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Geodetic¶
The library provides utilities to manage geodetic coordinates. There are other more exhaustive libraries that manage this domain, but some C++ objects need to receive this information from the Python code. This is why these objects have been developed.
World Geodetic System (WGS)¶
This class allows describing the geodetic coordinate system used in the calculation. By default, the class instantiates the WGS84 system.
import timeit
import cartopy.crs
import cartopy.feature
import matplotlib.pyplot
import numpy
import pyinterp.geodetic
wgs84 = pyinterp.geodetic.Spheroid()
print(wgs84)
Spheroid(6378137.0, 0.0033528106647474805)
You can instantiate other systems.
grs80 = pyinterp.geodetic.Spheroid((6378137, 1 / 298.257222101))
print(grs80)
Spheroid(6378137.0, 0.003352810681182319)
World Geodetic Coordinates System¶
This class is used internally to perform conversions from geodetic latitude, longitude, and altitude (LLA) coordinates to Earth-centered Earth-fixed (ECEF) coordinates. You can instantiate it from the Python, to do conversions or transformations.
generator = numpy.random.Generator(numpy.random.PCG64(0))
lon = generator.uniform(-180.0, 180.0, 1000000)
lat = generator.uniform(-90.0, 90.0, 1000000)
alt = generator.uniform(-10000, 100000, 1000000)
a = pyinterp.geodetic.Coordinates(wgs84)
b = pyinterp.geodetic.Coordinates(grs80)
elapsed = timeit.timeit('a.transform(b, lon, lat, alt, num_threads=0)',
number=100,
globals={
'a': a,
'b': b,
'lon': lon,
'lat': lat,
'alt': alt
})
print('transform: %f seconds' % (float(elapsed) / 100))
transform: 0.042175 seconds
Geodetic Point¶
This class represents a point determined by its longitude and latitude expressed in degrees.
paris = pyinterp.geodetic.Point(2.3488, 48.8534)
new_york = pyinterp.geodetic.Point(-73.9385, 40.6643)
It is possible to instantiate these objects from the representation in Well-known text (WKT) format or to display it.
print(paris.wkt())
print(pyinterp.geodetic.Point.read_wkt(paris.wkt()) == paris)
POINT(2.3488 48.8534)
True
It’s possible to calculate the distances between the points using different strategies.
print(paris.distance(new_york, strategy='thomas', wgs=wgs84))
print(paris.distance(new_york, strategy='andoyer', wgs=wgs84))
print(paris.distance(new_york, strategy='vincenty', wgs=wgs84))
5851422.737557736
5851415.8055499615
5851422.739380211
It is possible to do the same calculation on a large number of coordinates quickly.
lon = numpy.arange(0, 360, 10, dtype=numpy.float64)
lat = numpy.arange(-90, 90.5, 10, dtype=numpy.float64)
mx, my = numpy.meshgrid(lon, lat)
distances = pyinterp.geodetic.coordinate_distances(mx.ravel(),
my.ravel(),
mx.ravel() + 1.0,
my.ravel() + 1.0,
strategy='vincenty',
wgs=wgs84,
num_threads=1)
distances = distances.reshape(mx.shape)
print(distances[:, 0])
[ 111693.86491427 113492.0455989 118205.54783325 124972.060567
132725.47791087 140442.94773945 147269.62885486 152555.24897049
155851.49814427 156899.5682913 155620.20173848 152110.33851807
146647.19941715 139698.75539215 131935.96278038 124233.13141413
117624.97692781 113170.2681493 19892237.59370932]
Geodetic Box & Polygon¶
This class represents a box made of two describing points.
box = pyinterp.geodetic.Box(new_york, paris)
print(box.wkt())
# %%
# A box is a polygon, but it is more easily constructed.
polygon = pyinterp.geodetic.Polygon.read_wkt(box.wkt())
print(polygon.wkt())
POLYGON((-73.9385 40.6643,-73.9385 48.8534,2.3488 48.8534,2.3488 40.6643,-73.9385 40.6643))
POLYGON((-73.9385 40.6643,-73.9385 48.8534,2.3488 48.8534,2.3488 40.6643,-73.9385 40.6643))
It’s possible to use different algorithms on these objects.
