I am trying to check the error that is introduced when you compute the distance of two points on earth with the euclidean distance instead of using the great circle distance (gcd). I have two points that are defined by their lattitude and longtitude. I used the python geopy framework for the great circle distance. Here the code for the gcd:
def measure(self, a, b):
a, b = Point(a), Point(b)
lat1, lng1 = radians(degrees=a.latitude), radians(degrees=a.longitude)
lat2, lng2 = radians(degrees=b.latitude), radians(degrees=b.longitude)
sin_lat1, cos_lat1 = sin(lat1), cos(lat1)
sin_lat2, cos_lat2 = sin(lat2), cos(lat2)
delta_lng = lng2 - lng1
cos_delta_lng, sin_delta_lng = cos(delta_lng), sin(delta_lng)
d = atan2(sqrt((cos_lat2 * sin_delta_lng) ** 2 +
(cos_lat1 * sin_lat2 -
sin_lat1 * cos_lat2 * cos_delta_lng) ** 2),
sin_lat1 * sin_lat2 + cos_lat1 * cos_lat2 * cos_delta_lng)
return self.RADIUS * d
So or two points:
p1=[39.8616,-75.0748], p2=[-7.30933,112.76]
the
gcd = 78.8433004543197 klm
using the great_circle(p1,p2).kilometers
function from geopy
I then transformed these two points in cartesian coordinates using this formula:
def spherical_to_cartesian(r,la,lo):
x=r*np.sin(90-la)*np.cos(lo)
y=r*np.sin(90-la)*np.sin(lo)
z=r*np.cos(90-la)
return (x,y,z)
where r=6372.795
, which results in the following cartesians coordinates
p1=[ -765.81579368, -256.69640558, 6321.40405587],
p2=[480.8302149,-168.64726394,-6352.39140142]
Then by typing: np.linalg.norm(p2-p1)
i am getting 1103.4963114787836
as their euclidean norm which doesn't seem reasonable compared with ~78klm from the gcd. Am i inffering sth wrong?