Python计算两个大圆的交点

Question

我试图计算两个大圆的交点（纬度和经度），这两个大圆都是由圆上的两点定义的。我一直在尝试遵循概述的方法here。 但是我得到的答案是不正确的，我的代码在下面有人知道我哪里出错了吗？在

################################################
#### Intersection of two great circles.
# Points on great circle 1.
glat1 = 54.8639587
glon1 = -8.177818

glat2 = 52.65297082
glon2 = -10.78064876

# Points on great circle 2.
cglat1 = 51.5641564
cglon1 = -9.2754284

cglat2 = 53.35422063
cglon2 = -12.5767799

# 1. Put in polar coords.

x1 = cos(glat1) * sin(glon1)
y1 = cos(glat1) * cos(glon1)
z1 = sin(glat1)

x2 = cos(glat2) * sin(glon2)
y2 = cos(glat2) * cos(glon2)
z2 = sin(glat2)


cx1 = cos(cglat1) * sin(cglon1)
cy1 = cos(cglat1) * cos(cglon1)
cz1 = sin(cglat1)

cx2 = cos(cglat2) * sin(cglon2)
cy2 = cos(cglat2) * cos(cglon2)
cz2 = sin(cglat2)


# 2. Get normal to planes containing great circles.
#    It's the cross product of vector to each point from the origin.

N1 = cross([x1, y1, z1], [x2, y2, z2])
N2 = cross([cx1, cy1, cz1], [cx2, cy2, cz2])


# 3. Find line of intersection between two planes.
#    It is normal to the poles of each plane.

L = cross(N1, N2)


# 4. Find intersection points.

X1 = L / abs(L)
X2 = -X1


ilat = asin(X1[2]) * 180./np.pi
ilon = atan2(X1[1], X1[0]) * 180./np.pi

我还应该提到这是在地球表面（假设是一个球体）。在

Answer 1

另一个需要做的修正是在x和y维中改变“lon”之前的cos/sin：

x = cos(lat) * cos(lon)
y = cos(lat) * sin(lon)
z = sin(lat)

这是因为从角度到球面系统的原始转换是使用极轴/方位球角完成的，它们与lat/lon角不同（wiki ithttps://en.wikipedia.org/wiki/Spherical_coordinate_system）。在

Answer 2

DSM的解决方案在上面的注释中，您的角度是以度为单位，而sin和cos则期望弧度。 还有那条线

X1 = L / abs(L)

应该是

^{pr2}$