print(f'{polygon.area(wgs=wgs84) * 1e-3} km2')
4967683937.906208 km2
Transform this polygon into a bounding box
polygon = pyinterp.geodetic.Polygon.read_wkt('POLYGON((0 0,0 7,4 2,2 0,0 0))')
print(polygon.envelope())
((0, 0), (4, 7))
It is possible to use these objects to select coordinates in an area of interest.
coordinates = [[-36.25, -54.9238], [-36.5, -54.9238], [-36.75, -54.9238],
[-37, -54.9238], [-37.25, -54.9238], [-37.5, -54.9238],
[-37.75, -54.9238], [-38, -54.9238], [-38.25, -54.9238],
[-38.5, -54.9238], [-38.75, -54.9238], [-39, -54.9238],
[-39.25, -54.9238], [-39.5, -54.9238], [-39.75, -54.9238],
[-40, -54.9238], [-40.25, -54.9238], [-40.5, -54.9238],
[-40.75, -54.9238], [-41, -54.9238], [-41.25, -54.9238],
[-41.5, -54.9238], [-41.75, -54.9238], [-42, -54.9238],
[-42.25, -54.9238], [-42.5, -54.9238], [-42.75, -54.9238],
[-43, -54.9238], [-43.25, -54.9238], [-43.5, -54.9238],
[-43.75, -54.9238], [-44, -54.9238], [-44.25, -54.9238],
[-44.5, -54.9238], [-44.75, -54.9238], [-45, -54.9238],
[-45.25, -54.9238], [-45.5, -54.9238], [-45.75, -54.9238],
[-46, -54.9238], [-46.25, -54.9238], [-46.5, -54.9238],
[-46.75, -54.9238], [-47, -54.9238], [-47.25, -54.9238],
[-47.5, -54.9238], [-47.75, -54.9238], [-48, -54.9238],
[-48.25, -54.9238], [-48.5, -54.9238], [-48.75, -54.9238],
[-49, -54.9238], [-49.25, -54.9238], [-49.5, -54.9238],
[-49.75, -54.9238], [-50, -54.9238], [-50.25, -54.9238],
[-50.5, -54.9238], [-50.75, -54.9238], [-51, -54.9238],
[-51.25, -54.9238], [-51.5, -54.9238], [-51.75, -54.9238],
[-52, -54.9238], [-52.25, -54.9238], [-52.5, -54.9238],
[-52.75, -54.9238], [-53, -54.9238], [-53.25, -54.9238],
[-53.5, -54.9238], [-53.75, -54.9238], [-54, -54.9238],
[-54.25, -54.9238], [-54.5, -54.9238], [-54.75, -54.9238],
[-55, -54.9238], [-55.25, -54.9238], [-55.5, -54.9238],
[-55.75, -54.9238], [-56, -54.9238], [-56.25, -54.9238],
[-56.5, -54.9238], [-56.75, -54.9238], [-57, -54.9238],
[-57.25, -54.9238], [-57.5, -54.9238], [-57.75, -54.9238],
[-58, -54.9238], [-58.25, -54.9238], [-58.5, -54.9238],
[-58.75, -54.9238], [-59, -54.9238], [-59.25, -54.9238],
[-59.5, -54.9238], [-59.75, -54.9238], [-60, -54.9238],
[-60.25, -54.9238], [-60.5, -54.9238], [-60.75, -54.9238],
[-61, -54.9238], [-61.25, -54.9238], [-61.5, -54.9238],
[-61.75, -54.9238], [-62, -54.9238], [-62.25, -54.9238],
[-62.5, -54.9238], [-62.75, -54.9238], [-63, -54.9238],
[-63.25, -54.9238], [-63.5, -54.9238], [-63.75, -54.9238],
[-64, -54.9238], [-64.25, -54.9238], [-64.5, -54.9238],
[-64.75, -54.9238], [-65, -54.9238], [-65.25, -54.9238],
[-65.5, -54.9238], [-66.25, -54.4905], [-66.5, -54.345],
[-67.25, -54.0525], [-67.5, -53.9055], [-67.75, -53.7579],
[-68, -53.4613], [-69.25, -52.5588], [-69.25, -52.4066],
[-69.25, -52.2538], [-69, -51.1695], [-69, -51.0125],
