), (262.59, 215.31), (267.76, 213.81), (273.57, 201.84),
    (273.12, 192.16), (277.62, 189.03), (280.36, 181.41), (286.51, 177.74),
    (292.41, 159.37), (296.91, 155.64), (314.95, 151.37), (319.75, 145.16),
    (330.33, 137.57), (341.48, 139.96), (369.98, 137.89), (387.39, 142.51),
    (391.28, 139.39), (409.52, 141.14), (414.82, 139.75), (427.72, 127.30),
    (439.60, 119.74), (474.93, 107.87), (486.51, 106.75), (489.20, 109.45),
    (493.79, 108.63), (504.74, 119.66), (512.96, 122.35), (518.63, 120.89),
    (524.09, 126.88), (529.57, 127.86), (534.21, 140.93), (539.27, 147.24),
    (567.69, 148.91), (575.25, 157.26), (580.62, 158.15), (601.53, 156.85),
    (617.74, 159.86), (622.00, 167.04), (629.55, 194.60), (638.90, 195.61),
    (641.26, 200.81), (651.77, 204.56), (671.55, 222.55), (683.68, 217.45),
    (695.25, 219.15), (700.64, 217.98), (703.12, 214.36), (712.26, 215.87),
    (721.49, 212.81), (727.81, 213.36), (729.98, 208.73), (735.32, 208.20),
    (739.94, 204.77), (769.98, 208.42), (779.60, 216.87), (784.20, 218.16),
    (800.24, 214.62), (810.53, 219.73), (817.19, 226.82), (820.77, 236.17),
    (827.23, 236.16), (829.89, 239.89), (851.00, 248.94), (859.88, 255.49),
    (865.21, 268.53), (857.95, 280.30), (865.48, 291.45), (866.81, 298.66),
    (864.68, 302.71), (867.79, 306.17), (859.87, 311.37), (860.08, 314.35),
    (858.29, 314.94), (858.10, 327.60), (854.54, 335.40), (860.92, 343.00),
    (856.43, 350.15), (851.42, 352.96), (849.84, 359.59), (854.56, 365.53),
    (849.74, 370.38), (844.09, 371.89), (844.75, 380.44), (841.52, 383.67),
    (839.57, 390.40), (845.59, 399.05), (848.40, 407.55), (843.71, 411.30),
    (844.09, 419.88), (839.51, 432.76), (841.33, 441.04), (847.62, 449.22),
    (847.16, 458.44), (851.38, 462.79), (853.97, 471.15), (866.36, 480.77))]

PtsJS5 = [LatLon_(_y, _x) for _x, _y in (
    (224.55, 250.15), (267.76, 213.81), (296.91, 155.64), (330.33, 137.57),
    (409.52, 141.14), (439.60, 119.74), (486.51, 106.75), (529.57, 127.86),
    (539.27, 147.24), (617.74, 159.86), (629.55, 194.60), (671.55, 222.55),
    (727.81, 213.36), (739.94, 204.77), (769.98, 208.42), (779.60, 216.87),
    (800.24, 214.62), (820.77, 236.17), (859.88, 255.49), (865.21, 268.53),
    (857.95, 280.30), (867.79, 306.17), (859.87, 311.37), (854.54, 335.40),
    (860.92, 343.00), (849.84, 359.59), (854.56, 365.53), (844.09, 371.89),
    (839.57, 390.40), (848.40, 407.55), (839.51, 432.76), (853.97, 471.15),
    (866.36, 480.77))]

