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# (C) British Crown Copyright 2018 - 2019, 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 Orthographic coordinate system.
"""
from __future__ import (absolute_import, division, print_function)
import numpy as np
from numpy.testing import assert_almost_equal
import pytest
import cartopy.crs as ccrs
from .helpers import check_proj_params
def test_default():
ortho = ccrs.Orthographic()
other_args = {'a=6378137.0', 'lon_0=0.0', 'lat_0=0.0'}
check_proj_params('ortho', ortho, other_args)
# WGS84 radius * 0.99999
assert_almost_equal(np.array(ortho.x_limits),
[-6378073.21863, 6378073.21863])
assert_almost_equal(np.array(ortho.y_limits),
[-6378073.21863, 6378073.21863])
def test_sphere_globe():
globe = ccrs.Globe(semimajor_axis=1000, ellipse=None)
ortho = ccrs.Orthographic(globe=globe)
other_args = {'a=1000', 'lon_0=0.0', 'lat_0=0.0'}
check_proj_params('ortho', ortho, other_args)
assert_almost_equal(ortho.x_limits, [-999.99, 999.99])
assert_almost_equal(ortho.y_limits, [-999.99, 999.99])
def test_ellipse_globe():
globe = ccrs.Globe(ellipse='WGS84')
with pytest.warns(UserWarning,
match='does not handle elliptical globes.') as w:
ortho = ccrs.Orthographic(globe=globe)
assert len(w) == (2
if (5, 0, 0) <= ccrs.PROJ4_VERSION < (5, 1, 0)
else 1)
other_args = {'ellps=WGS84', 'lon_0=0.0', 'lat_0=0.0'}
check_proj_params('ortho', ortho, other_args)
# Limits are the same as default since ellipses are not supported.
assert_almost_equal(ortho.x_limits, [-6378073.21863, 6378073.21863])
assert_almost_equal(ortho.y_limits, [-6378073.21863, 6378073.21863])
def test_eccentric_globe():
globe = ccrs.Globe(semimajor_axis=1000, semiminor_axis=500,
ellipse=None)
with pytest.warns(UserWarning,
match='does not handle elliptical globes.') as w:
ortho = ccrs.Orthographic(globe=globe)
assert len(w) == (2
if (5, 0, 0) <= ccrs.PROJ4_VERSION < (5, 1, 0)
else 1)
other_args = {'a=1000', 'b=500', 'lon_0=0.0', 'lat_0=0.0'}
check_proj_params('ortho', ortho, other_args)
# Limits are the same as spheres since ellipses are not supported.
assert_almost_equal(ortho.x_limits, [-999.99, 999.99])
assert_almost_equal(ortho.y_limits, [-999.99, 999.99])
@pytest.mark.parametrize('lat', [-10, 0, 10])
@pytest.mark.parametrize('lon', [-10, 0, 10])
def test_central_params(lat, lon):
ortho = ccrs.Orthographic(central_latitude=lat, central_longitude=lon)
other_args = {'lat_0={}'.format(lat), 'lon_0={}'.format(lon),
'a=6378137.0'}
check_proj_params('ortho', ortho, other_args)
# WGS84 radius * 0.99999
assert_almost_equal(np.array(ortho.x_limits),
[-6378073.21863, 6378073.21863])
assert_almost_equal(np.array(ortho.y_limits),
[-6378073.21863, 6378073.21863])
def test_grid():
# USGS Professional Paper 1395, pg 151, Table 22
globe = ccrs.Globe(ellipse=None,
semimajor_axis=1.0, semiminor_axis=1.0)
ortho = ccrs.Orthographic(globe=globe)
geodetic = ortho.as_geodetic()
other_args = {'a=1.0', 'b=1.0', 'lon_0=0.0', 'lat_0=0.0'}
check_proj_params('ortho', ortho, other_args)
assert_almost_equal(np.array(ortho.x_limits),
[-0.99999, 0.99999])
assert_almost_equal(np.array(ortho.y_limits),
[-0.99999, 0.99999])
lats, lons = np.mgrid[0:100:10, 0:100:10].reshape((2, -1))
expected_x = np.array([
[0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000, 0.0000,
0.0000, 0.0000],
[0.0000, 0.0302, 0.0594, 0.0868, 0.1116, 0.1330, 0.1504, 0.1632,
0.1710, 0.1736],
[0.0000, 0.0594, 0.1170, 0.1710, 0.2198, 0.2620, 0.2962, 0.3214,
0.3368, 0.3420],
[0.0000, 0.0868, 0.1710, 0.2500, 0.3214, 0.3830, 0.4330, 0.4698,
0.4924, 0.5000],
[0.0000, 0.1116, 0.2198, 0.3214, 0.4132, 0.4924, 0.5567, 0.6040,
0.6330, 0.6428],
[0.0000, 0.1330, 0.2620, 0.3830, 0.4924, 0.5868, 0.6634, 0.7198,
0.7544, 0.7660],
[0.0000, 0.1504, 0.2962, 0.4330, 0.5567, 0.6634, 0.7500, 0.8138,
0.8529, 0.8660],
[0.0000, 0.1632, 0.3214, 0.4698, 0.6040, 0.7198, 0.8138, 0.8830,
0.9254, 0.9397],
[0.0000, 0.1710, 0.3368, 0.4924, 0.6330, 0.7544, 0.8529, 0.9254,
0.9698, 0.9848],
[0.0000, 0.1736, 0.3420, 0.5000, 0.6428, 0.7660, 0.8660, 0.9397,
0.9848, 1.0000],
])[::-1, :].ravel()
expected_y = np.array([
1.0000, 0.9848, 0.9397, 0.8660, 0.7660, 0.6428, 0.5000, 0.3420, 0.1736,
0.0000,
])[::-1].repeat(10)
# Test all quadrants; they are symmetrical.
for lon_sign in [1, -1]:
for lat_sign in [1, -1]:
result = ortho.transform_points(geodetic,
lon_sign * lons, lat_sign * lats)
assert_almost_equal(result[:, 0], lon_sign * expected_x, decimal=4)
assert_almost_equal(result[:, 1], lat_sign * expected_y, decimal=4)
def test_sphere_transform():
# USGS Professional Paper 1395, pp 311 - 312
globe = ccrs.Globe(semimajor_axis=1.0, semiminor_axis=1.0,
ellipse=None)
ortho = ccrs.Orthographic(central_latitude=40.0, central_longitude=-100.0,
globe=globe)
geodetic = ortho.as_geodetic()
other_args = {'a=1.0', 'b=1.0', 'lon_0=-100.0', 'lat_0=40.0'}
check_proj_params('ortho', ortho, other_args)
assert_almost_equal(np.array(ortho.x_limits),
[-0.99999, 0.99999])
assert_almost_equal(np.array(ortho.y_limits),
[-0.99999, 0.99999])
result = ortho.transform_point(-110.0, 30.0, geodetic)
assert_almost_equal(result, np.array([-0.1503837, -0.1651911]))
inverse_result = geodetic.transform_point(result[0], result[1], ortho)
assert_almost_equal(inverse_result, [-110.0, 30.0])
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