Add Lambert Equal Area Projection

docs/source/contributors.rst

@@ -28,6 +28,7 @@ the package wouldn't be as rich or diverse as it is today:
  * Lion Krischer
  * Nat Wilson
  * Elliott Sales de Andrade
+ * Laura Dreyer
 
 
 Thank you!

docs/source/crs/projections.rst

@@ -298,7 +298,7 @@ Geostationary
     import matplotlib.pyplot as plt
     import cartopy.crs as ccrs
 
-    plt.figure(figsize=(2.99893683337, 3))
+    plt.figure(figsize=(3, 3))
     ax = plt.axes(projection=ccrs.Geostationary())
     ax.coastlines(resolution='110m')
     ax.gridlines()
@@ -320,6 +320,22 @@ Gnomonic
     ax.gridlines()
 
 
+LambertAzimuthalEqualArea
+-------------------------
+
+.. autoclass:: cartopy.crs.LambertAzimuthalEqualArea
+
+.. plot::
+
+    import matplotlib.pyplot as plt
+    import cartopy.crs as ccrs
+
+    plt.figure(figsize=(3.00670336247, 3))
+    ax = plt.axes(projection=ccrs.LambertAzimuthalEqualArea())
+    ax.coastlines(resolution='110m')
+    ax.gridlines()
+
+
 NorthPolarStereo
 ----------------
 

lib/cartopy/crs.py

@@ -40,6 +40,10 @@
 __document_these__ = ['CRS', 'Geocentric', 'Geodetic', 'Globe']
 
 
+WGS84_SEMIMAJOR_AXIS = 6378137.0
+WGS84_SEMIMINOR_AXIS = 6356752.3142
+
+
 class RotatedGeodetic(CRS):
     """
     Defines a rotated latitude/longitude coordinate system with spherical
@@ -663,8 +667,9 @@ def __init__(self, central_longitude=0.0, globe=None):
         proj4_params = [('proj', 'eqc'), ('lon_0', central_longitude)]
         if globe is None:
             globe = Globe(semimajor_axis=math.degrees(1))
-        x_max = math.radians(globe.semimajor_axis or 6378137.0) * 180
-        y_max = math.radians(globe.semimajor_axis or 6378137.0) * 90
+        a_rad = math.radians(globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS)
+        x_max = a_rad * 180
+        y_max = a_rad * 90
         # Set the threshold around 0.5 if the x max is 180.
         self._threshold = x_max / 360.
         super(PlateCarree, self).__init__(proj4_params, x_max, y_max,
@@ -1000,8 +1005,8 @@ def y_limits(self):
 GOOGLE_MERCATOR = Mercator(min_latitude=-85.0511287798066,
                            max_latitude=85.0511287798066,
                            globe=Globe(ellipse=None,
-                                       semimajor_axis=6378137,
-                                       semiminor_axis=6378137,
+                                       semimajor_axis=WGS84_SEMIMAJOR_AXIS,
+                                       semiminor_axis=WGS84_SEMIMAJOR_AXIS,
                                        nadgrids='@null'))
 
 
@@ -1030,8 +1035,8 @@ def __init__(self, central_longitude=-96.0, central_latitude=39.0,
         """
         Kwargs:
 
-            * central_longitude - The central longitude. Defaults to 0.
-            * central_latitude - The central latitude. Defaults to 0.
+            * central_longitude - The central longitude. Defaults to -96.
+            * central_latitude - The central latitude. Defaults to 39.
             * false_easting - X offset from planar origin in metres.
                               Defaults to 0.
             * false_northing - Y offset from planar origin in metres.
@@ -1140,6 +1145,66 @@ def y_limits(self):
         return self._y_limits
 
