I would like to know how to get the distance and bearing between 2 GPS points. I have researched on the haversine formula. Someone told me that I could also find the bearing using the same data.
Everything is working fine but the bearing doesn't quite work right yet. The bearing outputs negative but should be between 0 - 360 degrees.
The set data should make the horizontal bearing 96.02166666666666
and is:
Start point: 53.32055555555556 , -1.7297222222222221
Bearing: 96.02166666666666
Distance: 2 km
Destination point: 53.31861111111111, -1.6997222222222223
Final bearing: 96.04555555555555
Here is my new code:
from math import *
Aaltitude = 2000
Oppsite = 20000
lat1 = 53.32055555555556
lat2 = 53.31861111111111
lon1 = -1.7297222222222221
lon2 = -1.6997222222222223
lon1, lat1, lon2, lat2 = map(radians, [lon1, lat1, lon2, lat2])
dlon = lon2 - lon1
dlat = lat2 - lat1
a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
c = 2 * atan2(sqrt(a), sqrt(1-a))
Base = 6371 * c
Bearing =atan2(cos(lat1)*sin(lat2)-sin(lat1)*cos(lat2)*cos(lon2-lon1), sin(lon2-lon1)*cos(lat2))
Bearing = degrees(Bearing)
print ""
print ""
print "--------------------"
print "Horizontal Distance:"
print Base
print "--------------------"
print "Bearing:"
print Bearing
print "--------------------"
Base2 = Base * 1000
distance = Base * 2 + Oppsite * 2 / 2
Caltitude = Oppsite - Aaltitude
a = Oppsite/Base
b = atan(a)
c = degrees(b)
distance = distance / 1000
print "The degree of vertical angle is:"
print c
print "--------------------"
print "The distance between the Balloon GPS and the Antenna GPS is:"
print distance
print "--------------------"
You can solve the negative bearing problem by adding 360°. Unfortunately, this might result in bearings larger than 360° for positive bearings. This is a good candidate for the modulo operator, so all in all you should add the line
Bearing = (Bearing + 360) % 360
at the end of your method.
The bearing calculation is incorrect, you need to swap the inputs to atan2.
bearing = atan2(sin(long2-long1)*cos(lat2), cos(lat1)*sin(lat2)-sin(lat1)*cos(lat2)*cos(long2-long1))
bearing = degrees(bearing)
bearing = (bearing + 360) % 360
This will give you the correct bearing.
Here's a numpy vectorized implementation of the Haversine Formula given by @Michael Dunn, gives a 10-50 times improvement over large vectors.
from numpy import radians, cos, sin, arcsin, sqrt
def haversine(lon1, lat1, lon2, lat2):
"""
Calculate the great circle distance between two points
on the earth (specified in decimal degrees)
"""
#Convert decimal degrees to Radians:
lon1 = np.radians(lon1.values)
lat1 = np.radians(lat1.values)
lon2 = np.radians(lon2.values)
lat2 = np.radians(lat2.values)
#Implementing Haversine Formula:
dlon = np.subtract(lon2, lon1)
dlat = np.subtract(lat2, lat1)
a = np.add(np.power(np.sin(np.divide(dlat, 2)), 2),
np.multiply(np.cos(lat1),
np.multiply(np.cos(lat2),
np.power(np.sin(np.divide(dlon, 2)), 2))))
c = np.multiply(2, np.arcsin(np.sqrt(a)))
r = 6371
return c*r
Here are two functions to calculate distance and bearing, which are based on the code in previous messages and https://gist.github.com/jeromer/2005586 (added tuple type for geographical points in lat, lon format for both functions for clarity). I tested both functions and they seem to work right.
#coding:UTF-8
from math import radians, cos, sin, asin, sqrt, atan2, degrees
def haversine(pointA, pointB):
if (type(pointA) != tuple) or (type(pointB) != tuple):
raise TypeError("Only tuples are supported as arguments")
lat1 = pointA[0]
lon1 = pointA[1]
lat2 = pointB[0]
lon2 = pointB[1]
# convert decimal degrees to radians
lat1, lon1, lat2, lon2 = map(radians, [lat1, lon1, lat2, lon2])
# haversine formula
dlon = lon2 - lon1
dlat = lat2 - lat1
a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlon/2)**2
c = 2 * asin(sqrt(a))
r = 6371 # Radius of earth in kilometers. Use 3956 for miles
return c * r
def initial_bearing(pointA, pointB):
if (type(pointA) != tuple) or (type(pointB) != tuple):
raise TypeError("Only tuples are supported as arguments")
lat1 = radians(pointA[0])
lat2 = radians(pointB[0])
diffLong = radians(pointB[1] - pointA[1])
x = sin(diffLong) * cos(lat2)
y = cos(lat1) * sin(lat2) - (sin(lat1)
* cos(lat2) * cos(diffLong))
initial_bearing = atan2(x, y)
# Now we have the initial bearing but math.atan2 return values
# from -180° to + 180° which is not what we want for a compass bearing
# The solution is to normalize the initial bearing as shown below
initial_bearing = degrees(initial_bearing)
compass_bearing = (initial_bearing + 360) % 360
return compass_bearing
pA = (46.2038,6.1530)
pB = (46.449, 30.690)
print haversine(pA, pB)
print initial_bearing(pA, pB)
Refer to this link :https://gis.stackexchange.com/questions/84885/whats-the-difference-between-vincenty-and-great-circle-distance-calculations
this actually gives two ways of getting distance. They are Haversine and Vincentys. From my research I came to know that Vincentys is relatively accurate. Also use import statement to make the implementation.
There is also a vectorized implementation, which allows to use 4 numpy arrays instead of scalar values for coordinates:
def distance(s_lat, s_lng, e_lat, e_lng):
# approximate radius of earth in km
R = 6373.0
s_lat = s_lat*np.pi/180.0
s_lng = np.deg2rad(s_lng)
e_lat = np.deg2rad(e_lat)
e_lng = np.deg2rad(e_lng)
d = np.sin((e_lat - s_lat)/2)**2 + np.cos(s_lat)*np.cos(e_lat) * np.sin((e_lng - s_lng)/2)**2
return 2 * R * np.arcsin(np.sqrt(d))
The Y in atan2 is, by default, the first parameter. Here is the documentation. You will need to switch your inputs to get the correct bearing angle.
bearing = atan2(sin(lon2-lon1)*cos(lat2), cos(lat1)*sin(lat2)in(lat1)*cos(lat2)*cos(lon2-lon1))
bearing = degrees(bearing)
bearing = (bearing + 360) % 360
Most of these answers are "rounding" the radius of the earth. If you check these against other distance calculators (such as geopy), these functions will be off.
This works well:
from math import radians, cos, sin, asin, sqrt
def haversine(lat1, lon1, lat2, lon2):
R = 3959.87433 # this is in miles. For Earth radius in kilometers use 6372.8 km
dLat = radians(lat2 - lat1)
dLon = radians(lon2 - lon1)
lat1 = radians(lat1)
lat2 = radians(lat2)
a = sin(dLat/2)**2 + cos(lat1)*cos(lat2)*sin(dLon/2)**2
c = 2*asin(sqrt(a))
return R * c
# Usage
lon1 = -103.548851
lat1 = 32.0004311
lon2 = -103.6041946
lat2 = 33.374939
print(haversine(lat1, lon1, lat2, lon2))
You can try the following:
from haversine import haversine
haversine((45.7597, 4.8422),(48.8567, 2.3508), unit='mi')
243.71209416020253
Source: Stackoverflow.com