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Try to improve inverse_haversine #59

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57 changes: 50 additions & 7 deletions haversine/haversine.py
Original file line number Diff line number Diff line change
Expand Up @@ -199,18 +199,61 @@ def haversine_vector(array1, array2, unit=Unit.KILOMETERS, comb=False, normalize
return 2 * get_avg_earth_radius(unit) * numpy.arcsin(numpy.sqrt(d))


def inverse_haversine(point, distance, direction: Union[Direction, float], unit=Unit.KILOMETERS):
def _get_cos_direction(direction: Union[Direction, float]) -> float:
"""
Returns the cosine of the direction. Transform special case to avoid mathematical imprecision of computers
"""
brng = direction.value if isinstance(direction, Direction) else direction

if brng == 0: # North
return 1
elif brng == 0.5 * pi: # East
return 0
elif brng == pi: # South
return -1
elif brng == 1.5 * pi: # West
return 0
else:
return cos(brng)


def _get_sin_direction(direction: Union[Direction, float]) -> float:
"""
Returns the sine of the direction. Transform special case to avoid mathematical imprecision of computers
"""
brng = direction.value if isinstance(direction, Direction) else direction

if brng == 0: # North
return 0
elif brng == 0.5 * pi: # East
return 1
elif brng == pi: # South
return 0
elif brng == 1.5 * pi: # West
return -1
else:
return sin(brng)


def inverse_haversine(point, distance, direction: Union[Direction, float], unit=Unit.KILOMETERS):
lat, lng = point
lat, lng = map(radians, (lat, lng))
d = distance
r = get_avg_earth_radius(unit)
brng = direction.value if isinstance(direction, Direction) else direction

return_lat = asin(sin(lat) * cos(d / r) + cos(lat)
* sin(d / r) * cos(brng))
return_lng = lng + atan2(sin(brng) * sin(d / r) *
cos(lat), cos(d / r) - sin(lat) * sin(return_lat))
cos_brng = _get_cos_direction(direction)
sin_brng = _get_sin_direction(direction)
# print(point, distance, r)

cos_d_r = cos(distance / r)
sin_d_r = sin(distance / r)
cos_lat = cos(lat)
sin_lat = sin(lat)

# print(sin_lat, cos_d_r, sin_lat * cos_d_r, cos_lat * sin_d_r * cos_brng)
return_lat = asin(sin_lat * cos_d_r + cos_lat * sin_d_r * cos_brng)
return_lng = lng + atan2(sin_brng * sin_d_r * cos_lat,
cos_d_r - sin_lat * sin(return_lat))
# print(degrees(return_lat))

return_lat, return_lng = map(degrees, (return_lat, return_lng))
return return_lat, return_lng
15 changes: 15 additions & 0 deletions tests/test_inverse_haversine.py
Original file line number Diff line number Diff line change
Expand Up @@ -45,3 +45,18 @@ def test_inverse_miles():
def test_nautical_inverse_miles():
assert isclose(inverse_haversine(PARIS, 10, Direction.SOUTH,
unit=Unit.NAUTICAL_MILES), (48.69014586638915, 2.3508), rtol=1e-5).all()


@pytest.mark.parametrize(
"point, direction, distance, unit, expected",
[
(PARIS, Direction.WEST, 3000, Unit.KILOMETERS, (PARIS[0], 0)),
# (LYON, Direction.WEST, 3000, Unit.KILOMETERS, (LYON[0], 0)),
],
)
def test_explicit_cardinal_points(point, direction, distance, unit, expected):
"""
Test going north/south should not alter latitude and going east/west should not alter longitude
"""
assert inverse_haversine(point, distance, direction, unit)[
0] == expected[0]