# Paris-Berlin-Warsaw-Minsk-Moscow, see
# <https://milkbread.GitHub.io/Visvalingam-Wyatt>
Pts = [LatLon_(_lat, _lon) for _lon, _lat in (
    (2.329860, 48.860050),  # lon, lat
    (2.330270, 48.860580),
    (2.330650, 48.860691),
    (2.331600, 48.860500),
    (2.333330, 48.860119),
    (2.336570, 48.859371),
    (2.336840, 48.859329),
    (2.337980, 48.859261),
    (2.338480, 48.859180),
    (2.339850, 48.858990),
    (2.340110, 48.859501),
    (2.340350, 48.859970),
    (2.340570, 48.860390),
    (2.340730, 48.860722),
    (2.340820, 48.860901),
    (2.340850, 48.860958),
    (2.340950, 48.861130),
    (2.341210, 48.861691),
    (2.341580, 48.862419),
    (2.341870, 48.862968),
    (2.341910, 48.863049),
    (2.341950, 48.863110),
    (2.342140, 48.863468),
    (2.342200, 48.863590),
    (2.342330, 48.863621),
    (2.342430, 48.863628),
    (2.342530, 48.863628),
    (2.342660, 48.863602),
    (2.342770, 48.863602),
    (2.342840, 48.863560),
    (2.343080, 48.863468),
    (2.343590, 48.863319),
    (2.344070, 48.863201),
    (2.344550, 48.863121),
    (2.345200, 48.862991),
    (2.345810, 48.863060),
    (2.346850, 48.862991),
    (2.347310, 48.862980),
    (2.347620, 48.863010),
    (2.347870, 48.863029),
    (2.347960, 48.863071),
    (2.348150, 48.863468),
    (2.348260, 48.863640),
    (2.348940, 48.863800),
    (2.349060, 48.863861),
    (2.349140, 48.863838),
    (2.350000, 48.863628),
    (2.350930, 48.863411),
    (2.351350, 48.864170),
    (2.351480, 48.864410),
    (2.351940, 48.865238),
    (2.352500, 48.866241),
    (2.352940, 48.867039),
    (2.353170, 48.867451),
    (2.353270, 48.867641),
    (2.353420, 48.867908),
    (2.353580, 48.868191),
    (2.353690, 48.868389),
    (2.353850, 48.868690),
    (2.353990, 48.868950),
    (2.354200, 48.869320),
    (2.354210, 48.869339),
    (2.354940, 48.870609),
    (2.355190, 48.871040),
    (2.355280, 48.871208),
    (2.355570, 48.871719),
    (2.355880, 48.872280),
    (2.356490, 48.873360),
    (2.356750, 48.873829),
    (2.357130, 48.874489),
    (2.357270, 48.874760),
    (2.357330, 48.874851),
    (2.357410, 48.874939),
    (2.357460, 48.875019),
    (2.357690, 48.875019),
    (2.358570, 48.875031),
    (2.358920, 48.874931),
    (2.359020, 48.874901),
    (2.359200, 48.875141),
    (2.359350, 48.875259),
    (2.359560, 48.875340),
    (2.360060, 48.875641),
    (2.360280, 48.875771),
    (2.360550, 48.876091),
    (2.360580, 48.876129),
    (2.361370, 48.877430),
    (2.361600, 48.877838),
    (2.362010, 48.878490),
    (2.362220, 48.878799),
    (2.362250, 48.878860),
    (2.362330, 48.878929),
    (2.362590, 48.879021),
    (2.362900, 48.879250),
    (2.364290, 48.880402),
    (2.364700, 48.880730),
    (2.365150, 48.881100),
    (2.365580, 48.881451),
    (2.365780, 48.881611),
    (2.365990, 48.881779),
    (2.366910, 48.882530),
    (2.368220, 48.883572),
    (2.368570, 48.883850),
    (2.368720, 48.883942),
    (2.368850, 48.884022),
    (2.368990, 48.884171),
    (2.369040, 48.884220),
    (2.369170, 48.884350),
    (2.369340, 48.884480),
    (2.370710, 48.885578),
    (2.370850, 48.885689),
    (2.370970, 48.885780),
    (2.371050, 48.885860),
    (2.372420, 48.886978),
    (2.372700, 48.887211),
    (2.372870, 48.887348),
    (2.373530, 48.887878),
    (2.373950, 48.888241),
    (2.374100, 48.888371),
    (2.374260, 48.888489),
    (2.375960, 48.889839),
    (2.376720, 48.890450),
    (2.376850, 48.890560),
    (2.377010, 48.890690),
    (2.377450, 48.891041),
    (2.377540, 48.891109),
    (2.377680, 48.891220),
    (2.378960, 48.892181),
    (2.379130, 48.892311),
    (2.379280, 48.892429),
    (2.379950, 48.892948),
    (2.380070, 48.893040),
    (2.380170, 48.893120),
    (2.381570, 48.894218),
    (2.381700, 48.894321),
    (2.382190, 48.894680),
    (2.382310, 48.894791),
    (2.382740, 48.895142),
    (2.383250, 48.895561),
    (2.383490, 48.895660),
    (2.383590, 48.895741),
    (2.383650, 48.895779),
    (2.383700, 48.895809),
    (2.383890, 48.895939),
    (2.384010, 48.896049),
    (2.384100, 48.896130),
    (2.384180, 48.896210),
    (2.384260, 48.896278),
    (2.384380, 48.896389),
    (2.385610, 48.897499),
    (2.385690, 48.897579),
    (2.385770, 48.897659),
    (2.386150, 48.898041),
    (2.386240, 48.898140),
    (2.386330, 48.898232),
    (2.386610, 48.898499),
    (2.387750, 48.899559),
    (2.387980, 48.899780),
    (2.388400, 48.900051),
    (2.388640, 48.900181),
    (2.388750, 48.900318),
    (2.388820, 48.900520),
    (2.388890, 48.900719),
    (2.389160, 48.900879),
    (2.389330, 48.900982),
    (2.389460, 48.901089),
    (2.390250, 48.901840),
    (2.391140, 48.902729),
    (2.391520, 48.903069),
    (2.392090, 48.903549),
    (2.392120, 48.903580),
    (2.393980, 48.905231),
    (2.394080, 48.905479),
    (2.394520, 48.905899),
    (2.395340, 48.906681),
    (2.395880, 48.907162),
    (2.396300, 48.907570),
    (2.397030, 48.908249),
    (2.398050, 48.909168),
    (2.398300, 48.909409),
    (2.399990, 48.910980),
    (2.400360, 48.911301),
    (2.403230, 48.913940),
    (2.404030, 48.914711),
    (2.404120, 48.914780),
    (2.404360, 48.915001),
    (2.404860, 48.915482),
    (2.405740, 48.916290),
    (2.406070, 48.916599),
    (2.406820, 48.917290),
    (2.407610, 48.918072),
    (2.408840, 48.919022),
    (2.409140, 48.919281),
    (2.409910, 48.920059),
    (2.411690, 48.921719),
    (2.411850, 48.921848),
    (2.412930, 48.922852),
    (2.413100, 48.923100),
    (2.413260, 48.923210),
    (2.413680, 48.923630),
    (2.413840, 48.923771),
    (2.414280, 48.924171),
    (2.415020, 48.924759),
    (2.415610, 48.925289),
    (2.416950, 48.926701),
    (2.417470, 48.927139),
    (2.417590, 48.927238),
    (2.417970, 48.927460),
    (2.418110, 48.927509),
    (2.418320, 48.927738),
    (2.418650, 48.928082),
    (2.419150, 48.928619),
    (2.420250, 48.929562),
    (2.420320, 48.929630),
    (2.420700, 48.930000),
    (2.421070, 48.930359),
    (2.422530, 48.931641),
    (2.423830, 48.932831),
    (2.424150, 48.933159),
    (2.424780, 48.933659),
    (2.425490, 48.934380),
    (2.426000, 48.934872),
    (2.426320, 48.935200),
    (2.426570, 48.935490),
    (2.427010, 48.935959),
    (2.427340, 48.936291),
    (2.427930, 48.936909),
    (2.428080, 48.937099),
    (2.428420, 48.937450),
    (2.428730, 48.937790),
    (2.429840, 48.938839),
    (2.430530, 48.939720),
    (2.431150, 48.940418),