[-69, -50.855], [-69, -50.6969], [-69, -50.5383],
[-68.75, -50.3791], [-67.5, -49.0865], [-67.5, -46.3975],
[-67.5, -46.2248], [-67.5, -46.0515], [-67.25, -45.7035],
[-67, -45.3532], [-66.25, -45.0007], [-65.25, -43.7499],
[-65, -42.1026], [-65, -41.9168], [-65, -41.7305],
[-65, -41.5437], [-65, -41.3563], [-65, -41.1684],
[-65, -40.9799], [-64.75, -40.9799], [-62.25, -39.0656],
[-62, -39.0656], [-61.75, -39.0656], [-61.5, -39.0656],
[-61.25, -39.0656], [-61, -39.0656], [-60, -38.8713],
[-59.75, -38.8713], [-58.25, -34.4619], [-58.25, -34.2555],
[-58, -34.2555], [-57, -34.6678], [-55.75, -34.8731],
[-55.5, -34.8731], [-53.5, -34.0486], [-53.25, -33.8412],
[-53, -33.6333], [-52.5, -33.0066], [-52.25, -32.3754],
[-52, -32.164], [-51.75, -31.9522], [-51.5, -31.7398],
[-51, -31.3136], [-50.25, -30.4554], [-50, -29.8068],
[-49.5, -29.1539], [-49.25, -28.9353], [-48.5, -27.1704],
[-48.5, -26.9478], [-48.5, -26.7247], [-48.5, -26.5012],
[-48.5, -26.2772], [-48.5, -26.0528], [-48.5, -25.828],
[-48.25, -25.3771], [-47.75, -24.9245], [-47, -24.4703],
[-46.75, -24.2425], [-46, -23.7858], [-44.5, -23.0977],
[-44.25, -23.0977], [-44, -23.0977], [-43.75, -23.0977],
[-43.5, -23.0977], [-41.75, -22.4061], [-41, -21.4785],
[-40.75, -21.0125], [-40.25, -20.3107], [-40, -19.8411],
[-39.5, -18.424], [-39.5, -18.1867], [-39, -16.7559],
[-39, -16.5164], [-39, -15.0731], [-39, -14.8315],
[-39, -14.5897], [-39, -14.3477], [-39, -14.1053],
[-38.75, -13.1335], [-37.5, -11.9132], [-37.25, -11.4236],
[-37, -10.933], [-35.75, -9.70328], [-35, -8.71619],
[-34.75, -7.72648], [-34.75, -7.47867], [-36.75, -4.99367],
[-37.25, -4.74457], [-38, -4.24611], [-38.25, -3.99675],
[-39.25, -3.24826], [-39.75, -2.99863], [-40.75, -2.74894],
[-41, -2.74894], [-41.25, -2.74894], [-41.5, -2.74894],
[-41.75, -2.74894], [-42, -2.74894], [-44.25, -2.74894],
[-44.5, -2.74894], [-46.5, -0.999949], [-48.25, -0.999949],
[-48.5, -0.999949], [-48.5, -0.749979], [-48.5, -0.499994],
[-48.5, -0.249999], [-48.25, -0.249999], [-48, -0.249999],
[-47.75, -0.249999], [-47.5, -0.249999], [-47.25, -0.249999],
[-47, -0.249999], [-46.75, -0.249999], [-46.5, -0.249999],
[-46.25, -0.249999], [-46, -0.249999], [-45.75, -0.249999],
[-45.5, -0.249999], [-45.25, -0.249999], [-45, -0.249999],
[-44.75, -0.249999], [-44.5, -0.249999], [-44.25, -0.249999],
[-44, -0.249999], [-43.75, -0.249999], [-43.5, -0.249999],
[-43.25, -0.249999], [-43, -0.249999], [-42.75, -0.249999],
[-42.5, -0.249999], [-42.25, -0.249999], [-42, -0.249999],
[-41.75, -0.249999], [-41.5, -0.249999], [-41.25, -0.249999],
[-41, -0.249999], [-40.75, -0.249999], [-40.5, -0.249999],
[-40.25, -0.249999], [-40, -0.249999], [-39.75, -0.249999],
[-39.5, -0.249999], [-39.25, -0.249999], [-39, -0.249999],
