I am trying to calculate the point of intersection (lat and lon in degrees) of two great circles that are each defined by two points on the circle. I have been trying to follow method outlined here. But the answer I get is incorrect, my code is below does anyone see where I went wrong?
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#### 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
I should also mention this is on the Earth's surface (assuming a sphere).