    (2.432060, 48.940479),
    (2.432480, 48.940559),
    (2.433640, 48.940731),
    (2.434080, 48.940842),
    (2.434770, 48.940929),
    (2.435000, 48.940971),
    (2.435260, 48.941090),
    (2.436180, 48.941540),
    (2.437190, 48.942059),
    (2.437280, 48.942101),
    (2.437840, 48.942329),
    (2.438350, 48.942539),
    (2.438780, 48.942669),
    (2.439050, 48.942730),
    (2.439940, 48.942848),
    (2.440410, 48.942909),
    (2.440930, 48.943031),
    (2.441960, 48.943218),
    (2.442970, 48.943329),
    (2.443940, 48.943481),
    (2.444340, 48.943581),
    (2.445940, 48.943939),
    (2.446270, 48.944019),
    (2.448270, 48.944538),
    (2.450060, 48.945000),
    (2.451370, 48.945351),
    (2.452680, 48.945728),
    (2.452900, 48.945728),
    (2.454310, 48.946060),
    (2.455540, 48.946369),
    (2.456860, 48.946690),
    (2.458690, 48.947109),
    (2.458730, 48.947060),
    (2.458800, 48.947021),
    (2.458930, 48.946991),
    (2.459000, 48.946999),
    (2.459080, 48.947029),
    (2.459150, 48.947079),
    (2.459180, 48.947151),
    (2.459170, 48.947208),
    (2.461370, 48.947720),
    (2.461940, 48.948311),
    (2.463250, 48.949650),
    (2.463490, 48.949940),
    (2.463760, 48.949928),
    (2.466330, 48.949871),
    (2.466370, 48.949799),
    (2.466430, 48.949749),
    (2.466520, 48.949711),
    (2.466580, 48.949699),
    (2.466730, 48.949699),
    (2.466860, 48.949741),
    (2.467400, 48.949692),
    (2.467820, 48.949692),
    (2.469920, 48.949829),
    (2.472930, 48.950180),
    (2.473820, 48.950272),
    (2.474330, 48.950298),
    (2.475240, 48.950352),
    (2.477710, 48.950611),
    (2.480360, 48.950851),
    (2.481900, 48.950981),
    (2.483330, 48.951099),
    (2.483900, 48.951092),
    (2.485350, 48.951141),
    (2.485500, 48.951180),
    (2.485930, 48.951149),
    (2.486160, 48.951180),
    (2.486300, 48.951248),
    (2.486330, 48.951271),
    (2.486410, 48.951241),
    (2.486720, 48.951328),
    (2.487290, 48.951401),
    (2.491060, 48.951740),
    (2.492490, 48.951920),
    (2.492850, 48.952030),
    (2.494550, 48.952229),
    (2.496230, 48.952419),
    (2.498810, 48.952721),
    (2.499010, 48.952740),
    (2.502680, 48.953178),
    (2.506410, 48.953678),
    (2.506450, 48.953690),
    (2.508050, 48.953918),
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    (36.926281, 55.117409),
    (36.927269, 55.117722),
    (36.929180, 55.117870),
    (36.930370, 55.117722),
    (36.931049, 55.117771),
    (36.932671, 55.118160),
    (36.934750, 55.118370),
    (36.936138, 55.118290),
    (36.936272, 55.118229),
    (36.936821, 55.118179),
    (36.937000, 55.118500),
    (36.938251, 55.119270),
    (36.939838, 55.119869),
    (36.940750, 55.120289),
    (36.941639, 55.120701),
    (36.941830, 55.120861),
    (36.941490, 55.121479),
    (36.943291, 55.121792),
    (36.944160, 55.121792),
    (36.944839, 55.121342),
    (36.946201, 55.120682),
    (36.946701, 55.120651),
    (36.947140, 55.120171),
    (36.947350, 55.119579),
    (36.947800, 55.119331),
    (36.950001, 55.118980),
    (36.952759, 55.118759),
    (36.954979, 55.118290),
    (36.956612, 55.117630),
    (36.959080, 55.116741),
    (36.959782, 55.116261),
    (36.960171, 55.115780),
    (36.961102, 55.115959),
    (36.963470, 55.116131),
    (36.964779, 55.116020),
    (36.966122, 55.115688),
    (36.967899, 55.115410),
    (36.969620, 55.115162),
    (36.971779, 55.114609),
    (36.972111, 55.114410),
    (36.975330, 55.113541),
    (36.976372, 55.113091),
    (36.979698, 55.112720),
    (36.981850, 55.112061),
    (36.982861, 55.111900),
    (36.983608, 55.111919),
    (36.983849, 55.111900),
    (36.984032, 55.111889),
    (36.984131, 55.111729),
    (36.984329, 55.111691),
    (36.985050, 55.111481),
    (36.986408, 55.111431),
    (36.986691, 55.111671),
    (36.986691, 55.112030),
    (36.986950, 55.112202),
    (36.988060, 55.112289),
    (36.990520, 55.112129),
    (36.995300, 55.112720),
    (36.997551, 55.113468),
    (37.002251, 55.112461),
    (37.002441, 55.112202),
    (37.002010, 55.111301),
    (37.002331, 55.111259),
    (37.002491, 55.111469),
    (37.003620, 55.112839),
    (37.004219, 55.112991),
    (37.004631, 55.113361),
    (37.004700, 55.113750),
    (37.004871, 55.113708),
    (37.005569, 55.112679),
    (37.006821, 55.112041),
    (37.009731, 55.110920),
    (37.011341, 55.110828),
    (37.012211, 55.111111),
    (37.013489, 55.111740),
    (37.015469, 55.112370),
    (37.025341, 55.113319),
    (37.028591, 55.113392),
    (37.033852, 55.113140),
    (37.038738, 55.113060),
    (37.039631, 55.113041),
    (37.040710, 55.113220),
    (37.041599, 55.113998),
    (37.041950, 55.114510),
    (37.042931, 55.114922),
    (37.043598, 55.114948),
    (37.045071, 55.114681),
    (37.045959, 55.114349),
    (37.048660, 55.112850),
    (37.050270, 55.111179),
    (37.055370, 55.108898),
    (37.056831, 55.108440),
    (37.057072, 55.108139),
    (37.057430, 55.107979),
    (37.057678, 55.107849),
    (37.057838, 55.107262),
    (37.058128, 55.107182),
    (37.058922, 55.106998),
    (37.059620, 55.107159),
    (37.060150, 55.107090),
    (37.060841, 55.106640),
    (37.062290, 55.106491),
    (37.063110, 55.106880),
    (37.064270, 55.106812),
    (37.065941, 55.106300),
    (37.066029, 55.105728),
    (37.066090, 55.105122),
    (37.066662, 55.105049),
    (37.070591, 55.105068),
    (37.072441, 55.105000),
    (37.074471, 55.105499),
    (37.076759, 55.106209),
    (37.077831, 55.106541),
    (37.081692, 55.107811),
    (37.082699, 55.108021),
    (37.084110, 55.107941),
    (37.086071, 55.107460),
    (37.090179, 55.107029),
    (37.092060, 55.106750),
    (37.094391, 55.106251),
    (37.096390, 55.105461),
    (37.096081, 55.104919),
    (37.096249, 55.104839),
    (37.096260, 55.104649),
    (37.096039, 55.104561),
    (37.096230, 55.104519),
    (37.096291, 55.104389),
    (37.096909, 55.104198),
    (37.097580, 55.103859),
    (37.098019, 55.103531),
    (37.100090, 55.103168),
    (37.103882, 55.103390),
    (37.107899, 55.102951),
    (37.108829, 55.105179),
    (37.109989, 55.106289),
    (37.114559, 55.108601),
    (37.126110, 55.112492),
    (37.132870, 55.113869),
    (37.135551, 55.114422),
    (37.143639, 55.114399),
    (37.160591, 55.113689),
    (37.167400, 55.112629),
    (37.168499, 55.112598),
    (37.173981, 55.113960),
    (37.177631, 55.115292),
