2 GPS Coordinates Distance Calculation

 

Introduction

In this article, we will implement Haversine formula to calculate shortest distance between 2 GPS coordinates.

The Haversine formula calculate the great-circle distance between two points on a sphere with given longitudes and latitudes. The shortest distance over the earth surface, ignoring any hills.

Earth is ellipsoidal. Calculate GPS coordinates distance by assuming earth is spherical will yield slight errors.

https://en.wikipedia.org/wiki/Haversine_formula

www.movable-type.co.uk/scripts/latlong.html

 

Haversine formula

R is earth radius (mean radius = 6,371km), ϕ latitude in radians, λ longitude in radians.

 

Calculate 2 GPS coordinates distance in C#

http://www.algoonline.net/Two_GPS_coordinate_distance_calculation/two_GPS_coordinate_distance.png

The above description and the formula from www.movable-type.co.uk/scripts/latlong.html. Hereby is the C# version of the program.

using System;

using System.Collections.Generic;

using System.ComponentModel;

using System.Data;

using System.Drawing;

using System.Linq;

using System.Text;

using System.Windows.Forms;

 

namespace two_GPS_coordinate_distance

{

    public partial class Form1 : Form

    {

        public Form1()

        {

            InitializeComponent();

        }

 

        private void Calculate_Distance_Click(object sender, EventArgs e)

        {

            int R = 6371;

            double lat1 = double.Parse(Latitude_1.Text) * Math.PI / 180;

            double lat2 = double.Parse(Latitude_2.Text) * Math.PI / 180;

            double lon1 = double.Parse(Longitude_1.Text) * Math.PI / 180;

            double lon2 = double.Parse(Longitude_2.Text) * Math.PI / 180;

 

            double dLat = (lat2 - lat1);

            double dLon = (lon2 - lon1);

 

            double a = Math.Sin(dLat / 2) * Math.Sin(dLat / 2) +

        Math.Sin(dLon / 2) * Math.Sin(dLon / 2) * Math.Cos(lat1) * Math.Cos(lat2);

 

            double c = 2 * Math.Atan2(Math.Sqrt(a), Math.Sqrt(1 - a));

            myDistance.Text = (Math.Round(R * c, 3)).ToString() + " km";

        }

    }

}

 

C# version of the Haversine formula program:

·         2GPS_distance.txt in Microsoft C#

·         2 GPS distance in Java Script from www.movable-type.co.uk/scripts/latlong.html website

I just happen to be using the Haversine formula during my work. For your reference.

 

Improve version of calculate 2 GPS coordinates distance in C#

There are number of GPS coordinate formats:

·         degrees minutes seconds (DMS): 40° 26′ 46″ N 79° 58′ 56″ W

·         degrees decimal minutes (DM): 40° 26.767′ N 79° 58.933′ W

·         decimal degrees: 40.446° N 79.982° W

These GPS coordinate format all showing the same value but in different display format.

 

https://en.wikipedia.org/wiki/Geographic_coordinate_conversion

There are 60 minutes in a degree and 60 seconds in a minute. Use the below formula to convert from a degrees minutes seconds format to a decimal degrees format:

To convert back from decimal degree format to degrees minutes seconds format,

degrees = ⌊ decimal degrees ⌋

minutes = ⌊ 60 * (decimal degrees – degrees) ⌋

seconds = 3600 * (decimal degrees – degrees) – 60 * minutes

where the notation ⌊ x ⌋ means take the integer part of x and is called a floor function.

 

Previous program allows GPS coordinates decimal degrees format input. New program allows all 3 formats and are interchangeable.

 C# version of the Haversine formula program:

·         Visual C# in zip – 3 GPS coordinate formats project

 

 

 

Calculate 2 GPS coordinates distance using Vincenty’s formulae by C#

Vincenty's formulae calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). The formulae assume that the figure of the Earth is an oblate spheroid, and hence are more accurate than Haversine formula (assume a spherical Earth).

Vincenty's formulae widely used in geodesy because they are accurate to within 0.5 mm (0.020″) on the Earth ellipsoid.

https://en.wikipedia.org/wiki/Vincenty%27s_formulae

However, one should that note that Vincenty's formulae is computation intensive. To achieve the desire accuracy, Vincenty's formulae need to re-iterate the calculation until λ has converged to the desired degree of accuracy (for example 10−12 corresponds to approximately 0.06mm).

 It can take very long computing time when 2 GPS coordinates distance are far away from each other (> 10 meters) and desired degree of accuracy is small. During the repetitive calculation process, the program will appear to be freeze and not responding.

In below program, Vincenty's formulae iteration limit is set to 0.1 billion times. Program will stop iterative calculation when reached 0.1 billion times to prevent program freeze. Also user can lower the Degree of Accuracy to speed up the iterative calculation.

Haversine formula in contrast does not need much computing efforts, and calculate the distance instantaneously.

two_GPS_coordinate_distance-3

 

C# version of the Haversine formula & Vincenty's formulae program:

·         Visual C# in zip – Haversine formula & Vincenty’s formulae