 
+class LambertAzimuthalEqualArea(Projection):
+    """
+    A Lambert Azimuthal Equal-Area projection.
+
+    """
+
+    def __init__(self, central_longitude=0.0, central_latitude=0.0,
+                 false_easting=0.0, false_northing=0.0,
+                 globe=None):
+        """
+        Kwargs:
+
+            * central_longitude - The central longitude. Defaults to 0.
+            * central_latitude - The central latitude. Defaults to 0.
+            * false_easting - X offset from planar origin in metres.
+                              Defaults to 0.
+            * false_northing - Y offset from planar origin in metres.
+                               Defaults to 0.
+            * globe - A :class:`cartopy.crs.Globe`.
+                      If omitted, a default globe is created.
+
+        """
+        proj4_params = [('proj', 'laea'),
+                        ('lon_0', central_longitude),
+                        ('lat_0', central_latitude),
+                        ('x_0', false_easting),
+                        ('y_0', false_northing)]
+
+        super(LambertAzimuthalEqualArea, self).__init__(proj4_params,
+                                                        globe=globe)
+
+        a = np.float(self.globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS)
+        b = np.float(self.globe.semiminor_axis or WGS84_SEMIMINOR_AXIS)
+        lon, lat = central_longitude + 180, - central_latitude + 0.01
+        x, max_y = self.transform_point(lon, lat, PlateCarree())
+
+        coords = _ellipse_boundary(a * 1.9999, max_y - false_northing,
+                                   false_easting, false_northing, 61)
+        self._boundary = sgeom.polygon.LinearRing(coords.T)
+        self._x_limits = self._boundary.bounds[::2]
+        self._y_limits = self._boundary.bounds[1::2]
+        self._threshold = np.diff(self._x_limits)[0] * 1e-3
+
+    @property
+    def boundary(self):
+        return self._boundary
+
+    @property
+    def threshold(self):
+        return self._threshold
+
+    @property
+    def x_limits(self):
+        return self._x_limits
+
+    @property
+    def y_limits(self):
+        return self._y_limits
+
+
 class Miller(_RectangularProjection):
     def __init__(self, central_longitude=0.0):
         proj4_params = [('proj', 'mill'), ('lon_0', central_longitude)]
@@ -1235,14 +1300,14 @@ def __init__(self, central_latitude=0.0, central_longitude=0.0,
         super(Stereographic, self).__init__(proj4_params, globe=globe)
 
         # TODO: Let the globe return the semimajor axis always.
-        a = np.float(self.globe.semimajor_axis or 6378137.0)
-        b = np.float(self.globe.semiminor_axis or 6356752.3142)
+        a = np.float(self.globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS)
+        b = np.float(self.globe.semiminor_axis or WGS84_SEMIMINOR_AXIS)
 
         # Note: The magic number has been picked to maintain consistent
         # behaviour with a wgs84 globe. There is no guarantee that the scaling
         # should even be linear.
-        x_axis_offset = 5e7 / 6378137.
-        y_axis_offset = 5e7 / 6356752.3142
+        x_axis_offset = 5e7 / WGS84_SEMIMAJOR_AXIS
+        y_axis_offset = 5e7 / WGS84_SEMIMINOR_AXIS
         self._x_limits = (-a * x_axis_offset + false_easting,
                           a * x_axis_offset + false_easting)
         self._y_limits = (-b * y_axis_offset + false_northing,
@@ -1295,7 +1360,7 @@ def __init__(self, central_longitude=0.0, central_latitude=0.0,
         super(Orthographic, self).__init__(proj4_params, globe=globe)
 
         # TODO: Let the globe return the semimajor axis always.
-        a = np.float(self.globe.semimajor_axis or 6378137.0)
+        a = np.float(self.globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS)
         b = np.float(self.globe.semiminor_axis or a)
 
         if b != a:
@@ -1545,7 +1610,7 @@ def __init__(self, central_longitude=0.0, satellite_height=35785831,
         super(Geostationary, self).__init__(proj4_params, globe=globe)
 