    (37.181881, 55.111858),
    (37.184792, 55.110481),
    (37.186169, 55.109829),
    (37.197540, 55.109692),
    (37.206772, 55.106010),
    (37.211079, 55.105511),
    (37.222580, 55.106209),
    (37.228321, 55.106129),
    (37.233238, 55.105061),
    (37.244549, 55.103298),
    (37.247639, 55.103149),
    (37.251339, 55.102421),
    (37.252621, 55.102470),
    (37.253731, 55.102798),
    (37.256569, 55.103989),
    (37.267151, 55.105621),
    (37.275108, 55.106789),
    (37.276058, 55.107079),
    (37.286098, 55.111752),
    (37.287560, 55.112240),
    (37.291851, 55.112679),
    (37.304550, 55.116409),
    (37.308929, 55.117290),
    (37.312279, 55.117882),
    (37.324741, 55.121410),
    (37.327599, 55.122120),
    (37.335152, 55.123531),
    (37.337212, 55.123909),
    (37.337811, 55.123749),
    (37.338638, 55.123631),
    (37.339630, 55.123581),
    (37.343979, 55.123459),
    (37.345379, 55.123421),
    (37.346241, 55.123451),
    (37.347469, 55.123619),
    (37.348919, 55.123890),
    (37.351589, 55.123871),
    (37.353069, 55.123852),
    (37.354549, 55.123878),
    (37.356030, 55.123951),
    (37.359230, 55.124241),
    (37.365318, 55.124741),
    (37.369572, 55.125099),
    (37.374989, 55.125599),
    (37.376949, 55.125889),
    (37.380440, 55.126400),
    (37.381500, 55.126640),
    (37.384418, 55.127621),
    (37.387081, 55.128578),
    (37.387680, 55.128719),
    (37.388451, 55.128849),
    (37.391029, 55.129051),
    (37.391918, 55.129059),
    (37.392891, 55.128929),
    (37.393860, 55.128700),
    (37.395061, 55.128460),
    (37.396061, 55.128349),
    (37.396832, 55.128281),
    (37.401058, 55.128029),
    (37.404419, 55.127831),
    (37.405540, 55.127850),
    (37.406551, 55.127918),
    (37.407661, 55.128029),
    (37.407982, 55.128071),
    (37.408821, 55.128250),
    (37.410431, 55.128651),
    (37.415249, 55.130058),
    (37.416939, 55.130619),
    (37.418121, 55.131161),
    (37.418579, 55.131500),
    (37.419781, 55.132660),
    (37.421021, 55.133739),
    (37.421600, 55.134079),
    (37.422401, 55.134399),
    (37.423740, 55.134689),
    (37.430691, 55.135429),
    (37.439819, 55.136429),
    (37.444241, 55.137070),
    (37.445789, 55.137390),
    (37.446259, 55.137711),
    (37.446480, 55.137909),
    (37.446522, 55.138149),
    (37.446522, 55.138840),
    (37.446651, 55.139130),
    (37.446819, 55.139309),
    (37.447330, 55.139400),
    (37.448231, 55.139309),
    (37.449612, 55.139111),
    (37.450611, 55.139000),
    (37.450859, 55.139011),
    (37.451141, 55.139160),
    (37.451370, 55.140060),
    (37.451740, 55.141350),
    (37.451839, 55.141541),
    (37.452782, 55.141369),
    (37.453220, 55.142189),
    (37.455021, 55.141769),
    (37.455151, 55.141739),
    (37.456871, 55.141331),
    (37.457401, 55.141209),
    (37.457920, 55.141090),
    (37.458149, 55.141060),
    (37.458469, 55.141041),
    (37.458759, 55.141090),
    (37.460041, 55.141430),
    (37.461380, 55.141788),
    (37.462379, 55.142052),
    (37.462780, 55.142170),
    (37.463261, 55.142288),
    (37.465839, 55.143002),
    (37.467461, 55.143429),
    (37.468800, 55.143780),
    (37.468929, 55.143810),
    (37.470261, 55.144161),
    (37.472549, 55.144730),
    (37.472809, 55.144791),
    (37.472919, 55.144821),
    (37.473640, 55.145000),
    (37.473930, 55.145069),
    (37.474579, 55.145241),
    (37.475269, 55.145409),
    (37.476589, 55.145729),
    (37.477341, 55.145920),
    (37.477928, 55.146061),
    (37.478760, 55.146271),
    (37.480831, 55.146721),
    (37.481369, 55.146839),
    (37.484119, 55.147449),
    (37.484379, 55.147511),
    (37.486080, 55.147911),
    (37.487350, 55.148220),
    (37.487560, 55.148270),
    (37.487820, 55.148331),
    (37.487961, 55.148350),
    (37.488129, 55.148338),
    (37.488251, 55.148319),
    (37.488350, 55.148300),
    (37.488491, 55.148300),
    (37.488590, 55.148289),
    (37.488670, 55.148258),
    (37.488750, 55.148201),
    (37.489029, 55.147820),
    (37.489441, 55.147301),
    (37.489552, 55.147141),
    (37.489601, 55.146950),
    (37.489651, 55.146370),
    (37.489910, 55.143520),
    (37.489929, 55.143330),
    (37.489910, 55.143139),
    (37.489658, 55.142712),
    (37.489529, 55.142540),
    (37.489479, 55.142349),
    (37.489471, 55.142250),
    (37.489460, 55.142078),
    (37.489571, 55.141670),
    (37.490040, 55.140911),
    (37.490170, 55.140800),
    (37.490341, 55.140751),
    (37.490551, 55.140739),
    (37.490761, 55.140751),
    (37.490978, 55.140789),
    (37.491161, 55.140881),
    (37.492050, 55.141529),
    (37.492809, 55.141972),
    (37.493599, 55.142300),
    (37.494450, 55.142559),
    (37.495399, 55.142799),
    (37.499352, 55.143520),
    (37.500710, 55.143681),
    (37.502541, 55.143810),
    (37.503448, 55.143860),
    (37.504372, 55.143829),
    (37.510361, 55.143398),
    (37.512569, 55.143269),
    (37.520920, 55.143978),
    (37.522591, 55.144081),
    (37.523918, 55.144058),
    (37.524540, 55.144039),
    (37.524780, 55.143970),
    (37.525200, 55.143761),
    (37.525620, 55.143398),
    (37.526211, 55.142811),
    (37.528091, 55.140289),
    (37.529202, 55.139511),
    (37.532959, 55.137581),
    (37.537201, 55.134258),
    (37.538979, 55.132900),
    (37.541039, 55.131809),
    (37.542179, 55.131199),
    (37.545330, 55.129169),
    (37.546650, 55.129459),
    (37.546921, 55.129520),
    (37.555550, 55.130920),
    (37.556320, 55.130970),
    (37.557949, 55.131062),
    (37.559521, 55.131149),
    (37.560650, 55.131229),
    (37.567589, 55.128361),
    (37.575562, 55.117641),
    (37.579189, 55.112530),
    (37.580021, 55.111240),
    (37.580830, 55.109951),
    (37.581760, 55.108349),
    (37.582611, 55.106709),
    (37.583469, 55.104809),
    (37.584179, 55.102982),
    (37.584450, 55.101910),
    (37.584751, 55.100800),
    (37.585098, 55.098652),
    (37.585129, 55.096741),
    (37.585041, 55.095650),
    (37.584900, 55.094589),
    (37.584690, 55.093491),
    (37.584419, 55.092388),
    (37.584171, 55.091629),
    (37.583961, 55.091049),
    (37.583450, 55.089729),
    (37.582878, 55.088551),
    (37.582291, 55.087399),
    (37.582001, 55.086880),
    (37.581619, 55.086182),
    (37.581181, 55.085449),
    (37.580238, 55.084030),
    (37.579189, 55.082489),
    (37.578209, 55.081131),
    (37.577320, 55.080040),
    (37.577030, 55.079651),
    (37.576401, 55.078850),
    (37.576080, 55.078442))]