[-38.75, -0.249999], [-38.5, -0.249999], [-38.25, -0.249999],
[-38, -0.249999], [-37.75, -0.249999], [-37.5, -0.249999],
[-37.25, -0.249999], [-37, -0.249999], [-36.75, -0.249999],
[-36.5, -0.249999], [-36.25, -0.249999], [-36, -0.249999],
[-35.75, -0.249999], [-35.5, -0.249999], [-35.25, -0.249999],
[-35, -0.249999], [-34.75, -0.249999], [-34.5, -0.249999],
[-34.25, -0.249999], [-34, -0.249999], [-33.75, -0.249999],
[-33.5, -0.249999], [-33.25, -0.249999], [-33, -0.249999],
[-32.75, -0.249999], [-32.5, -0.249999], [-32.25, -0.249999],
[-32, -0.249999], [-31.75, -0.249999], [-31.5, -0.249999],
[-31.25, -0.249999], [-31, -0.249999], [-30.75, -0.249999],
[-30.5, -0.249999], [-30.25, -0.249999], [-30, -0.249999],
[-29.75, -0.249999], [-29.5, -0.249999], [-29.25, -0.249999],
[-29, -0.249999], [-28.75, -0.249999], [-28.5, -0.249999],
[-28.25, -0.249999], [-28, -0.249999], [-27.75, -0.249999],
[-27.5, -0.249999], [-27.25, -0.249999], [-27, -0.249999],
[-26.75, -0.249999], [-26.5, -0.249999], [-26.25, -0.249999],
[-26, -0.249999], [-25.75, -0.249999], [-25.5, -0.249999],
[-25.25, -0.249999], [-25, -0.249999], [-24.75, -0.249999],
[-24.5, -0.249999], [-24.25, -0.249999], [-24, -0.249999],
[-23.75, -0.249999], [-23.5, -0.249999], [-23.25, -0.249999],
[-23, -0.249999], [-22.75, -0.249999], [-22.5, -0.249999],
[-22.25, -0.249999], [-22, -0.249999], [-21.75, -0.249999],
[-21.5, -0.249999], [-21.25, -0.249999], [-21, -0.249999],
[-20.75, -0.249999], [-20.5, -0.249999], [-20.25, -0.249999],
[-20, -0.249999], [-19.75, -0.249999], [-19.5, -0.249999],
[-19.25, -0.249999], [-19, -0.249999], [-18.75, -0.249999],
[-18.5, -0.249999], [-18.25, -0.249999], [-18, -0.249999],
[-17.75, -0.249999], [-17.5, -0.249999], [-17.25, -0.249999],
[-17, -0.249999], [-16.75, -0.249999], [-16.5, -0.249999],
[-16.25, -0.249999], [-16, -0.249999], [-15.75, -0.249999],
[-15.5, -0.249999], [-15.25, -0.249999], [-15, -0.249999],
[-14.75, -0.249999], [-14.5, -0.249999], [-14.25, -0.249999],
[-14, -0.249999], [-13.75, -0.249999], [-13.5, -0.249999],
[-13.25, -0.249999], [-13, -0.249999], [-12.75, -0.249999],
[-12.5, -0.249999], [-12.25, -0.249999], [-12, -0.249999],
[-11.75, -0.249999], [-11.5, -0.249999], [-11.25, -0.249999],
[-11, -0.249999], [-10.75, -0.249999], [-10.5, -0.249999],
[-10.25, -0.249999], [-10, -0.249999], [-9.75, -0.249999],
[-9.5, -0.249999], [-9.25, -0.249999], [-9, -0.249999],
[-8.75, -0.249999], [-8.5, -0.249999], [-8.25, -0.249999],
[-8, -0.249999], [-7.75, -0.249999], [-7.5, -0.249999],
[-7.25, -0.249999], [-7, -0.249999], [-6.75, -0.249999],
[-6.5, -0.249999], [-6.25, -0.249999], [-6, -0.249999],
[-5.75, -0.249999], [-5.5, -0.249999], [-5.25, -0.249999],
[-5, -0.249999], [-4.75, -0.249999], [-4.5, -0.249999],
[-4.25, -0.249999], [-4, -0.249999], [-3.75, -0.249999],