         # TODO: Let the globe return the semimajor axis always.
-        a = np.float(self.globe.semimajor_axis or 6378137.0)
+        a = np.float(self.globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS)
         b = np.float(self.globe.semiminor_axis or a)
         h = np.float(satellite_height)
         max_x = h * math.atan(a / (a + h))
@@ -1686,7 +1751,7 @@ def __init__(self, central_longitude=0.0, central_latitude=0.0,
         super(AzimuthalEquidistant, self).__init__(proj4_params, globe=globe)
 
         # TODO: Let the globe return the semimajor axis always.
-        a = np.float(self.globe.semimajor_axis or 6378137.0)
+        a = np.float(self.globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS)
         b = np.float(self.globe.semiminor_axis or a)
 
         coords = _ellipse_boundary(a * np.pi, b * np.pi,

lib/cartopy/tests/crs/test_lambert_azimuthal_equal_area.py

@@ -0,0 +1,71 @@
+# (C) British Crown Copyright 2015, Met Office
+#
+# This file is part of cartopy.
+#
+# cartopy is free software: you can redistribute it and/or modify it under
+# the terms of the GNU Lesser General Public License as published by the
+# Free Software Foundation, either version 3 of the License, or
+# (at your option) any later version.
+#
+# cartopy is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU Lesser General Public License for more details.
+#
+# You should have received a copy of the GNU Lesser General Public License
+# along with cartopy.  If not, see <http://www.gnu.org/licenses/>.
+
+from __future__ import (absolute_import, division, print_function)
+
+import unittest
+
+import numpy as np
+from numpy.testing import assert_almost_equal
+from nose.tools import assert_equal
+
+import cartopy.crs as ccrs
+
+
+class TestLambertAzimuthalEqualArea(unittest.TestCase):
+    def test_default(self):
+        crs = ccrs.LambertAzimuthalEqualArea()
+        expected = ('+ellps=WGS84 +proj=laea +lon_0=0.0 '
+                    '+lat_0=0.0 +x_0=0.0 +y_0=0.0 +no_defs')
+        assert_equal(crs.proj4_init, expected)
+
+        assert_almost_equal(np.array(crs.x_limits),
+                            [-12755636.1863, 12755636.1863],
+                            decimal=4)
+        assert_almost_equal(np.array(crs.y_limits),
+                            [-12727770.598700099, 12727770.598700099],
+                            decimal=4)
+
+    def test_eccentric_globe(self):
+        globe = ccrs.Globe(semimajor_axis=1000, semiminor_axis=500,
+                           ellipse=None)
+        crs = ccrs.LambertAzimuthalEqualArea(globe=globe)
+        expected = ('+a=1000 +b=500 +proj=laea +lon_0=0.0 +lat_0=0.0 '
+                    '+x_0=0.0 +y_0=0.0 +no_defs')
+        assert_equal(crs.proj4_init, expected)
+
+        assert_almost_equal(np.array(crs.x_limits),
+                            [-1999.9, 1999.9], decimal=1)
+        assert_almost_equal(np.array(crs.y_limits),
+                            [-1380.17298647, 1380.17298647], decimal=4)
+
+    def test_offset(self):
+        crs = ccrs.LambertAzimuthalEqualArea()
+        crs_offset = ccrs.LambertAzimuthalEqualArea(false_easting=1234,
+                                                    false_northing=-4321)
+        expected = ('+ellps=WGS84 +proj=laea +lon_0=0.0 +lat_0=0.0 '
+                    '+x_0=1234 +y_0=-4321 +no_defs')
+        assert_equal(crs_offset.proj4_init, expected)
+        assert_equal(tuple(np.array(crs.x_limits) + 1234),
+                     crs_offset.x_limits)
+        assert_equal(tuple(np.array(crs.y_limits) - 4321),
+                     crs_offset.y_limits)
+
+
+if __name__ == '__main__':
+    import nose
+    nose.runmodule(argv=['-s', '--with-doctest'], exit=False)