我有三点:A,B和C(纬度,WGS84中的长坐标)
我想计算C与A,B之间的最小路径之间的距离。(这必须适用于任何纬度,长,所以我无法进行投影)
pyproj或geographiclib.geodesic能为我做到吗?
编辑:不重复,因为我想在WGS84中工作而不是在球体上工作。正如我所说,这必须与任何纬度,长期。我知道这个问题没有简单的解决办法,这就是为什么我要问有一个简单的方法来处理像pyproj或geographiclib.geodesic这样的库。
答案 0 :(得分:0)
这是一种方法。它不是向量化的,可能效率不高。我尚未测试所有可能的情况。这是一个图形示例:
#!/usr/bin/env python3
__author__ = 'hrmd'
from geographiclib.geodesic import Geodesic
import numpy as np
def dist_from_great_circle_to_point(a, b, p):
'''
Calculates the shortest distance between a point P and a great
circle passing through A and B. The method is:
1. Find azimuth for line AP.
2. Find azimuth for line AB.
3. Consider point M which is the mirror image of point P
in the great circle. Find azimuth AM from the first
two azimuths.
4. Find great circle between P and M. The point of interest
is half-way along this line.
Input
a [lon, lat] of first point defining the great circle.
b [lon, lat] of second point defining the great circle.
p [lon, lat] of query point.
Output
h [lon, lat] on great circle closest to query point.
d Perpendicular distance between great circle and point.
m [lon, lat] of mirror image point.
'''
# Ellipsoid.
ell = Geodesic.WGS84
# ab Geodesic from A to B.
# az_ab Azimuth of geodesic from A to B.
ab = ell.Inverse(a[1], a[0], b[1], b[0])
az_ab = ab['azi1']
# ap Geodesic from A to P.
# az_ap Azimuth of geodesic from A to P.
# d_p Distance between A and P along geodesic.
ap = ell.Inverse(a[1], a[0], p[1], p[0])
az_ap = ap['azi1']
d_ap = ap['s12']
# Point M is the image of P on the other side of line AB.
# az_am Azimuth of geodesic from A to M.
# am Geodesic from A to M.
# m [lon, lat] of point M.
az_am = az_ab + (az_ab - az_ap)
am = ell.Direct(a[1], a[0], az_am, d_ap)
m = np.array([am['lon2'], am['lat2']])
# Point H is the half-way between P and M along a great circle.
# pm Geodesic from P to M.
# d Half of the distance from P to M.
# ph Geodesic from P to H.
# h [lon, lat] of point H.
pm = ell.Inverse(p[1], p[0], m[1], m[0])
d = pm['s12']/2.0
ph = ell.Direct(p[1], p[0], pm['azi1'], d)
h = np.array([ph['lon2'], ph['lat2']])
return h, d, m
def test():
import matplotlib.pyplot as plt
from mpl_toolkits.basemap import Basemap
a = np.array([ 80.0, 30.0])
b = np.array([100.0, 50.0])
p = np.array([ 70.0, 45.0])
h, d, m = dist_from_great_circle_to_point(a, b, p)
fig = plt.figure()
ax = plt.gca()
bm = Basemap( projection = 'ortho',
lat_0 = 35.0,
lon_0 = 85.0)
bm.drawcoastlines(linewidth=0.25)
points = [a, b, p, m, h]
point_names = ['A', 'B', 'P', 'M', 'H']
point_colors = ['k', 'k', 'k', 'r', 'r']
point_label_xy = [(-10, -10), (10, 10), (-10, 5), (10, -5), (10, -3)]
lines = [[a, b], [p, m]]
line_colors = ['k', 'r']
for point, color, name, label_xy in zip(
points, point_colors, point_names, point_label_xy):
bm.scatter( point[0], point[1],
color = color,
marker = '.',
latlon = True)
plt.annotate( name,
xy = bm(point[0], point[1]),
xycoords = 'data',
xytext = label_xy,
textcoords = 'offset points',
color = color)
for line, color in zip(lines, line_colors):
bm.drawgreatcircle(
line[0][0], line[0][1],
line[1][0], line[1][1],
color = color)
plt.show()
if __name__ == '__main__':
test()