Merge pull request #1138 from QuLogic/miller-radius

Add support for other radii in Miller projection + tests

lib/cartopy/crs.py

@@ -1258,11 +1258,24 @@ def y_limits(self):
 
 
 class Miller(_RectangularProjection):
-    def __init__(self, central_longitude=0.0):
+    def __init__(self, central_longitude=0.0, globe=None):
+        if globe is None:
+            globe = Globe(semimajor_axis=math.degrees(1), ellipse=None)
+
+        # TODO: Let the globe return the semimajor axis always.
+        a = np.float(globe.semimajor_axis or WGS84_SEMIMAJOR_AXIS)
+        b = np.float(globe.semiminor_axis or a)
+
+        if b != a or globe.ellipse is not None:
+            warnings.warn('The proj4 "mill" projection does not handle '
+                          'elliptical globes.')
+
         proj4_params = [('proj', 'mill'), ('lon_0', central_longitude)]
-        globe = Globe(semimajor_axis=math.degrees(1))
-        # XXX How can we derive the vertical limit of 131.98?
-        super(Miller, self).__init__(proj4_params, 180, 131.98, globe=globe)
+        # See Snyder, 1987. Eqs (11-1) and (11-2) substituting maximums of
+        # (lambda-lambda0)=180 and phi=90 to get limits.
+        super(Miller, self).__init__(proj4_params,
+                                     a * np.pi, a * 2.303412543376391,
+                                     globe=globe)
 
     @property
     def threshold(self):

lib/cartopy/tests/crs/test_miller.py

@@ -0,0 +1,104 @@
+# (C) British Crown Copyright 2018, 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 <https://www.gnu.org/licenses/>.
+"""
+Tests for the Miller coordinate system.
+
+"""
+
+from __future__ import (absolute_import, division, print_function)
+
+import numpy as np
+from numpy.testing import assert_almost_equal
+
+import cartopy.crs as ccrs
+
+
+def check_proj4_params(crs, other_args):
+    expected = other_args | {'proj=mill', 'no_defs'}
+    pro4_params = set(crs.proj4_init.lstrip('+').split(' +'))
+    assert expected == pro4_params
+
+
+def test_default():
+    mill = ccrs.Miller()
+    other_args = {'a=57.29577951308232', 'lon_0=0.0'}
+    check_proj4_params(mill, other_args)
+
+    assert_almost_equal(np.array(mill.x_limits),
+                        [-180, 180])
+    assert_almost_equal(np.array(mill.y_limits),
+                        [-131.9758172, 131.9758172])
+
+
+def test_central_longitude():
+    cl = 10.0
+    mill = ccrs.Miller(central_longitude=cl)
+    other_args = {'a=57.29577951308232', 'lon_0={}'.format(cl)}
+    check_proj4_params(mill, other_args)
+
+    assert_almost_equal(np.array(mill.x_limits),
+                        [-180, 180])
+    assert_almost_equal(np.array(mill.y_limits),
+                        [-131.9758172, 131.9758172])
+
+
+def test_grid():
+    # USGS Professional Paper 1395, p 89, Table 14
+    globe = ccrs.Globe(semimajor_axis=1.0, ellipse=None)
+    mill = ccrs.Miller(central_longitude=0.0, globe=globe)
+    geodetic = mill.as_geodetic()
+
+    other_args = {'a=1.0', 'lon_0=0.0'}
+    check_proj4_params(mill, other_args)
+
+    assert_almost_equal(np.array(mill.x_limits),
+                        [-3.14159265, 3.14159265])
+    assert_almost_equal(np.array(mill.y_limits),
+                        [-2.3034125, 2.3034125])
+
+    lats, lons = np.mgrid[0:91:5, 0:91:10].reshape((2, -1))
+    expected_x = np.deg2rad(lons)
+    expected_y = np.array([
+        2.30341, 2.04742, 1.83239, 1.64620, 1.48131, 1.33270, 1.19683, 1.07113,
+        0.95364, 0.84284, 0.73754, 0.63674, 0.53962, 0.44547, 0.35369, 0.26373,
+        0.17510, 0.08734, 0.00000,
+    ])[::-1].repeat(10)
+
+    result = mill.transform_points(geodetic, lons, lats)
+    assert_almost_equal(result[:, 0], expected_x, decimal=5)
+    assert_almost_equal(result[:, 1], expected_y, decimal=5)
+
+
+def test_sphere_transform():
+    # USGS Professional Paper 1395, pp 287 - 288
+    globe = ccrs.Globe(semimajor_axis=1.0, ellipse=None)
+    mill = ccrs.Miller(central_longitude=0.0, globe=globe)
+    geodetic = mill.as_geodetic()
+
+    other_args = {'a=1.0', 'lon_0=0.0'}
+    check_proj4_params(mill, other_args)
+
+    assert_almost_equal(np.array(mill.x_limits),
+                        [-3.14159265, 3.14159265])
+    assert_almost_equal(np.array(mill.y_limits),
+                        [-2.3034125, 2.3034125])
+
+    result = mill.transform_point(-75.0, 50.0, geodetic)
+    assert_almost_equal(result, [-1.3089969, 0.9536371])
+
+    inverse_result = geodetic.transform_point(result[0], result[1], mill)
+    assert_almost_equal(inverse_result, [-75.0, 50.0])