[-3.5, -0.249999], [-3.25, -0.249999], [-3, -0.249999],
[-2.75, -0.249999], [-2.5, -0.249999], [-2.25, -0.249999],
[-2, -0.249999], [-1.75, -0.249999], [-1.5, -0.249999],
[-1.25, -0.249999], [-1, -0.249999], [-0.75, -0.249999],
[-0.5, -0.249999], [-0.25, -0.249999], [0, -0.249999],
[0.25, -0.249999], [0.5, -0.249999], [0.75, -0.249999],
[1, -0.249999], [1.25, -0.249999], [1.5, -0.249999],
[1.75, -0.249999], [2, -0.249999], [2.25, -0.249999],
[2.5, -0.249999], [2.75, -0.249999], [3, -0.249999],
[3.25, -0.249999], [3.5, -0.249999], [3.75, -0.249999],
[4, -0.249999], [4.25, -0.249999], [4.5, -0.249999],
[4.75, -0.249999], [5, -0.249999], [5.25, -0.249999],
[5.5, -0.249999], [5.75, -0.249999], [6, -0.249999],
[6.25, -0.249999], [6.5, -0.249999], [6.75, -0.249999],
[7, -0.249999], [7.25, -0.249999], [7.5, -0.249999],
[7.75, -0.249999], [8, -0.249999], [8.25, -0.249999],
[8.5, -0.249999], [8.75, -0.249999], [9, -0.249999],
[9.25, -0.249999], [9.75, -2.49921], [10.25, -2.99863],
[10.75, -3.49783], [11.25, -3.99675], [11.75, -4.74457],
[12, -5.24267], [12.25, -5.98906], [12.75, -6.98265],
[13, -7.72648], [13.25, -8.22164], [13.25, -8.46899],
[13.25, -8.71619], [13.5, -10.4417], [13.75, -10.933],
[13.75, -11.1784], [13.75, -11.4236], [13.75, -11.6685],
[13.75, -11.9132], [13.5, -12.402], [12.5, -13.6199],
[12.25, -14.5897], [12, -15.5553], [11.75, -16.7559],
[12.5, -19.1341], [12.75, -19.6058], [13, -20.0761],
[13.25, -20.545], [13.5, -21.0125], [13.75, -21.4785],
[14.25, -22.1747], [14.5, -22.637], [14.5, -22.8675],
[14.5, -24.2425], [14.75, -24.9245], [14.75, -25.151],
[14.75, -25.3771], [15, -26.5012], [16, -28.2769],
[16.5, -28.7163], [16.75, -29.1539], [17, -29.8068],
[17.25, -30.4554], [17.5, -30.8855], [18, -31.5269],
[18.25, -31.9522], [18.25, -32.164], [18.25, -32.3754],
[19.25, -34.4619], [19.75, -34.8731], [19.75, -35.078],
[19.75, -35.2823], [19.75, -35.4861], [19.75, -35.6894],
[19.75, -35.8922], [19.75, -36.0945], [19.75, -36.2962],
[19.75, -36.4975], [19.75, -36.6982], [19.75, -36.8984],
[19.75, -37.098], [19.75, -37.2972], [19.75, -37.4958],
[19.75, -37.6939], [19.75, -37.8914], [19.75, -38.0885],
[19.75, -38.285], [19.75, -38.4809], [19.75, -38.6764],
[19.75, -38.8713], [19.75, -39.0656], [19.75, -39.2595],
[19.75, -39.4528], [19.75, -39.6456], [19.75, -39.8378],
[19.75, -40.0295], [19.75, -40.2206], [19.75, -40.4113],
[19.75, -40.6013], [19.75, -40.7909], [19.75, -40.9799],
[19.75, -41.1684], [19.75, -41.3563], [19.75, -41.5437],
[19.75, -41.7305], [19.75, -41.9168], [19.75, -42.1026],
[19.75, -42.2878], [19.75, -42.4725], [19.75, -42.6566],
[19.75, -42.8402], [19.75, -43.0232], [19.75, -43.2057],
[19.75, -43.3877], [19.75, -43.5691], [19.75, -43.7499],
[19.75, -43.9303], [19.75, -44.11], [19.75, -44.2893],
