Approximate longitude & latitude rectangle for specified location and distance.

georange.py

import math


def georange(origin, distance):
    """
    Returns approximate longitude & latitude rectangle range for
    specified origin and distance in km. Works good when:

        distance is far smaller 6400 km (approximate Earth radius)
        origin isn't too close to North and South poles

    Parameters:

        origin -- tuple (lat, lng) in degrees
        distance -- float > 0 in km

    Result:

        ((lat1, lat2), (lng1, lng2), (lng3, lng4))

    We should produce 2 ranges for longitude as it may have
    gap at edges, e.g. [-190, -170] is invalid range and it's
    splitted into [-180, -170] and [170, 180] ranges.

    Examples:

        >>> georange((55.45, 37.37), 2.0)[0]
        (55.432013567881626, 55.46798643211838)

        >>> georange((55.45, 37.37), 2.0)[1]
        (37.33828490093818, 37.40171509906182)

        >>> georange((55.45, 37.37), 2.0)[2]
        (37.33828490093818, 37.40171509906182)

        >>> georange((200.0, 0), 2.0)
        Traceback (most recent call last):
        ...
        Exception: Latitude must be in range [-90.0, 90.0]

        >>> georange((0.0, 190), 2.0)
        Traceback (most recent call last):
        ...
        Exception: Longitude must be in range [-180.0, 180.0]

    NO COPYRIGHT
    ------------

    You can copy, modify, distribute and perform the work, even for
    commercial purposes, all without asking permission.
    See Other Information below.

    CC0 1.0 Universal (CC0 1.0) Public Domain Dedication
    http://creativecommons.org/publicdomain/zero/1.0/
    """
    radius = 6371.0  # in km
    lat, lng = map(float, origin)

    # Validate values range
    if not (-90.0 <= lat <= 90.0):
        raise ValueError("Latitude must be in range [%s, %s]" % (-90.0, 90.0))

    if not (-180.0 <= lng <= 180.0):
        raise ValueError("Longitude must be in range [%s, %s]" % (-180.0, 180.0))

    # Range for latitude
    dlat = math.degrees(distance / radius)
    lat1, lat2 = max(-90.0, lat - dlat), min(90.0, lat + dlat)

    # Ranges for longitude
    r = radius * math.cos(math.radians(lat))
    dlng = (r > 0) and min(180.0, math.degrees(distance / r)) or 180.0
    lng1, lng2 = lng - dlng, lng + dlng
    lng3, lng4 = lng1, lng2

    # Split longitude range if required
    if lng1 < -180.0:
        lng3, lng4 = (360.0 + lng1, 180.0)
        lng1, lng2 = (-180.0, lng2)
    elif lng2 > 180.0:
        lng3, lng4 = (-180.0, lng2 - 360)
        lng1, lng2 = (lng1, 180.0)

    return ((lat1, lat2), (lng1, lng2), (lng3, lng4))


if __name__ == "__main__":
    import doctest
    doctest.testmod()