Daily Archives: May 27, 2011

Simple Geographical Calculations

This entry was posted in Research in General on by

In this post, I would like to share some simple code to calculate geographical distances by using latitude and longitude points from some third-party services. This is particular useful when we wish to compute the average distances users travel from the check-in or geo-tagging information from Twitter, for instance. The code is straightforward and simple.

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60

import math
import sys
import os
 
## Convert a location into 3d Corordinates
## location is a list of [latitude,longtidue]
## return: a list of [x,y,z]
def convert_location_cor(location):
    x_n = math.cos(math.radians(location[0])) * math.cos(math.radians(location[1]))
    y_n = math.cos(math.radians(location[0])) * math.sin(math.radians(location[1]))
    z_n = math.sin(math.radians(location[0]))
    return [x_n,y_n,z_n]
 
## Convert a 3d Corordinates into a location
## cor is a list of [x,y,z]                                                                                                                          
## return: a list of [latitude, longtitude]
def convert_cor_location(cor):
    r = math.sqrt(cor[0] * cor[0] + cor[1] * cor[1]+ cor[2] * cor[2])
    lat = math.asin(cor[2] / r)
    log = math.atan2(cor[1], cor[0])
    return [math.degrees(lat),math.degrees(log),math.degrees(r)]
 
## Compute the geographical midpoint of a set of locations
## location_list is a list of locations [locaiton 0, location 1, location 2]
## return: the location of midpoint                                                                                              
def geo_midpoint(location_list):
    x_list = []
    y_list = []
    z_list = []
    for i in range(len(location_list)):
	m = convert_location_cor(location_list[i])
	x_list.append(m[0])
	y_list.append(m[1])
	z_list.append(m[2])
    x_mean = sum(x_list) / float(len(location_list))
    y_mean = sum(y_list) / float(len(location_list))
    z_mean = sum(z_list) / float(len(location_list))
    return convert_cor_location([x_mean,y_mean,z_mean])
 
## Compute the distance between two locations
## a and b are two locations: [lat 1, lon 1] [lat 2, lon 2]
## return: the distance in KM
def geo_distance(a,b):
    theta = a[1] - b[1]
    dist = math.sin(math.radians(a[0])) * math.sin(math.radians(b[0])) \
     + math.cos(math.radians(a[0])) * math.cos(math.radians(b[0])) * math.cos(math.radians(theta))
    dist = math.acos(dist)
    dist = math.degrees(dist)
    distance = dist * 60 * 1.1515 * 1.609344
    return distance
 
## main program
if __name__ == '__main__':
    l_list = []
    l_list.append([-8.70934,115.173695])
    l_list.append([-8.70934,115.235514])
    l_list.append([-8.591728,115.235514])
    l_list.append([-8.591728,115.173695])
    midpoint = geo_midpoint(l_list)
    print geo_distance([-8.70934,115.173695],[-8.70934,115.235514])