[19.75, -44.4679], [19.75, -44.6461], [19.75, -44.8237],
[19.75, -45.0007], [19.75, -45.1772], [19.75, -45.3532],
[19.75, -45.5286], [19.75, -45.7035], [19.75, -45.8778],
[19.75, -46.0515], [19.75, -46.2248], [19.75, -46.3975],
[19.75, -46.5696], [19.75, -46.7412], [19.75, -46.9123],
[19.75, -47.0828], [19.75, -47.2527], [19.75, -47.4221],
[19.75, -47.591], [19.75, -47.7593], [19.75, -47.9271],
[19.75, -48.0944], [19.75, -48.2611], [19.75, -48.4273],
[19.75, -48.5929], [19.75, -48.758], [19.75, -48.9225],
[19.75, -49.0865], [19.75, -49.25], [19.75, -49.4129],
[19.75, -49.5753], [19.75, -49.7371], [19.75, -49.8984],
[19.75, -50.0592], [19.75, -50.2194], [19.75, -50.3791],
[19.75, -50.5383], [19.75, -50.6969], [19.75, -50.855],
[19.75, -51.0125], [19.75, -51.1695], [19.75, -51.326],
[19.75, -51.482], [19.75, -51.6374], [19.75, -51.7923],
[19.75, -51.9467], [19.75, -52.1005], [19.75, -52.2538],
[19.75, -52.4066], [19.75, -52.5588], [19.75, -52.7106],
[19.75, -52.8618], [19.75, -53.0124], [19.75, -53.1626],
[19.75, -53.3122], [19.75, -53.4613], [19.75, -53.6099],
[19.75, -53.7579], [19.75, -53.9055], [19.75, -54.0525],
[19.75, -54.199], [19.75, -54.345], [19.75, -54.4905],
[19.75, -54.6354], [19.75, -54.7799], [19.75, -54.9238],
[19.5, -54.9238], [19.25, -54.9238], [19, -54.9238],
[18.75, -54.9238], [18.5, -54.9238], [18.25, -54.9238],
[18, -54.9238], [17.75, -54.9238], [17.5, -54.9238],
[17.25, -54.9238], [17, -54.9238], [16.75, -54.9238],
[16.5, -54.9238], [16.25, -54.9238], [16, -54.9238],
[15.75, -54.9238], [15.5, -54.9238], [15.25, -54.9238],
[15, -54.9238], [14.75, -54.9238], [14.5, -54.9238],
[14.25, -54.9238], [14, -54.9238], [13.75, -54.9238],
[13.5, -54.9238], [13.25, -54.9238], [13, -54.9238],
[12.75, -54.9238], [12.5, -54.9238], [12.25, -54.9238],
[12, -54.9238], [11.75, -54.9238], [11.5, -54.9238],
[11.25, -54.9238], [11, -54.9238], [10.75, -54.9238],
[10.5, -54.9238], [10.25, -54.9238], [10, -54.9238],
[9.75, -54.9238], [9.5, -54.9238], [9.25, -54.9238],
[9, -54.9238], [8.75, -54.9238], [8.5, -54.9238],
[8.25, -54.9238], [8, -54.9238], [7.75, -54.9238],
[7.5, -54.9238], [7.25, -54.9238], [7, -54.9238],
[6.75, -54.9238], [6.5, -54.9238], [6.25, -54.9238],
[6, -54.9238], [5.75, -54.9238], [5.5, -54.9238],
[5.25, -54.9238], [5, -54.9238], [4.75, -54.9238],
[4.5, -54.9238], [4.25, -54.9238], [4, -54.9238],
[3.75, -54.9238], [3.5, -54.9238], [3.25, -54.9238],
[3, -54.9238], [2.75, -54.9238], [2.5, -54.9238],
[2.25, -54.9238], [2, -54.9238], [1.75, -54.9238],
[1.5, -54.9238], [1.25, -54.9238], [1, -54.9238],
[0.75, -54.9238], [0.5, -54.9238], [0.25, -54.9238],
[-1.81899e-12, -54.9238], [-0.25, -54.9238], [-0.5, -54.9238],
[-0.75, -54.9238], [-1, -54.9238], [-1.25, -54.9238],
[-1.5, -54.9238], [-1.75, -54.9238], [-2, -54.9238],