# "threshold": "0.0005", ...  # lon, lat, area?
VwPts = [LatLon_(_lat, _lon) for _lon, _lat, _a2 in (
    (2.32986, 48.86005,  0),  # lon, lat
    (2.35093, 48.863411, 0.0006764590350000889),
    (2.43115, 48.940418, 0.005275181324999963),
    (2.54246, 48.960732, 0.0013039877850000996),
    (2.63999, 49.001961, 0.010534887319999823),
    (2.80339, 49.144669, 0.024102912679999897),
    (2.85119, 49.159790, 0.0007342628499998849),
    (2.99549, 49.236160, 0.0034791586549993733),
    (3.08543, 49.265160, 0.0006159743600001309),
    (3.13198, 49.266472, 0.003311627689999829),
    (3.21429, 49.302959, 0.0009464529800000195),
    (3.28301, 49.356419, 0.0018893187500001478),
    (3.32890, 49.358730, 0.09552116839999703),
    (3.37508, 49.387329, 0.0005483386499999484),
    (3.36840, 49.406940, 0.0008029409999999435),
    (3.43405, 49.446411, 0.002959171529999519),
    (3.51661, 49.463291, 0.0026900486400000365),
    (3.62701, 49.551029, 0.015417812199999662),
    (3.65985, 49.594040, 0.0005695053100000875),
    (3.71867, 49.705761, 0.00977195401000054),
    (3.80852, 49.780540, 0.0014305421600002072),
    (3.93060, 49.850300, 0.011768190849826103),
    (4.00552, 49.867611, 0.0006279938350000511),
    (4.02625, 49.889511, 0.0006053469450000905),
    (4.09659, 49.905418, 0.0021937935149999514),
    (4.10586, 49.934929, 0.0008882974199991181),
    (4.16724, 49.974251, 0.0006570687600002264),
    (4.31856, 50.027500, 0.004801179380001489),
    (4.37885, 50.030609, 0.0010781928850002172),
    (4.46792, 50.070969, 0.03488412753500111),
    (4.49368, 50.127609, 0.0008648552000000303),
    (4.57809, 50.246059, 0.0010913535349680074),
    (4.60485, 50.252739, 0.0005071614200001603),
    (4.65955, 50.304298, 0.001078659360000252),
    (4.71331, 50.316250, 0.005746164855001361),
    (4.86628, 50.422180, 0.0012534538349999722),
    (4.85599, 50.445961, 0.0036526170449996402),
    (4.94456, 50.503571, 0.0007576398200001946),
    (5.00459, 50.525509, 0.0019311189600001934),
    (5.06250, 50.582500, 0.01865430001500212),
    (5.12338, 50.591831, 0.0014397069050002618),
    (5.19067, 50.649441, 0.0005253489150003868),
    (5.32410, 50.724720, 0.0013054674849995174),
    (5.46203, 50.782970, 0.38402723349999696),
    (5.59527, 50.811749, 0.003648713830000012),
    (5.70955, 50.859509, 0.0009227223999996644),
    (5.78653, 50.907829, 0.0012011808400062926),
    (5.83605, 50.912300, 0.0013927635499998384),
    (5.96387, 50.980091, 0.0013384183800003785),
    (6.14661, 51.039459, 0.0032356071399997893),
    (6.21046, 51.077419, 0.0008143443249999117),
    (6.33651, 51.126850, 0.04902457900000075),
    (6.36855, 51.158169, 0.0007331124400002367),
    (6.48883, 51.229980, 0.003027862770000432),
    (6.47779, 51.252701, 0.0015974398750002344),
    (6.58010, 51.331532, 0.026891873830001863),
    (6.75227, 51.371132, 0.007320081329999557),
    (6.84989, 51.429039, 0.0016811635150002966),
    (6.87801, 51.431438, 0.000512130390000089),
    (6.97855, 51.476440, 0.0011294343550004844),
    (7.01853, 51.508781, 0.0005533025450000715),
    (7.08124, 51.531830, 30.637291359080464),
    (7.24011, 51.558880, 0.0005946596100000248),
    (7.31798, 51.557789, 0.0031382185750001104),
    (7.42589, 51.595341, 0.0014381680599997108),
    (7.54105, 51.608761, 0.023957451864999257),
    (7.59659, 51.636028, 0.0007998361400001845),
    (7.70191, 51.658932, 0.0011498674699997706),
    (7.74593, 51.686958, 0.004628844099999091),
    (7.92157, 51.708809, 0.004967921119997949),
    (8.03324, 51.755070, 0.0006727705950003259),
    (8.19468, 51.804260, 0.0005307743000001811),
    (8.35782, 51.849621, 0.05281267402498393),
    (8.44433, 51.859482, 0.0006462804050000689),
    (8.49079, 51.879719, 0.0005782189850000984),
    (8.5841000, 51.884579, 0.0009925159049999634),
    (8.6627700, 51.909950, 0.0038223860100000872),
    (8.7726000, 51.906609, 0.00667983440999894),
    (8.9343000, 51.956890, 0.002762111659999994),
    (9.0024100, 51.956379, 0.0012302698100002585),
    (9.0968700, 51.990940, 0.0009850244750002075),
    (9.1550200, 51.991360, 0.00463162946500384),
    (9.3353500, 52.079762, 0.00102454309500001),
    (9.3618400, 52.104111, 0.016210181225000855),
    (9.4800700, 52.106560, 0.0008511323199998173),
    (9.5323100, 52.122040, 0.003928847264999778),
    (9.6133500, 52.084469, 0.024710846605002817),
    (9.7386200, 52.124001, 0.0009839387999998684),
    (9.7681500, 52.149029, 0.007084765800000054),
    (9.8509100, 52.159939, 0.00086617153000034),
    (9.9341700, 52.153461, 0.0005665361000000064),
    (10.015680, 52.160728, 0.007558770084999596),
    (10.159670, 52.200970, 0.0006649291799999768),
    (10.330790, 52.258030, 2.6073560327749523),
    (10.514200, 52.262520, 0.001902058545000699),
    (10.669100, 52.245571, 0.004948494300001596),
    (10.790770, 52.257530, 0.0024091588200003456),
    (10.881130, 52.226810, 0.0011020893599978292),
    (10.997780, 52.229191, 0.0013778860650000852),
    (11.118510, 52.208031, 0.0006157936350002171),
    (11.352270, 52.187160, 0.000984766875000195),
    (11.436680, 52.188049, 0.18220487750999814),
    (11.521640, 52.164879, 0.005529395700000094),
    (11.622380, 52.187531, 0.0008918949599999886),
    (11.680520, 52.218311, 0.0013726619999999356),
    (11.763740, 52.229019, 0.0079287214000009),
    (12.056750, 52.232670, 0.0016880092800002455),
    (12.214300, 52.252441, 0.0012197837899998105),
    (12.343050, 52.264950, 0.0005295360450000073),
    (12.442440, 52.279900, 0.003422048374999983),
    (12.509530, 52.338360, 0.0008390861550002213),
    (12.552950, 52.351181, 0.026837878589999302),
    (12.660930, 52.335209, 0.001307028479999809),
    (12.807680, 52.337711, 0.005270944050000337),
    (12.918790, 52.290451, 0.02498763803498333),
    (12.977330, 52.303600, 0.0018784250500008376),
    (13.248490, 52.300331, 0.0016729491000007984),
    (13.279420, 52.308590, 0.0007041621900002286),
    (13.440540, 52.306080, 0.0010678526499998911),
    (13.510740, 52.319302, 0.0012690690550003036),
    (13.646030, 52.310699, 0.0012363328449999094),
    (13.824100, 52.310299, 0.0010152788399996218),
    (13.957590, 52.311550, 0.005348844410000293),
    (14.063500, 52.334190, 0.0008116855400002243),
    (14.180730, 52.343922, 0.20303513344984891),
    (14.291050, 52.324291, 0.0019266052749997023),
    (14.543540, 52.314289, 0.01409927991499738),
    (14.755990, 52.335320, 0.005373102765001079),
    (14.842560, 52.328499, 0.0008129688600002133),
    (14.955640, 52.338371, 0.001625489265000505),
    (15.062210, 52.324680, 0.0007415078349998441),
    (15.165720, 52.325298, 0.002478634384999817),
    (15.284460, 52.294231, 0.005768687434999004),
    (15.394060, 52.318531, 0.0014994112999996828),
    (15.542090, 52.323990, 0.014535860675002775),
    (15.653580, 52.299480, 0.0005582185399998018),
    (15.712540, 52.296532, 0.06615280913498117),
