LatLong

A simple Java datatype to store the Latitude and the Longitude. Distance calculations are included.

Calculation of the distance between two points

Formular

The formular for the calculation of the distance is from https://www.calculator.net/distance-calculator.html.

Note

For this project I used the Lambert's formula for distance calculations on an earth elipsoid.

This is the formula:


In code:

double d = a * (o - (f / 2) * (X + Y));

• double d is the distance to be calculated, unit: meter
  
• a is the equatorial radius of the earth, unit: meter
  
• o means σ and stands for the central angle, (we will calculate it later) unit: radiand
  
• f is the flattening of the earth, (we will calculate it later)
  
• X and Yis calculated later.
  
  

So to calculate the distance we have to get a, o, f, X and Y.

First we have to get a, the equatorial radius. You can get it by calling my class:

double a = LatLong.radiusEquatorial;

Tip

Alternatively you can go to https://www.heret.de/mathe/erde.shtml and copy the "Äquatorradius", which is 6378137m.

Next we have to calculate o. There is a formula for this on wikipedia:

• is our o. unit: radiand
  
• is the latitude of a given point. In our case is 1 the latitude of Point A and 2 the latitude of Point B. unit: radiand
  
• are the differences of the latitudes and longitudes of the two points. unit: radiand
  

In code it looks like that:

double deltaLongitude = Math.abs(longitudeA - longitudeB);
double o = Math.acos(Math.sin(latitudeA) * Math.sin(latitudeB) + Math.cos(latitudeA) * Math.cos(latitudeB) * Math.cos(deltaLongitude));

Caution

Don't forget to convert the latitude and longitude values from degree to radiand, because the Math.acos(), Math.sin()and Math.cos() need or return angles in radiands.

latitudeA = Math.toRadians(latitudeA);
latitudeB = Math.toRadians(latitudeB);
longitudeA = Math.toRadians(longitudeA);
longitudeB = Math.toRadians(longitudeB);

Now we calculate f. fis the flattening of the earth and is calculated like that:

In code:

f = (a - b) / a;

• a is still the equatorial radius of the earth unit: meter
  
• b is the polar radius of the earth unit: meter
  

After that we can calculate X and Y. The calculation of that is a little bit complex and we need some other values. The formulas are:

Note

For those who don't know, sin²() and cos²() is a short writing for (sin())² and (cos())².

In Code it looks like that:

double X = (o - Math.sin(o)) * ((Math.pow(Math.sin(P), 2) * Math.pow(Math.cos(Q), 2)) / (Math.pow(Math.cos(o / 2), 2)));
double Y = (o + Math.sin(o)) * ((Math.pow(Math.cos(P), 2) * Math.pow(Math.sin(Q), 2)) / (Math.pow(Math.sin(o / 2), 2)));

• o is the variable we calculated earlier unit: radiand
  
• P and Q are Variables which have to be calculated.

So for using the formula we have to calculate P and Q. Here is the formula for that:

P = (β1 + β2)/2
and
Q = (β2 - β1)/2

Now we have to calculate β1 and β2. And as you may already know, there is a formular for this:

tan(β) = (1 - f)tan(ϕ)

That means that you have to calculate one β for each of the two points.

• f is the value which we calculated earlier,
  
• ϕ is the latitude of the given point,
  

When we have all values, we can calculate X and Y. Here is the Code for that:

betaA = Math.atan((1 - f) * Math.tan(latitudeA));
betaB = Math.atan((1 - f) * Math.tan(latitudeB));

P = (betaA + betaB) / 2;
Q = (betaB - betaA) / 2;

double X = (o - Math.sin(o)) * ((Math.pow(Math.sin(P), 2) * Math.pow(Math.cos(Q), 2)) / (Math.pow(Math.cos(o / 2), 2)));
double Y = (o + Math.sin(o)) * ((Math.pow(Math.cos(P), 2) * Math.pow(Math.sin(Q), 2)) / (Math.pow(Math.sin(o / 2), 2)));

Tip

You can test the code with the Distance Calculator (It uses the same Code).

Usage of the distance calculation

There are different ways to use the distance calculation with the LatLong class integrated in your project:

• Use the static distance function of the class:

  LatLong.distance(latitudeFromPointA, longitudeFromPointA, latitudeFromPointB, longitudeFromPointB);
  

  LatLong PointA = new LatLong(latitudeFromPointA, longitudeFromPointA);
  LatLong PointB = new LatLong(latitudeFromPointB, longitudeFromPointB);
  LatLong.distance(PointA, PointB);
  

• Use the distance function from an LatLong object:

  LatLong PointA = new LatLong(latitudeFromPointA, longitudeFromPointA);
  LatLong PointB = new LatLong(latitudeFromPointB, longitudeFromPointB);
  PointA.distanceTo(PointB);
  

General Usage

Creating an LatLong object

There are three different ways to make an object of the LatLong class in your project:

1. LatLong location = new LatLong();
   

   Creates an LatLong object with the cooridinates 0, 0.
   
   

2. LatLong location = new LatLong(latitude, longitude);
   

   Creates an LatLong object with the given cooridinates.
   
   

3. Location mylocation = getmylocation();
   LatLong location = new LatLong(mylocation);
   

   In this example we have an (imaginary) function which returns an value of type Location. The constructor converts the Location into an LatLong datatype.
   
   

Getting or setting the values of an LatLong object

You can set the latitude and longitude values by calling the setLatitude() or the setLongitude() functions:

LatLong location = new LatLong();
location.setLatitude(latitude);
location.setLongitude(longitude);

You can get the latitude and longitude values by calling the getLatitude() or the getLongitude() functions:

LatLong location = new LatLong();
double latitude = location.getLatitude();
double longitude = location.getLongitude();

Constants

radiusEquatorial

Returns the euatorial radius in meter:

double eqatorialRadius = LatLong.radiusEquatorial;

radiusPolar

Returns the polar radius in meter:

double polarRadius = LatLong.radiusPolar;

Other Constants

The other Constants only return Locations in LatLong Datatype. They are not very useful and you can delete them if you want. They are not used in the program.