[-2.25, -54.9238], [-2.5, -54.9238], [-2.75, -54.9238],
[-3, -54.9238], [-3.25, -54.9238], [-3.5, -54.9238],
[-3.75, -54.9238], [-4, -54.9238], [-4.25, -54.9238],
[-4.5, -54.9238], [-4.75, -54.9238], [-5, -54.9238],
[-5.25, -54.9238], [-5.5, -54.9238], [-5.75, -54.9238],
[-6, -54.9238], [-6.25, -54.9238], [-6.5, -54.9238],
[-6.75, -54.9238], [-7, -54.9238], [-7.25, -54.9238],
[-7.5, -54.9238], [-7.75, -54.9238], [-8, -54.9238],
[-8.25, -54.9238], [-8.5, -54.9238], [-8.75, -54.9238],
[-9, -54.9238], [-9.25, -54.9238], [-9.5, -54.9238],
[-9.75, -54.9238], [-10, -54.9238], [-10.25, -54.9238],
[-10.5, -54.9238], [-10.75, -54.9238], [-11, -54.9238],
[-11.25, -54.9238], [-11.5, -54.9238], [-11.75, -54.9238],
[-12, -54.9238], [-12.25, -54.9238], [-12.5, -54.9238],
[-12.75, -54.9238], [-13, -54.9238], [-13.25, -54.9238],
[-13.5, -54.9238], [-13.75, -54.9238], [-14, -54.9238],
[-14.25, -54.9238], [-14.5, -54.9238], [-14.75, -54.9238],
[-15, -54.9238], [-15.25, -54.9238], [-15.5, -54.9238],
[-15.75, -54.9238], [-16, -54.9238], [-16.25, -54.9238],
[-16.5, -54.9238], [-16.75, -54.9238], [-17, -54.9238],
[-17.25, -54.9238], [-17.5, -54.9238], [-17.75, -54.9238],
[-18, -54.9238], [-18.25, -54.9238], [-18.5, -54.9238],
[-18.75, -54.9238], [-19, -54.9238], [-19.25, -54.9238],
[-19.5, -54.9238], [-19.75, -54.9238], [-20, -54.9238],
[-20.25, -54.9238], [-20.5, -54.9238], [-20.75, -54.9238],
[-21, -54.9238], [-21.25, -54.9238], [-21.5, -54.9238],
[-21.75, -54.9238], [-22, -54.9238], [-22.25, -54.9238],
[-22.5, -54.9238], [-22.75, -54.9238], [-23, -54.9238],
[-23.25, -54.9238], [-23.5, -54.9238], [-23.75, -54.9238],
[-24, -54.9238], [-24.25, -54.9238], [-24.5, -54.9238],
[-24.75, -54.9238], [-25, -54.9238], [-25.25, -54.9238],
[-25.5, -54.9238], [-25.75, -54.9238], [-26, -54.9238],
[-26.25, -54.9238], [-26.5, -54.9238], [-26.75, -54.9238],
[-27, -54.9238], [-27.25, -54.9238], [-27.5, -54.9238],
[-27.75, -54.9238], [-28, -54.9238], [-28.25, -54.9238],
[-28.5, -54.9238], [-28.75, -54.9238], [-29, -54.9238],
[-29.25, -54.9238], [-29.5, -54.9238], [-29.75, -54.9238],
[-30, -54.9238], [-30.25, -54.9238], [-30.5, -54.9238],
[-30.75, -54.9238], [-31, -54.9238], [-31.25, -54.9238],
[-31.5, -54.9238], [-31.75, -54.9238], [-32, -54.9238],
[-32.25, -54.9238], [-32.5, -54.9238], [-32.75, -54.9238],
[-33, -54.9238], [-33.25, -54.9238], [-33.5, -54.9238],
[-33.75, -54.9238], [-34, -54.9238], [-34.25, -54.9238],
[-34.5, -54.9238], [-34.75, -54.9238], [-35, -54.9238],
[-35.25, -54.9238], [-35.5, -54.9238], [-35.75, -54.9238],
[-36, -54.9238], [-36.25, -54.9238]]
lon = numpy.arange(0, 360, 10, dtype=numpy.float64)
lat = numpy.arange(-80, 90, 10, dtype=numpy.float64)
mx, my = numpy.meshgrid(lon, lat)
Creates the polython
Display of the selection.
