def test_for_errors(
name: str,
lat_lon_to_x_z: Transformer,
x_z_to_lat_lon: Transformer,
coords: Coordinates,
) -> bool:
errors = False
x, z = lat_lon_to_x_z.transform(coords.latitude, coords.longitude)
if not math.isclose(x, coords.x) or not math.isclose(z, coords.z):
error_x = x - coords.x
error_z = z - coords.z
error_pct_x = error_x / coords.x * 100
error_pct_z = error_z / coords.z * 100
print(f"{name} has error of {error_pct_x}% {error_pct_z}%")
errors = True
lat, lon = x_z_to_lat_lon.transform(coords.x, coords.z)
if not math.isclose(lat, coords.latitude) or not math.isclose(
lon, coords.longitude):
error_lat = lat - coords.latitude
error_lon = lon - coords.longitude
error_pct_lon = error_lat / coords.latitude * 100
error_pct_lat = error_lon / coords.longitude * 100
print(f"{name} has error of {error_pct_lat}% {error_pct_lon}%")
errors = True
return errors
def _split_points_along_anti_meridian(
wgs84_to_proj: Transformer,
points: List[Tuple[float, float]],
threshold=0.01) -> List[List[Tuple[float, float]]]:
total_points = len(points)
groups: List = []
group: List[Tuple[float, float]] = []
for i in range(len(points)):
current_point = points[i]
next_point = points[(i + 1) % total_points]
group.append(current_point)
if abs(current_point[1] - next_point[1]) > 90:
longitude = _sign(points[i][1]) * 180
anti_meridian_at_current_lat = wgs84_to_proj.transform(
current_point[0], 180)
anti_meridian_at_next_lat = wgs84_to_proj.transform(
next_point[0], 180)
if anti_meridian_at_current_lat[0] == float('inf') and \
anti_meridian_at_next_lat[0] == float('inf'):
error = (
'The anti-meridian at between the latitudes ' +
"%f and %f " % (current_point[0], next_point[0]) +
'could not be transformed with the projection. This is ' +
'unexpected. Please fix the algorithm!')
raise RuntimeError(error)
if anti_meridian_at_current_lat[0] == float('inf'):
latitude = _binary_search_edge_wgs84(
wgs84_to_proj,
next_point[0], # Valid latitude
current_point[0], # Invalid latitude
threshold)
elif anti_meridian_at_next_lat[0] == float('inf'):
latitude = _binary_search_edge_wgs84(
wgs84_to_proj,
current_point[0], # Valid latitude
next_point[0], # Invalid latitude
threshold)
else:
latitude = next_point[0]
if not math.isclose(current_point[1], longitude, abs_tol=0.0001):
group.append((latitude, longitude))
groups.append(group)
group = []
if not math.isclose(next_point[1], -longitude, abs_tol=0.0001):
group.append((latitude, -longitude))
if len(groups) != 0 and groups[0][0] == next_point:
group.extend(groups[0])
groups[0] = group
elif i == total_points - 1:
groups.append(group)
return groups
def _covers_hemisphere(wgs84_to_proj: Transformer) -> bool:
covers_northern = wgs84_to_proj.transform(90, 0)[0] != float('inf')
covers_southern = wgs84_to_proj.transform(-90, 0)[0] != float('inf')
# We don't really support projections like this, where the north and south
# poles are visible at the same, but it is possible in azimuthal
# projections where the lat_0 is 0. For our purposes, we don't consider
# this projection as covering both hemisphere; it merely touches it.
if covers_northern and covers_southern:
return False
return covers_northern or covers_southern
def calculate_raster_coordinate(
longitude: float,
latitude: float,
padf_transform: List[float],
transformer: Transformer):
""" From a given longitude and latitude, calculate the raster coordinate corresponding to the
top left point of the grid surrounding the given geographic coordinate.
"""
# Because not all model types use EPSG:4269 projection, we first convert longitude and latitude
# to whichever projection and coordinate system the grib file is using
raster_long, raster_lat = transformer.transform(longitude, latitude)
# Calculate the j index for point i,j in the grib file
x_numerator = (raster_long - padf_transform[0] - raster_lat/padf_transform[5] *
padf_transform[2] + padf_transform[3] / padf_transform[5] *
padf_transform[2]) / padf_transform[1]
y_numerator = (raster_lat - padf_transform[3] - raster_long/padf_transform[1] *
padf_transform[4] + padf_transform[0] / padf_transform[1] *
padf_transform[4]) / padf_transform[5]
denominator = 1 - \
padf_transform[4]/padf_transform[5]*padf_transform[2]/padf_transform[1]
i_index = math.floor(x_numerator/denominator)
j_index = math.floor(y_numerator/denominator)
return (i_index, j_index)
def calculate_geographic_coordinate(
point: Tuple[int],
padf_transform: List[float],
transformer: Transformer):
""" Calculate the geographic coordinates for a given points """
x_coordinate = padf_transform[0] + point[0] * \
padf_transform[1] + point[1]*padf_transform[2]
y_coordinate = padf_transform[3] + point[0] * \
padf_transform[4] + point[1]*padf_transform[5]
lon, lat = transformer.transform(x_coordinate, y_coordinate)
return (lon, lat)
def _binary_search_edge_crs(transformer: Transformer,
angle: float,
threshold=1) -> float:
min_r = 0
crs = transformer.source_crs
if crs.coordinate_operation.method_name == 'Orthographic':
# Speeds up binary search a bit
min_r = min(crs.ellipsoid.semi_minor_metre,
crs.ellipsoid.semi_major_metre) * 0.9
max_r = max(crs.ellipsoid.semi_minor_metre, crs.ellipsoid.semi_major_metre)
while max_r - min_r > threshold:
pivot_r = (min_r + max_r) / 2
x = math.cos(angle) * pivot_r
y = math.sin(angle) * pivot_r
if (transformer.transform(x, y))[0] == float('inf'):
max_r = pivot_r
else:
min_r = pivot_r
return min_r
def _binary_search_edge_wgs84(
wgs84_to_proj: Transformer,
valid_lat: float,
invalid_lat: float,
threshold=0.01,
) -> float:
"""
:param wgs84_to_proj:
:param valid_lat:
:param invalid_lat:
:param threshold: Defaults to 0.01, since this level of precision usually
is the size of a neighbourhood.
See https://xkcd.com/2170/
:return:
"""
while abs(valid_lat - invalid_lat) > threshold:
pivot_lat = (invalid_lat + valid_lat) / 2
if (wgs84_to_proj.transform(pivot_lat, 180))[0] == float('inf'):
invalid_lat = pivot_lat
else:
valid_lat = pivot_lat
return valid_lat
def transform(tf: Transformer, cell):
return tf.transform(cell[0], cell[1])
