from math import atan, tan, sin, cos, pi, sqrt, atan2, acos, asin
from geopy.units import radians
from geopy import units, util
from geopy.point import Point

# Average great-circle radius in kilometers, from Wikipedia.
# Using a sphere with this radius results in an error of up to about 0.5%.
EARTH_RADIUS = 6372.795

# From http://www.movable-type.co.uk/scripts/LatLongVincenty.html:
#   The most accurate and widely used globally-applicable model for the earth
#   ellipsoid is WGS-84, used in this script. Other ellipsoids offering a
#   better fit to the local geoid include Airy (1830) in the UK, International
#   1924 in much of Europe, Clarke (1880) in Africa, and GRS-67 in South
#   America. America (NAD83) and Australia (GDA) use GRS-80, functionally
#   equivalent to the WGS-84 ellipsoid.
ELLIPSOIDS = {
    # model           major (km)   minor (km)     flattening
    'WGS-84':        (6378.137,    6356.7523142,  1 / 298.257223563),
    'GRS-80':        (6378.137,    6356.7523141,  1 / 298.257222101),
    'Airy (1830)':   (6377.563396, 6356.256909,   1 / 299.3249646),
    'Intl 1924':     (6378.388,    6356.911946,   1 / 297.0),
    'Clarke (1880)': (6378.249145, 6356.51486955, 1 / 293.465),
    'GRS-67':        (6378.1600,   6356.774719,   1 / 298.25)
}

class Distance(object):
    def __init__(self, *args, **kwargs):
        kilometers = kwargs.pop('kilometers', 0)
        if len(args) == 1:
            # if we only get one argument we assume
            # it's a known distance instead of 
            # calculating it first
            kilometers += args[0]
        elif len(args) > 1:
            for a, b in util.pairwise(args):
                kilometers += self.measure(a, b)
       
        kilometers += units.kilometers(**kwargs)
        self.__kilometers = kilometers
    
    def __add__(self, other):
        if isinstance(other, Distance):
            return self.__class__(self.kilometers + other.kilometers)
        else:
            raise TypeError(
                "Distance instance must be added with Distance instance."
            )
    
    def __neg__(self):
        return self.__class__(-self.kilometers)
    
    def __sub__(self, other):
        return self + -other
    
    def __mul__(self, other):
        return self.__class__(self.kilometers * other)
    
    def __div__(self, other):
        if isinstance(other, Distance):
            return self.kilometers / other.kilometers
        else:
            return self.__class__(self.kilometers / other)
    
    def __abs__(self):
        return self.__class__(abs(self.kilometers))
    
    def __nonzero__(self):
        return bool(self.kilometers)
    
    def measure(self, a, b):
        raise NotImplementedError
    
    @property
    def kilometers(self):
        return self.__kilometers
    
    @property
    def km(self):
        return self.kilometers
    
    @property
    def meters(self):
        return units.meters(kilometers=self.kilometers)
    
    @property
    def m(self):
        return self.meters
    
    @property
    def miles(self):
        return units.miles(kilometers=self.kilometers)
    
    @property
    def mi(self):
        return self.miles
    
    @property
    def feet(self):
        return units.feet(kilometers=self.kilometers)

    @property
    def ft(self):
        return self.feet
    
    @property
    def nautical(self):
        return units.nautical(kilometers=self.kilometers)

    @property
    def nm(self):
        return self.nautical


class GreatCircleDistance(Distance):
    """
    Use spherical geometry to calculate the surface distance between two
    geodesic points. This formula can be written many different ways,
    including just the use of the spherical law of cosines or the haversine
    formula.
    
    The class attribute `RADIUS` indicates which radius of the earth to use,
    in kilometers. The default is to use the module constant `EARTH_RADIUS`,
    which uses the average great-circle radius.
    
    """
    
    RADIUS = EARTH_RADIUS
    
    def measure(self, a, b):
        a, b = Point(a), Point(b)
        lat1, lng1 = radians(degrees=a.latitude), radians(degrees=a.longitude)
        lat2, lng2 = radians(degrees=b.latitude), radians(degrees=b.longitude)
        
        sin_lat1, cos_lat1 = sin(lat1), cos(lat1)
        sin_lat2, cos_lat2 = sin(lat2), cos(lat2)
        
        delta_lng = lng2 - lng1
        cos_delta_lng, sin_delta_lng = cos(delta_lng), sin(delta_lng)
        
        central_angle = acos(sin_lat1 * sin_lat2 +
                             cos_lat1 * cos_lat2 * cos_delta_lng)
        