fig = matplotlib.pyplot.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection=cartopy.crs.PlateCarree())
ax.add_feature(cartopy.feature.LAND)
ax.gridlines(draw_labels=True, dms=True, x_inline=False, y_inline=False)
ax.coastlines()
ax.scatter(mx.ravel(),
my.ravel(),
c=mask,
cmap='bwr_r',
transform=cartopy.crs.PlateCarree(),
vmin=0,
vmax=1)
fig.show()
Crossover¶
The class handle the calculation of the crossover between two lines. We initialize two lines corresponding to two half-orbits of a satellite.
lon1 = numpy.array([234.068292, 234.092812, 234.117362, 234.141943],
dtype=numpy.float64)
lat1 = numpy.array([-67.11689, -67.132143, -67.147393, -67.162639],
dtype=numpy.float64)
lon2 = numpy.array([234.061488, 234.086091, 234.110664, 234.135205],
dtype=numpy.float64)
lat2 = numpy.array([-67.183321, -67.168076, -67.152826, -67.137573],
dtype=numpy.float64)
We create the two lines and the crossover.
We can check if there is a crossing between these two lines.
print(f'There is a crossover between these two lines: {crossover.exists()}')
There is a crossover between these two lines: True
We can get the crossing point.
coordinates = crossover.search()
assert coordinates is not None
print(f'The crossing point is: {coordinates}')
The crossing point is: (-125.882, -67.148)
It is possible to obtain the points on the two lines nearest to the crossing point.
nearest_indices = crossover.nearest(coordinates)
assert nearest_indices is not None
print('The nearest points on the line #1: ' +
str(crossover.half_orbit_1[nearest_indices[0]]))
print('The nearest points on the line #2: ' +
str(crossover.half_orbit_2[nearest_indices[1]]))
The nearest points on the line #1: (234.117, -67.1474)
The nearest points on the line #2: (234.111, -67.1528)
Finally, the information found is displayed to verify the data found.
fig = matplotlib.pyplot.figure(figsize=(10, 8))
ax = fig.add_subplot(111, projection=cartopy.crs.PlateCarree())
ax.add_feature(cartopy.feature.LAND)
ax.plot(lon1, lat1, '-o', color='red', transform=cartopy.crs.PlateCarree())
ax.plot(lon2, lat2, '-o', color='blue', transform=cartopy.crs.PlateCarree())
ax.plot(coordinates.lon,
coordinates.lat,
'-o',
color='green',
transform=cartopy.crs.PlateCarree())
ax.plot(lon1[nearest_indices[0]],
lat1[nearest_indices[0]],
'o',
color='orange',
transform=cartopy.crs.PlateCarree())
ax.plot(lon2[nearest_indices[1]],
lat2[nearest_indices[1]],
'o',
color='orange',
transform=cartopy.crs.PlateCarree())
ax.gridlines(draw_labels=True, dms=True, x_inline=False, y_inline=False)
<cartopy.mpl.gridliner.Gridliner object at 0x12c7de570>
Total running time of the script: (0 minutes 6.023 seconds)
