.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/ex_geodetic.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code. or to run this example in your browser via Binder .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_ex_geodetic.py: ******** 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. .. GENERATED FROM PYTHON SOURCE LINES 18-30 .. code-block:: Python import timeit import cartopy.crs import cartopy.feature import matplotlib.pyplot import numpy import pyinterp.geodetic wgs84 = pyinterp.geodetic.Spheroid() print(wgs84) .. rst-class:: sphx-glr-script-out .. code-block:: none Spheroid(6378137.0, 0.0033528106647474805) .. GENERATED FROM PYTHON SOURCE LINES 31-32 You can instantiate other systems. .. GENERATED FROM PYTHON SOURCE LINES 32-35 .. code-block:: Python grs80 = pyinterp.geodetic.Spheroid((6378137, 1 / 298.257222101)) print(grs80) .. rst-class:: sphx-glr-script-out .. code-block:: none Spheroid(6378137.0, 0.003352810681182319) .. GENERATED FROM PYTHON SOURCE LINES 36-43 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. .. GENERATED FROM PYTHON SOURCE LINES 43-62 .. code-block:: Python 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)) .. rst-class:: sphx-glr-script-out .. code-block:: none transform: 0.042175 seconds .. GENERATED FROM PYTHON SOURCE LINES 63-68 Geodetic Point ============== This class represents a point determined by its longitude and latitude expressed in degrees. .. GENERATED FROM PYTHON SOURCE LINES 68-71 .. code-block:: Python paris = pyinterp.geodetic.Point(2.3488, 48.8534) new_york = pyinterp.geodetic.Point(-73.9385, 40.6643) .. GENERATED FROM PYTHON SOURCE LINES 72-74 It is possible to instantiate these objects from the representation in Well-known text (WKT) format or to display it. .. GENERATED FROM PYTHON SOURCE LINES 74-77 .. code-block:: Python print(paris.wkt()) print(pyinterp.geodetic.Point.read_wkt(paris.wkt()) == paris) .. rst-class:: sphx-glr-script-out .. code-block:: none POINT(2.3488 48.8534) True .. GENERATED FROM PYTHON SOURCE LINES 78-81 It's possible to calculate the distances between the points using different strategies. .. GENERATED FROM PYTHON SOURCE LINES 81-85 .. code-block:: Python 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)) .. rst-class:: sphx-glr-script-out .. code-block:: none 5851422.737557736 5851415.8055499615 5851422.739380211 .. GENERATED FROM PYTHON SOURCE LINES 86-88 It is possible to do the same calculation on a large number of coordinates quickly. .. GENERATED FROM PYTHON SOURCE LINES 88-101 .. code-block:: Python 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]) .. rst-class:: sphx-glr-script-out .. code-block:: none [ 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] .. GENERATED FROM PYTHON SOURCE LINES 102-106 Geodetic Box & Polygon ====================== This class represents a box made of two describing points. .. GENERATED FROM PYTHON SOURCE LINES 106-114 .. code-block:: Python 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()) .. rst-class:: sphx-glr-script-out .. code-block:: none 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)) .. GENERATED FROM PYTHON SOURCE LINES 115-116 It's possible to use different algorithms on these objects. .. GENERATED FROM PYTHON SOURCE LINES 116-117 .. code-block:: Python print(f'{polygon.area(wgs=wgs84) * 1e-3} km2') .. rst-class:: sphx-glr-script-out .. code-block:: none 4967683937.906208 km2 .. GENERATED FROM PYTHON SOURCE LINES 118-119 Transform this polygon into a bounding box .. GENERATED FROM PYTHON SOURCE LINES 119-122 .. code-block:: Python polygon = pyinterp.geodetic.Polygon.read_wkt('POLYGON((0 0,0 7,4 2,2 0,0 0))') print(polygon.envelope()) .. rst-class:: sphx-glr-script-out .. code-block:: none ((0, 0), (4, 7)) .. GENERATED FROM PYTHON SOURCE LINES 123-125 It is possible to use these objects to select coordinates in an area of interest. .. GENERATED FROM PYTHON SOURCE LINES 125-411 .. code-block:: Python 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, 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[-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, 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-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]] .. GENERATED FROM PYTHON SOURCE LINES 412-416 .. code-block:: Python lon = numpy.arange(0, 360, 10, dtype=numpy.float64) lat = numpy.arange(-80, 90, 10, dtype=numpy.float64) mx, my = numpy.meshgrid(lon, lat) .. GENERATED FROM PYTHON SOURCE LINES 417-418 Creates the polython .. GENERATED FROM PYTHON SOURCE LINES 418-423 .. code-block:: Python polygon = pyinterp.geodetic.Polygon( [pyinterp.geodetic.Point(*item) for item in coordinates]) mask = polygon.covered_by(mx.ravel(), my.ravel()) mask = mask.reshape(mx.shape) .. GENERATED FROM PYTHON SOURCE LINES 424-425 Display of the selection. .. GENERATED FROM PYTHON SOURCE LINES 425-439 .. code-block:: Python 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() .. image-sg:: /auto_examples/images/sphx_glr_ex_geodetic_001.png :alt: ex geodetic :srcset: /auto_examples/images/sphx_glr_ex_geodetic_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 440-445 Crossover ========= The class handle the calculation of the crossover between two lines. We initialize two lines corresponding to two half-orbits of a satellite. .. GENERATED FROM PYTHON SOURCE LINES 445-454 .. code-block:: Python 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) .. GENERATED FROM PYTHON SOURCE LINES 455-456 We create the two lines and the crossover. .. GENERATED FROM PYTHON SOURCE LINES 456-460 .. code-block:: Python crossover = pyinterp.geodetic.Crossover( pyinterp.geodetic.LineString(lon1, lat1), pyinterp.geodetic.LineString(lon2, lat2)) .. GENERATED FROM PYTHON SOURCE LINES 461-462 We can check if there is a crossing between these two lines. .. GENERATED FROM PYTHON SOURCE LINES 462-464 .. code-block:: Python print(f'There is a crossover between these two lines: {crossover.exists()}') .. rst-class:: sphx-glr-script-out .. code-block:: none There is a crossover between these two lines: True .. GENERATED FROM PYTHON SOURCE LINES 465-466 We can get the crossing point. .. GENERATED FROM PYTHON SOURCE LINES 466-470 .. code-block:: Python coordinates = crossover.search() assert coordinates is not None print(f'The crossing point is: {coordinates}') .. rst-class:: sphx-glr-script-out .. code-block:: none The crossing point is: (-125.882, -67.148) .. GENERATED FROM PYTHON SOURCE LINES 471-473 It is possible to obtain the points on the two lines nearest to the crossing point. .. GENERATED FROM PYTHON SOURCE LINES 473-480 .. code-block:: Python 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]])) .. rst-class:: sphx-glr-script-out .. code-block:: none The nearest points on the line #1: (234.117, -67.1474) The nearest points on the line #2: (234.111, -67.1528) .. GENERATED FROM PYTHON SOURCE LINES 481-482 Finally, the information found is displayed to verify the data found. .. GENERATED FROM PYTHON SOURCE LINES 482-503 .. code-block:: Python 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) .. image-sg:: /auto_examples/images/sphx_glr_ex_geodetic_002.png :alt: ex geodetic :srcset: /auto_examples/images/sphx_glr_ex_geodetic_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 6.023 seconds) .. _sphx_glr_download_auto_examples_ex_geodetic.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/CNES/pangeo-pyinterp/master?urlpath=lab/tree/notebooks/auto_examples/ex_geodetic.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: ex_geodetic.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: ex_geodetic.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: ex_geodetic.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_