        # From http://en.wikipedia.org/wiki/Great_circle_distance:
        #   Historically, the use of this formula was simplified by the
        #   availability of tables for the haversine function. Although this
        #   formula is accurate for most distances, it too suffers from
        #   rounding errors for the special (and somewhat unusual) case of
        #   antipodal points (on opposite ends of the sphere). A more
        #   complicated formula that is accurate for all distances is: (below)
        
        d = atan2(sqrt((cos_lat2 * sin_delta_lng) ** 2 +
                       (cos_lat1 * sin_lat2 -
                        sin_lat1 * cos_lat2 * cos_delta_lng) ** 2),
                  sin_lat1 * sin_lat2 + cos_lat1 * cos_lat2 * cos_delta_lng)
        
        return self.RADIUS * d

    def destination(self, point, bearing, distance=None):
        point = Point(point)
        lat1 = units.radians(degrees=point.latitude)
        lng1 = units.radians(degrees=point.longitude)
        bearing = units.radians(degrees=bearing)

        if distance is None:
            distance = self
        if isinstance(distance, Distance):
            distance = distance.kilometers

        d_div_r = float(distance) / self.RADIUS

        lat2 = asin(
            sin(lat1) * cos(d_div_r) +
            cos(lat1) * sin(d_div_r) * cos(bearing)
        )

        lng2 = lng1 + atan2(
            sin(bearing) * sin(d_div_r) * cos(lat1),
            cos(d_div_r) - sin(lat1) * sin(lat2)
        )

        return Point(units.degrees(radians=lat2), units.degrees(radians=lng2))


class VincentyDistance(Distance):
    """
    Calculate the geodesic distance between two points using the formula
    devised by Thaddeus Vincenty, with an accurate ellipsoidal model of the
    earth.

    The class attribute `ELLIPSOID` indicates which ellipsoidal model of the
    earth to use. If it is a string, it is looked up in the `ELLIPSOIDS`
    dictionary to obtain the major and minor semiaxes and the flattening.
    Otherwise, it should be a tuple with those values. The most globally
    accurate model is WGS-84. See the comments above the `ELLIPSOIDS`
    dictionary for more information.
    
    """

    ELLIPSOID = 'WGS-84'
    
    def measure(self, a, b):
        a, b = Point(a), Point(b)
        lat1, lng1 = radians(degrees=a.latitude), radians(degrees=a.longitude)
        lat2, lng2 = radians(degrees=b.latitude), radians(degrees=b.longitude)

        if isinstance(self.ELLIPSOID, basestring):
            major, minor, f = ELLIPSOIDS[self.ELLIPSOID]
        else:
            major, minor, f = self.ELLIPSOID

        delta_lng = lng2 - lng1

        reduced_lat1 = atan((1 - f) * tan(lat1))
        reduced_lat2 = atan((1 - f) * tan(lat2))

        sin_reduced1, cos_reduced1 = sin(reduced_lat1), cos(reduced_lat1)
        sin_reduced2, cos_reduced2 = sin(reduced_lat2), cos(reduced_lat2)

        lambda_lng = delta_lng
        lambda_prime = 2 * pi

        iter_limit = 20

        while abs(lambda_lng - lambda_prime) > 10e-12 and iter_limit > 0:
            sin_lambda_lng, cos_lambda_lng = sin(lambda_lng), cos(lambda_lng)

            sin_sigma = sqrt(
                (cos_reduced2 * sin_lambda_lng) ** 2 +
                (cos_reduced1 * sin_reduced2 -
                 sin_reduced1 * cos_reduced2 * cos_lambda_lng) ** 2
            )

            if sin_sigma == 0:
                return 0 # Coincident points

            cos_sigma = (
                sin_reduced1 * sin_reduced2 +
                cos_reduced1 * cos_reduced2 * cos_lambda_lng
            )

            sigma = atan2(sin_sigma, cos_sigma)

            sin_alpha = (
                cos_reduced1 * cos_reduced2 * sin_lambda_lng / sin_sigma
            )
            cos_sq_alpha = 1 - sin_alpha ** 2

            if cos_sq_alpha != 0:
                cos2_sigma_m = cos_sigma - 2 * (
                    sin_reduced1 * sin_reduced2 / cos_sq_alpha
                )
            else:
                cos2_sigma_m = 0.0 # Equatorial line

            C = f / 16. * cos_sq_alpha * (4 + f * (4 - 3 * cos_sq_alpha))

            lambda_prime = lambda_lng
            lambda_lng = (
                delta_lng + (1 - C) * f * sin_alpha * (
                    sigma + C * sin_sigma * (
                        cos2_sigma_m + C * cos_sigma * (
                            -1 + 2 * cos2_sigma_m ** 2
                        )
                    )
                )
            )
            iter_limit -= 1

        if iter_limit == 0:
            raise ValueError("Vincenty formula failed to converge!")

