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Android – Distance between two points on the Earth

2013年03月06日 ⁄ 综合 ⁄ 共 1896字 ⁄ 字号 评论关闭

When working with geo data, it is sometimes necessary to calculate
the distance between two geolocations on the surface of the Earth. This
is also a problem where I came upon and I will therefore describe my
findings in this post.

Working in this area means that one has to brush of his trigonometry
skills. But luckily there are some good resources on the web, that
explain the theory perfectly. The formula you need is the haversine
formula, which gets its name from the use of the haversine function:
haversin(/Theta) = sin^2(/Theta / 2)

.

The haversine formula is:

R =

earth’s radius (mean radius = 6367.45 km)

/Delta lat = lat_2 - lat_1

/Delta long = long_2 - long_1

a = sin^2(/Delta lat / 2) + cos(lat_1)cos(lat_2)sin^2(/Delta long / 2)

c = 2 atan2(/sqrt{a}, /sqrt{(1-a)})

d = Rc

Here the distance d

in kilometers will be calculated based on the latitudes and longitudes
of the two points on the earth, expressed in radians. To convert from
degrees to radians, simply multiply the value in degrees by /pi / 180

. The atan2()

function is a function implemented in many computer languages and is a variation

on the arctangent function.

The error of this formula in calculating distances is about 0.1% and
mostly due to the fact that the Earth is not a perfect sphere (see the
resources below for a more in-depth discussion). Also numerical
rounding errors can occur, but this is mainly an issue when the two
locations are very nearly antipodal (on opposite sites of the Earth),
which is generally not something you will use very often.

But enough now of the theoretics, I will show how to put this to a
practical use. The code to calculate the distance between two points
can be expressed in Java code as:

One thing you need to make sure, is that the latitude and longitude are expressed in radians (see above).

Put this code into a method and you are done.

This post is based on a few web resources, that will give a bit more information on distance calculations. There is a nice wikipedia

article on the Haversine formula. Here

and here

you can find a bit more information on calculating distances on a sphere.

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