    (15.837110, 52.327572, 0.0013612283400006745),
    (16.130489, 52.363850, 0.005248244294000376),
    (16.448879, 52.390018, 0.08860175424850196),
    (16.535200, 52.385269, 0.0012601281000001862),
    (16.671410, 52.348579, 0.005768998621500028),
    (16.888260, 52.354610, 0.001358722025499731),
    (17.004881, 52.345322, 0.006050716657500223),
    (17.170919, 52.307411, 0.029430887288497232),
    (17.440769, 52.319050, 0.0007205185349998619),
    (17.620930, 52.326950, 0.0013525745904998316),
    (17.783670, 52.318829, 1.150875008088602),
    (17.890829, 52.282341, 0.01088199056599956),
    (17.986370, 52.313019, 0.0007916693010001785),
    (18.009010, 52.336861, 0.0006768038859996414),
    (18.130541, 52.365410, 0.0013594757285001848),
    (18.158409, 52.394329, 0.010194835151500213),
    (18.418810, 52.389400, 0.0023208751200005082),
    (18.527161, 52.386780, 0.0005453816600001758),
    (18.615891, 52.398628, 0.0006317860959999628),
    (18.681290, 52.393120, 0.003998675989999382),
    (18.762569, 52.420631, 0.0012300901194997852),
    (18.805080, 52.412800, 0.0005289674395001868),
    (18.868090, 52.426079, 0.018334857585000558),
    (19.052900, 52.404129, 0.01182622432000123),
    (19.164961, 52.405380, 0.0009709318260000118),
    (19.248480, 52.423641, 0.0005799199539998452),
    (19.305229, 52.413750, 0.0007908931205001335),
    (19.482149, 52.444271, 0.0007165993455001046),
    (19.611401, 52.465778, 0.13340130416599558),
    (19.706430, 52.546162, 0.009254246704500575),
    (19.816271, 52.573441, 0.000855054029499975),
    (19.885170, 52.606121, 0.0014355817200004946),
    (20.056530, 52.647541, 0.21623071443998879),
    (20.331970, 52.616940, 0.029833217064998682),
    (20.440701, 52.624760, 0.0013162869750000267),
    (20.493790, 52.652790, 0.0026567240250003573),
    (20.570709, 52.663910, 0.0007827753049998423),
    (20.655951, 52.655880, 0.0016156096159978728),
    (20.890230, 52.694012, 0.007938527149999652),
    (21.043341, 52.678680, 0.005578297333500103),
    (21.115641, 52.708408, 0.002397200585999842),
    (21.315540, 52.724289, 0.03672012526000031),
    (21.398420, 52.698738, 0.0024483483700000817),
    (21.633520, 52.685341, 0.6855450359339951),
    (21.859060, 52.784401, 0.0043868435999998906),
    (22.246490, 52.987999, 0.002620540360000784),
    (22.466600, 53.090141, 0.06174189788000266),
    (22.924431, 53.164379, 1.3505344985999352),
    (22.975700, 53.163528, 0.0008491012775003619),
    (23.233709, 53.126122, 0.0050751893489986806),
    (23.418150, 53.125820, 0.0017231361000003742),
    (23.506680, 53.144360, 0.006176253293999816),
    (23.643511, 53.108250, 0.0389964381259985),
    (23.796881, 53.108688, 0.001176999713999742),
    (23.871290, 53.124249, 0.0024300958499996546),
    (24.068720, 53.116779, 0.0062176423539992195),
    (24.450899, 53.153690, 0.008191595654608464),
    (24.478390, 53.142380, 0.0005606419294997695),
    (24.717630, 53.137539, 0.00233563516000034),
    (24.851120, 53.146969, 0.00970452865549962),
    (25.131519, 53.118011, 0.0023665216855005135),
    (25.251310, 53.088760, 0.006705846240499901),
    (25.417540, 53.097252, 0.0010895988389995814),
    (25.488529, 53.087769, 0.037688359720497694),
    (25.598780, 53.107700, 0.0009777281950000749),
    (25.715191, 53.146481, 0.007753966616000042),
    (25.901340, 53.139820, 0.0005876681744998979),
    (25.925850, 53.132629, 15.624207141311611),
    (26.067511, 53.181671, 0.0006953675744998947),
    (26.120001, 53.209660, 0.0025667765099997154),
    (26.330429, 53.266708, 0.015442059139498357),
    (26.599449, 53.402821, 0.00306352640349959),
    (26.761070, 53.507370, 0.014732591120000332),
    (26.813770, 53.512680, 0.0006814578999998298),
    (26.966890, 53.553970, 0.05847813158500108),
    (27.039070, 53.589420, 0.0018875338250001297),
    (27.089849, 53.666660, 0.007829284025000079),
    (27.303511, 53.735130, 0.005011199784500702),
    (27.391319, 53.803421, 0.0005928050575001501),
    (27.432171, 53.817829, 0.0006160187779998591),
    (27.494040, 53.869808, 0.0016981824205002005),
    (27.585680, 53.916759, 0.9355083148300166),
    (27.719620, 53.955311, 0.0009746368959998464),
    (27.854549, 54.008701, 0.009018125029501734),
    (27.997959, 54.030449, 0.0017747047010011285),
    (28.337090, 54.106628, 0.011066727375504988),
    (28.481810, 54.202950, 0.0005153089800003474),
    (28.512350, 54.237518, 0.0007449054899999776),
    (28.571150, 54.255291, 0.027840016371499444),
    (28.770069, 54.277180, 0.0006223182559984489),
    (29.036091, 54.312710, 0.04917403952351433),
    (29.166031, 54.364811, 0.003102402454000118),
    (29.304399, 54.372540, 0.0010403242859962842),
    (29.807631, 54.477001, 0.005650901765488488),
    (29.896370, 54.473911, 0.0017798839699999177),
    (30.119080, 54.506271, 0.013423775744500646),
    (30.195641, 54.542679, 0.0009894983555001128),
    (30.275570, 54.554840, 0.0018340367199999046),
    (30.409130, 54.619732, 0.10448855816644895),
    (30.591089, 54.642479, 0.001543720579999872),
    (30.780769, 54.683159, 0.009890022788000625),
    (31.064070, 54.689949, 0.007023433094500995),
    (31.201559, 54.703480, 0.0012718874155001928),
    (31.372890, 54.738861, 0.0010077760915000265),
    (31.481560, 54.749538, 0.08998507272699677),
    (31.637960, 54.814232, 0.0011683243500004794),
    (31.673710, 54.843960, 0.01575373942200063),
    (32.004681, 54.865780, 0.0029648347299996514),
    (32.101212, 54.890060, 0.02520276334899922),
    (32.147099, 54.925900, 0.0006533915870000944),
    (32.299351, 55.016338, 2.5306121627785108),
    (32.504452, 55.056099, 0.0014501986585007901),
    (32.597309, 55.059959, 0.0024946020060057374),
    (32.674419, 55.078171, 0.000604723479999913),
    (33.195610, 55.132179, 0.000745868490499901),
    (33.346119, 55.152840, 0.007396271786001787),
    (33.471249, 55.183289, 0.04676558635650117),
    (33.647659, 55.179359, 0.002276000220000347),
    (33.897350, 55.199600, 0.0039050867449983546),
    (34.061390, 55.187550, 0.06661104649048372),
    (34.237122, 55.222080, 0.0033569191450003952),
    (34.389042, 55.265400, 0.000708731580000381),
    (34.562809, 55.324280, 0.0073479436810012224),
    (34.946049, 55.486511, 0.010486538965999144),
    (35.120701, 55.505718, 0.17555820487549917),
    (35.398941, 55.491329, 0.002017215894500156),
    (35.519581, 55.470581, 0.0007216633059995171),
    (35.618980, 55.465450, 0.007075233160503159),
    (35.913269, 55.465580, 0.0011515429755005692),
    (36.064789, 55.457821, 0.27428072454153984),
    (36.175480, 55.494419, 0.002097421690499958),
    (36.455029, 55.548950, 0.01867971054849846),
    (37.198662, 55.626869, 0.0554204532515025),
    (37.297470, 55.657600, 0.0015273776339998135),
    (37.366482, 55.709980, 0.002582013140000326),
    (37.537930, 55.737560, 0.003194690800000177),
    (37.569962, 55.779980, 0))]