        u_sq = cos_sq_alpha * (major ** 2 - minor ** 2) / minor ** 2

        A = 1 + u_sq / 16384. * (
            4096 + u_sq * (-768 + u_sq * (320 - 175 * u_sq))
        )

        B = u_sq / 1024. * (256 + u_sq * (-128 + u_sq * (74 - 47 * u_sq)))

        delta_sigma = (
            B * sin_sigma * (
                cos2_sigma_m + B / 4. * (
                    cos_sigma * (
                        -1 + 2 * cos2_sigma_m ** 2
                    ) - B / 6. * cos2_sigma_m * (
                        -3 + 4 * sin_sigma ** 2
                    ) * (
                        -3 + 4 * cos2_sigma_m ** 2
                    )
                )
            )
        )

        s = minor * A * (sigma - delta_sigma)
        return s

    def destination(self, point, bearing, distance=None):
        point = Point(point)
        lat1 = units.radians(degrees=point.latitude)
        lng1 = units.radians(degrees=point.longitude)
        bearing = units.radians(degrees=bearing)

        if distance is None:
            distance = self
        if isinstance(distance, Distance):
            distance = distance.kilometers
        
        ellipsoid = self.ELLIPSOID
        if isinstance(ellipsoid, basestring):
            ellipsoid = ELLIPSOIDS[ellipsoid]

        major, minor, f = ellipsoid
        
        tan_reduced1 = (1 - f) * tan(lat1)
        cos_reduced1 = 1 / sqrt(1 + tan_reduced1 ** 2)
        sin_reduced1 = tan_reduced1 * cos_reduced1
        sin_bearing, cos_bearing = sin(bearing), cos(bearing)
        sigma1 = atan2(tan_reduced1, cos_bearing)
        sin_alpha = cos_reduced1 * sin_bearing
        cos_sq_alpha = 1 - sin_alpha ** 2
        u_sq = cos_sq_alpha * (major ** 2 - minor ** 2) / minor ** 2
        
        A = 1 + u_sq / 16384. * (
            4096 + u_sq * (-768 + u_sq * (320 - 175 * u_sq))
        )
        B = u_sq / 1024. * (256 + u_sq * (-128 + u_sq * (74 - 47 * u_sq)))
        
        sigma = distance / (minor * A)
        sigma_prime = 2 * pi

        while abs(sigma - sigma_prime) > 10e-12:
            cos2_sigma_m = cos(2 * sigma1 + sigma)
            sin_sigma, cos_sigma = sin(sigma), cos(sigma)
            delta_sigma = B * sin_sigma * (
                cos2_sigma_m + B / 4. * (
                    cos_sigma * (
                        -1 + 2 * cos2_sigma_m
                    ) - B / 6. * cos2_sigma_m * (
                        -3 + 4 * sin_sigma ** 2) * (
                        -3 + 4 * cos2_sigma_m ** 2
                    )
                )
            )
            sigma_prime = sigma
            sigma = distance / (minor * A) + delta_sigma

        sin_sigma, cos_sigma = sin(sigma), cos(sigma)

        lat2 = atan2(
            sin_reduced1 * cos_sigma + cos_reduced1 * sin_sigma * cos_bearing,
            (1 - f) * sqrt(
                sin_alpha ** 2 + (
                    sin_reduced1 * sin_sigma -
                    cos_reduced1 * cos_sigma * cos_bearing
                ) ** 2
            )
        )

        lambda_lng = atan2(
            sin_sigma * sin_bearing,
            cos_reduced1 * cos_sigma - sin_reduced1 * sin_sigma * cos_bearing
        )

        C = f / 16. * cos_sq_alpha * (4 + f * (4 - 3 * cos_sq_alpha))

        delta_lng = (
            lambda_lng - (1 - C) * f * sin_alpha * (
                sigma + C * sin_sigma * (
                    cos2_sigma_m + C * cos_sigma * (
                        -1 + 2 * cos2_sigma_m ** 2
                    )
                )
            )
        )

        final_bearing = atan2(
            sin_alpha,
            cos_reduced1 * cos_sigma * cos_bearing - sin_reduced1 * sin_sigma
        )

        lng2 = lng1 + delta_lng
        
        return Point(units.degrees(radians=lat2), units.degrees(radians=lng2))


# Set the default distance formula to the most generally accurate.
distance = VincentyDistance