Peter Lubbers - Pro HTML 5 Programming

Listing 4-6. The Haversine formula
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scos� f sin 2 �
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CHAPTER 4 ■ USING THE HTML5 GEOLOCATION API
If you're hoping to learn how the Haversine formula works, you’ll be sorely disappointed. Instead,
we’ll present you a JavaScript implementation of the formula, which allows anyone to use it to calculate
the distance between two positions (see Listing 4-7).
Listing 4-7. A JavaScript Haversine implementation
function toRadians(degree) {
return degree * Math.PI / 180;
}
function distance(latitude1, longitude1, latitude2, longitude2) {
// R is the radius of the earth in kilometers
var R = 6371;
var deltaLatitude = toRadians(latitude2-latitude1);
var deltaLongitude = toRadians(longitude2-longitude1);
latitude1 =toRadians(latitude1);
latitude2 =toRadians(latitude2);
var a = Math.sin(deltaLatitude/2) *
Math.sin(deltaLatitude/2) +
Math.cos(latitude1) *
Math.cos(latitude2) *
Math.sin(deltaLongitude/2) *
Math.sin(deltaLongitude/2);
var c = 2 * Math.atan2(Math.sqrt(a),
Math.sqrt(1-a));
var d = R * c;
return d;
}
If you want to know why or how this formula works, consult a teenager’s math textbook. For our
purposes, we have written a conversion from degrees to radians, and we provided a distance() function
to calculate the distance between two latitude and longitude position values.
If we check the user’s position and calculate the distance traveled at frequent and regular intervals,
it gives a reasonable approximation of distance traveled over time. This assumes that the user is moving
in a straight direction during each interval, but we’ll make that assumption for the sake of our example.
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