# <https://GeographicLib.SourceForge.io/html/python/examples.html>
_JFK_LHR1 = [LatLon_(_lat, _lon) for _lat, _lon in (
    ( 0,   73.8),  # equator
    (40.6, 73.8),  # JFK
    (51.6,  0.5),  # LHR
    ( 0,    0.5))]

_JFK_LHR2 = [LatLon_(_lat, _lon) for _lat, _lon in (
    (-40.6, 73.8),  # double the area
    ( 40.6, 73.8),  # JFK
    ( 51.6,  0.5),  # LHR
    (-51.6,  0.5))]

# del _lat, _lon


def _2LL(pts, LL):
    # map LatLon_ instances to LL
    for p in pts:
        yield LL(p.lat, p.lon)


class Tests(TestsBase):

    def test7(self, f, xs, fmt='%.3f', LL=None, known=False, **kwds):
        n = f.__name__
        if n.endswith('Of'):
            n = '.'.join(f.__module__.split('.')[-1:] + [n])

        g = globals()
        for x, p in zip(xs, ('Antarctica',
                             'PtsFFI', 'RdpFFI', 'Pts', 'VwPts',
                             '_JFK_LHR1', '_JFK_LHR2')):
            pts = g[p]
            if LL:
                pts = _2LL(pts, LL)
            t = unstr(n, p, wrap=True, **kwds)
            # wrap since GeographicLib LONG_UNROLL is always set
            r = f(pts, wrap=True, **kwds)
            self.test(t, r, x, fmt=fmt, known=known)

