distance_metrics.py 4.44 KB
Newer Older
Joseph Siddons's avatar
Joseph Siddons committed
1
"""
2 3
Distance Metrics
----------------
Joseph Siddons's avatar
Joseph Siddons committed
4 5 6 7 8
Functions for computing navigational information. Can be used to add
navigational information to DataFrames.
"""

from math import acos, asin, atan2, cos, sin, degrees, radians, sqrt
9
from typing import Tuple
Joseph Siddons's avatar
Joseph Siddons committed
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129


def gcd_slc(
    lon0: float,
    lat0: float,
    lon1: float,
    lat1: float,
) -> float:
    """
    Compute great circle distance on earth surface between two locations.

    Parameters
    ----------
    lon0 : float
        Longitude of position 0
    lat0 : float
        Latitude of position 0
    lon1 : float
        Longitude of position 1
    lat1 : float
        Latitude of position 1

    Returns
    -------
    dist : float
        Great circle distance between position 0 and position 1.

    """
    if abs(lat0 - lat1) <= 1e-6 and abs(lon0 - lon1) <= 1e-6:
        return 0

    r_earth = 6371

    # Convert to radians
    lat0, lat1, lon0, lon1 = map(radians, [lat0, lat1, lon0, lon1])

    return r_earth * acos(
        sin(lat0) * sin(lat1) + cos(lat0) * cos(lat1) * cos(lon1 - lon0)
    )


def haversine(
    lon0: float,
    lat0: float,
    lon1: float,
    lat1: float,
) -> float:
    """
    Compute Haversine distance between two points.

    Parameters
    ----------
    lon0 : float
        Longitude of position 0
    lat0 : float
        Latitude of position 0
    lon1 : float
        Longitude of position 1
    lat1 : float
        Latitude of position 1

    Returns
    -------
    dist : float
        Haversine distance between position 0 and position 1.

    """
    lat0, lat1, dlon, dlat = map(
        radians, [lat0, lat1, lon1 - lon0, lat1 - lat0]
    )
    if abs(dlon) < 1e-6 and abs(dlat) < 1e-6:
        return 0

    r_earth = 6371

    a = sin(dlat / 2) ** 2 + cos(lat0) * cos(lat1) * sin(dlon / 2) ** 2
    c = 2 * asin(sqrt(a))
    return c * r_earth


def bearing(
    lon0: float,
    lat0: float,
    lon1: float,
    lat1: float,
) -> float:
    """
    Compute the bearing of a track from (lon0, lat0) to (lon1, lat1).

    Duplicated from geo-py

    Parameters
    ----------
    lon0 : float,
        Longitude of start point
    lat0 : float,
        Latitude of start point
    lon1 : float,
        Longitude of target point
    lat1 : float,
        Latitude of target point

    Returns
    -------
    bearing : float
        The bearing from point (lon0, lat0) to point (lon1, lat1) in degrees.
    """
    lon0, lat0, lon1, lat1 = map(radians, [lon0, lat0, lon1, lat1])

    dlon = lon1 - lon0
    numerator = sin(dlon) * cos(lat1)
    denominator = cos(lat0) * sin(lat1) - (sin(lat0) * cos(lat1) * cos(dlon))

    theta = atan2(numerator, denominator)
    theta_deg = (degrees(theta) + 360) % 360
    return theta_deg


def destination(
    lon: float, lat: float, bearing: float, distance: float
130
) -> Tuple[float, float]:
Joseph Siddons's avatar
Joseph Siddons committed
131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178
    """
    Compute destination of a great circle path.

    Compute the destination of a track started from 'lon', 'lat', with
    'bearing'. Distance is in units of km.

    Duplicated from geo-py

    Parameters
    ----------
    lon : float
        Longitude of initial position
    lat : float
        Latitude of initial position
    bearing : float
        Direction of track
    distance : float
        Distance to travel

    Returns
    -------
    destination : tuple[float, float]
        Longitude and Latitude of final position
    """
    lon, lat = radians(lon), radians(lat)
    radians_bearing = radians(bearing)
    r_earth = 6371
    delta = distance / r_earth

    lat2 = asin(
        sin(lat) * cos(delta) + cos(lat) * sin(delta) * cos(radians_bearing)
    )
    numerator = sin(radians_bearing) * sin(delta) * cos(lat)
    denominator = cos(delta) - sin(lat) * sin(lat2)

    lon2 = lon + atan2(numerator, denominator)

    lon2_deg = (degrees(lon2) + 540) % 360 - 180
    lat2_deg = degrees(lat2)

    return lon2_deg, lat2_deg


def midpoint(
    lon0: float,
    lat0: float,
    lon1: float,
    lat1: float,
179
) -> Tuple[float, float]:
Joseph Siddons's avatar
Joseph Siddons committed
180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203
    """
    Compute the midpoint of a great circle track

    Parameters
    ----------
    lon0 : float
        Longitude of position 0
    lat0 : float
        Latitude of position 0
    lon1 : float
        Longitude of position 1
    lat1 : float
        Latitude of position 1

    Returns
    -------
    lon, lat
        Positions of midpoint between position 0 and position 1

    """
    bear = bearing(lon0, lat0, lon1, lat1)
    dist = haversine(lon0, lat0, lon1, lat1)

    return destination(lon0, lat0, bear, dist / 2)