Haversine公式

半正矢公式(haversine equation)用于计算两经纬度点的距离，公式为：
d = 2 r argsin ⁡ ( sin ⁡ 2 ( l a t 2 − l a t 1 2 ) + cos ⁡ ( l a t 2 ) cos ⁡ ( l a t 1 ) sin ⁡ 2 ( l o n 2 − l o n 1 2 ) ) d=2r\operatorname{argsin}(\sqrt{\sin^2(\frac{lat2-lat1}{2})+\cos(lat2)\cos(lat1)\sin^2(\frac{lon2-lon1}{2})}) d=2rargsin(sin2(2lat2−lat1​)+cos(lat2)cos(lat1)sin2(2lon2−lon1​) ​)
式子中R为半径。

python代码实现

地球半径为6378km，R=6378*1000m，则haversine公式可写为：

import numpy as np
def haversine(lon1, lat1, lon2, lat2):
    lon1, lat1, lon2, lat2 = map(np.radians, [lon1, lat1, lon2, lat2])
    dlon = lon2 - lon1
    dlat = lat2 - lat1
    a = np.sin(dlat/2.0)**2 + np.cos(lat1) * np.cos(lat2) * np.sin(dlon/2.0)**2
    c = 2 * np.arcsin(np.sqrt(a))
    return c * 6367 * 1000