    def testAreas(self):
        self.test7(areaOf, (13552524.8,
                   1.288, 1.241, 131184.240, 140310.144,
                   4.00413688487425e7, 2*4.00413688487425e7),
                   known=True, radius=R_KM, adjust=True)
        self.test7(areaOf, (13552524.8,
                   1.288, 1.241, 131184.240, 140310.144,
                   4.00413688487425e7, 2*4.00413688487425e7),
                   known=True, radius=R_KM, adjust=False)
        # spherical areaOf requires spherical LatLon
        self.test7(sphericalTrigonometry.areaOf, (13552524.810,  # 13552524.8096748
                   1.338, 1.289, 125942.444, 118897.757,
                   40105639.197, 80211278.393),  # 2*40105639.197 == .394
                   LL=sphericalTrigonometry.LatLon, radius=R_KM)
        try:  # no LatLon restrictions for ellipsoidal areaOf
            # XXX keep ellipsoidalVincenty for backward compatibility
            self.test7(ellipsoidalVincenty.areaOf, (1.366270e+13,  # 13662703680020.1
                       1.343272e+06, 1.294375e+06, 1.271286e+11, 1.200540e+11,
                       4.00413688487425e13, 2*4.00413688487425e13),
                       fmt='%.6e')
            self.test7(ellipsoidalVincenty.areaOf, (1.366270e+13,  # 13662703680020.1
                       1.343272e+06, 1.294375e+06, 1.271286e+11, 1.200540e+11,
                       4.00413688487425e13, 2*4.00413688487425e13),
                       fmt='%.6e', LL=ellipsoidalVincenty.LatLon)
        except (DeprecationWarning, ImportError) as x:
            t = ' '.join(str(x).split())
            # XXX keep ellipsoidalVincenty for backward compatibility
            self.test('ellipsoidalVincenty.areaOf', t, 'DEPRECATED', known=True)

    def testClockwise(self):
        self.test7(isclockwise, (True,  # XXX False if ispolar is True?
                   True, True, True, True,
                   False, False),
                   adjust=False)

    def testPerimeters(self):
        self.test7(perimeterOf, (16765661.499,
                   3224.123, 3185.467, 2762313.129, 2672557.850,
                   15766750.804, 25981742.208),
                   known=True, radius=R_M, closed=False)
        # spherical perimeterOf requires spherical LatLon
        self.test7(sphericalTrigonometry.perimeterOf, (15470624.834,  # 16765661.499 closed
                   3224.123, 3185.467, 2762313.116, 2672556.441,
                   15789078.314, 26041264.665),  # 15766750.804, 25981742.208
                   LL=sphericalTrigonometry.LatLon, radius=R_M, closed=False)
        try:  # no LatLon restrictions for ellipsoidal perimeterOf
            # XXX keep ellipsoidalVincenty for backward compatibility
            self.test7(ellipsoidalVincenty.perimeterOf, (15531947.149,
                       3229.337, 3190.602, 2769709.679, 2679915.858,
                       15766750.804, 25981742.208),  # assumed
                       LL=ellipsoidalVincenty.LatLon, closed=False)
            self.test7(ellipsoidalVincenty.perimeterOf, (16831067.893,
                       5491.045, 5452.310, 5259077.510, 5171947.931,
                       23926469.479, 31533501.608), closed=True)  # assumed
        except (DeprecationWarning, ImportError) as x:
            t = ' '.join(str(x).split())
            # XXX keep ellipsoidalVincenty for backward compatibility
            self.test('ellipsoidalVincenty.perimeterOf', t, 'DEPRECATED', known=True)

    def testGeodesic(self):
        # <https://GeographicLib.SourceForge.io/html/python/examples.html>
        def _s(n, m='(Sphere)'):
            return 'geographiclib.' + n + m

        def _w(n, m='(WGS84)'):
            return 'geographiclib.' + n + m

        if Geodesic:
            wgs = Geodesic.WGS84
            sph = Geodesic(R_M, 0)

            w = wgs.Inverse(-41.32, 174.81, 40.96, -5.50, Geodesic.DISTANCE | Geodesic.LONG_UNROLL)
            self.test(_w('WNZ-SAL'), w['s12'], 19959679.267, fmt='%.3f')
            self.test(_w('WNZ-SAL'), w['lon2'], 354.50, fmt='%.2f')
            s = sph.Inverse(-41.32, 174.81, 40.96, -5.50, Geodesic.DISTANCE | Geodesic.LONG_UNROLL)
            self.test(_s('WNZ-SAL'), s['s12'], 19967403.498, fmt='%.3f')
            self.test(_s('WNZ-SAL'), s['lon2'], 354.50, fmt='%.2f')

            w = wgs.Inverse(40.1, 116.6, 37.6, -122.4, Geodesic.DISTANCE | Geodesic.LONG_UNROLL)
            self.test(_w('BJS-SFO'), w['s12'], 9513998.0, fmt='%.1f')
            self.test(_w('BJS-SFO'), w['lon2'], 237.6, fmt='%.1f')
            s = sph.Inverse(40.1, 116.6, 37.6, -122.4, Geodesic.DISTANCE | Geodesic.LONG_UNROLL)
            self.test(_s('BJS-SFO'), s['s12'], 9491734.6, fmt='%.1f')
            self.test(_s('BJS-SFO'), s['lon2'], 237.6, fmt='%.1f')

            w = wgs.Direct(-32.06, 115.74, 225, 20000e3)
            self.test(_w('SW-Perth'), w['lat2'],  32.11195529, fmt='%.8f')
            self.test(_w('SW-Perth'), w['lon2'], -63.95925278, fmt='%.8f')
            s = sph.Direct(-32.06, 115.74, 225, 20000e3)
            self.test(_s('SW-Perth'), s['lat2'],  31.96383509, fmt='%.8f')
            self.test(_s('SW-Perth'), s['lon2'], -64.14670854, fmt='%.8f')

            w = wgs.Inverse(40.6, -73.8, 51.6, -0.5, Geodesic.DISTANCE | Geodesic.AREA | Geodesic.LONG_UNROLL)
            self.test(_w('JFK-LHR'), w['S12'], 40041368848742.5, fmt='%.1f')
            self.test(_w('JFK-LHR'), w['s12'], 5551759.4, fmt='%.1f')
            s = sph.Inverse(40.6, -73.8, 51.6, -0.5, Geodesic.DISTANCE | Geodesic.AREA | Geodesic.LONG_UNROLL)
            self.test(_s('JFK-LHR'), s['S12'], 40105639196534.8, fmt='%.1f')
            self.test(_s('JFK-LHR'), s['s12'], 5536892.0, fmt='%.1f')

            p = wgs.Polygon()
            for ll in Antarctica:
                p.AddPoint(ll.lat, ll.lon)
            _, p, a = p.Compute()
            self.test(_w('Antarctica Peri'), p, 16831067.893, fmt='%.3f')
            self.test(_w('Antarctica Area'), a, 13662703680020.1, fmt='%.1f')

            p = sph.Polygon()
            for ll in Antarctica:
                p.AddPoint(ll.lat, ll.lon)
            _, p, a = p.Compute()
            self.test(_s('Antarctica Peri'), p, 16765661.499, fmt='%.3f')
            self.test(_s('Antarctica Area'), a, 13552524809674.8, fmt='%.1f')

        else:
            self.test('no module', _s('Geodesic', ''), _s('Geodesic', ''))


if __name__ == '__main__':

    t = Tests(__file__, __version__)
    t.testAreas()
    t.testPerimeters()
    t.testGeodesic()
    t.testClockwise()
    t.results()
    t.exit()