def test_geod_inverse_transform():
gg = Geod(ellps="clrk66")
lat1pt = 42.0 + (15.0 / 60.0)
lon1pt = -71.0 - (7.0 / 60.0)
lat2pt = 45.0 + (31.0 / 60.0)
lon2pt = -123.0 - (41.0 / 60.0)
"""
distance between boston and portland, clrk66:
-66.531 75.654 4164192.708
distance between boston and portland, WGS84:
-66.530 75.654 4164074.239
testing pickling of Geod instance
distance between boston and portland, clrk66 (from pickle):
-66.531 75.654 4164192.708
distance between boston and portland, WGS84 (from pickle):
-66.530 75.654 4164074.239
inverse transform
from proj.4 invgeod:
b'-66.531\t75.654\t4164192.708\n'
"""
true_az12 = -66.5305947876623
true_az21 = 75.65363415556968
print("from pyproj.Geod.inv:")
az12, az21, dist = gg.inv(lon1pt, lat1pt, lon2pt, lat2pt)
assert_almost_equal((az12, az21, dist),
(true_az12, true_az21, 4164192.708),
decimal=3)
print("forward transform")
print("from proj.4 geod:")
endlon, endlat, backaz = gg.fwd(lon1pt, lat1pt, az12, dist)
assert_almost_equal((endlon, endlat, backaz), (lon2pt, lat2pt, true_az21),
decimal=3)
inc_exc = ["excluding", "including"]
res_az12_az21_dists_all = [
(180.0, 0.0, 0.0),
(-66.53059478766238, 106.79071710136431, 832838.5416198927),
(-73.20928289863558, 99.32289055927389, 832838.5416198935),
(-80.67710944072617, 91.36325611787134, 832838.5416198947),
(-88.63674388212858, 83.32809401477382, 832838.5416198922),
(-96.67190598522616, 75.65363415556973, 832838.5416198926),
]
point_count = len(res_az12_az21_dists_all)
for include_initial, include_terminus in itertools.product((False, True),
(False, True)):
initial_idx = int(not include_initial)
terminus_idx = int(not include_terminus)
npts = point_count - initial_idx - terminus_idx
print("intermediate points:")
print("from geod with +lat_1,+lon_1,+lat_2,+lon_2,+n_S:")
print(
f"{lat1pt:6.3f} {lon1pt:7.3f} {lat2pt:6.3f} {lon2pt:7.3f} {npts}")
lonlats = gg.npts(
lon1pt,
lat1pt,
lon2pt,
lat2pt,
npts,
initial_idx=initial_idx,
terminus_idx=terminus_idx,
)
assert len(lonlats) == npts
npts1 = npts + initial_idx + terminus_idx - 1
del_s = dist / npts1
print(
f"Total distnace is {dist}, "
f"Points count: {npts}, "
f"{inc_exc[include_initial]} initial point, "
f"{inc_exc[include_terminus]} terminus point. "
f"The distance between successive points is {dist}/{npts1} = {del_s}"
)
from_idx = initial_idx
to_idx = point_count - terminus_idx
res_az12_az21_dists = res_az12_az21_dists_all[from_idx:to_idx]
lonprev = lon1pt
latprev = lat1pt
for (lon, lat), (res12, res21, resdist) in zip(lonlats,
res_az12_az21_dists):
o_az12, o_az21, o_dist = gg.inv(lonprev, latprev, lon, lat)
if resdist == 0:
assert_almost_equal(o_dist, 0)
else:
assert_almost_equal((o_az12, o_az21, o_dist),
(res12, res21, resdist))
latprev = lat
lonprev = lon
if not include_terminus:
o_az12, o_az21, o_dist = gg.inv(lonprev, latprev, lon2pt, lat2pt)
assert_almost_equal((lat2pt, lon2pt, o_dist),
(45.517, -123.683, 832838.542),
decimal=3)
if include_initial and include_terminus:
lons, lats, azis12, azis21, dists = np.hstack(
(lonlats, res_az12_az21_dists)).transpose()
del_s = dist / (point_count - 1)
lons_a = np.empty(point_count)
lats_a = np.empty(point_count)
azis_a = np.empty(point_count)
print("test inv_intermediate (by npts) with azi output")
res = gg.inv_intermediate(
out_lons=lons_a,
out_lats=lats_a,
out_azis=azis_a,
lon1=lon1pt,
lat1=lat1pt,
lon2=lon2pt,
lat2=lat2pt,
npts=point_count,
initial_idx=0,
terminus_idx=0,
)
assert res.npts == point_count
assert_almost_equal(res.del_s, del_s)
assert_almost_equal(res.dist, dist)
assert_almost_equal(res.lons, lons)
assert_almost_equal(res.lats, lats)
assert_almost_equal(res.azis[:-1], azis12[1:])
assert res.lons is lons_a
assert res.lats is lats_a
assert res.azis is azis_a
for flags in (GeodIntermediateFlag.AZIS_DISCARD,
GeodIntermediateFlag.AZIS_KEEP):
print("test inv_intermediate (by npts) without azi output, no buffers")
res = gg.inv_intermediate(
lon1=lon1pt,
lat1=lat1pt,
lon2=lon2pt,
lat2=lat2pt,
npts=point_count,
initial_idx=0,
terminus_idx=0,
flags=flags,
)
assert res.npts == point_count
assert_almost_equal(res.del_s, del_s)
assert_almost_equal(res.dist, dist)
assert_almost_equal(res.lons, lons_a)
assert_almost_equal(res.lats, lats_a)
if flags == GeodIntermediateFlag.AZIS_DISCARD:
assert res.azis is None
else:
assert_almost_equal(res.azis, azis_a)
lons_b = np.empty(point_count)
lats_b = np.empty(point_count)
azis_b = np.empty(point_count)
print("test inv_intermediate (by npts) without azi output")
res = gg.inv_intermediate(
out_lons=lons_b,
out_lats=lats_b,
out_azis=None,
lon1=lon1pt,
lat1=lat1pt,
lon2=lon2pt,
lat2=lat2pt,
npts=point_count,
initial_idx=0,
terminus_idx=0,
flags=flags,
)
assert res.npts == point_count
assert_almost_equal(res.del_s, del_s)
assert_almost_equal(res.dist, dist)
assert_almost_equal(res.lons, lons_a)
assert_almost_equal(res.lats, lats_a)
assert res.lons is lons_b
assert res.lats is lats_b
if flags == GeodIntermediateFlag.AZIS_DISCARD:
assert res.azis is None
else:
assert_almost_equal(res.azis, azis_a)
print("test fwd_intermediate")
res = gg.fwd_intermediate(
out_lons=lons_b,
out_lats=lats_b,
out_azis=azis_b,
lon1=lon1pt,
lat1=lat1pt,
azi1=true_az12,
npts=point_count,
del_s=del_s,
initial_idx=0,
terminus_idx=0,
)
assert res.npts == point_count
assert_almost_equal(res.del_s, del_s)
assert_almost_equal(res.dist, dist)
assert_almost_equal(res.lons, lons_a)
assert_almost_equal(res.lats, lats_a)
assert_almost_equal(res.azis, azis_a)
assert res.lons is lons_b
assert res.lats is lats_b
assert res.azis is azis_b
print("test inv_intermediate (by del_s)")
for del_s_fact, flags in (
(1, GeodIntermediateFlag.NPTS_ROUND),
((point_count - 0.5) / point_count, GeodIntermediateFlag.NPTS_TRUNC),
((point_count + 0.5) / point_count, GeodIntermediateFlag.NPTS_CEIL),
):
res = gg.inv_intermediate(
out_lons=lons_b,
out_lats=lats_b,
out_azis=azis_b,
lon1=lon1pt,
lat1=lat1pt,
lon2=lon2pt,
lat2=lat2pt,
del_s=del_s * del_s_fact,
initial_idx=0,
terminus_idx=0,
flags=flags,
)
assert res.npts == point_count
assert_almost_equal(res.del_s, del_s)
assert_almost_equal(res.dist, dist)
assert_almost_equal(res.lons, lons_a)
assert_almost_equal(res.lats, lats_a)
assert_almost_equal(res.azis, azis_a)
assert res.lons is lons_b
assert res.lats is lats_b
assert res.azis is azis_b
