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Thread: Compute the distance between two points on the surface of earth

  1. #1
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    Default Compute the distance between two points on the surface of earth

    I wanted to know if my code for finding the distance between two points on the surface of Earth is correct. I had to research online and found the formula for the great circle distance formula for the shortest path between two points on a sphere (I didn't really go in depth, but I do understand the concept of great circle distance and I am familiar with some of the math concepts from Multivariable Calculus and Linear Algebra, though that doesn't matter that much here), which was

    d = acos^-1[cos(x1)cos(x2)cos(y1 - y2) + sin(x1)sin(x2)]
    where a is the radius of the Earth (here, in kilometers), (x1, y1) are the coordinates for distance 1 and (x2, y2) are the coordinates for distance 2.

    I want to know if my code looks fine, because I looked at the solution for this problem and it was kind of different from mines. Also, how would go about this problem, out of curiosity?:

    import java.lang.Math;
    import java.util.Scanner;
     
    class RicMain
    {
    	public static void main(String args[])
    	{
    		Scanner ip = new Scanner(System.in);
    		double x1, x2, y1, y2, a, d;
     
    		          //a is the radius of the sphere.
    		a = 6371.01; //radius of Earth is 6371.01 km.
     
    		System.out.print("Input the latitude of coordinate 1: ");
    		x1 = ip.nextDouble();
    		System.out.print("Input the longitude of coordinate 1: ");
    		y1 = ip.nextDouble();
    		System.out.print("Input the latitude of coordinate 2: ");
    		x2 = ip.nextDouble();
    		System.out.print("Input the longitude of coordinate 2: ");
    		y2 = ip.nextDouble();
    		//x1 and x2 are the latitude (x-axis).
    		//y1 and y2 are the longitude (y-axis).
     
    		//d is the great circle distance (distance between the two points (x1, y1) and (x2, y2).
    		d = a * Math.atan((Math.cos(x1)*Math.cos(x2)*Math.cos(y1 - y2)) + (Math.sin(x1)*Math.sin(x2)));
    		System.out.println("\nThe distance between points (x1, y1) and (x2, y2) is " + d);
    	}
    }

    Also, I inputted the following:
    Input the latitude of coordinate 1: 25
    Input the longitude of coordinate 1: 35
    Input the latitude of coordinate 2: 35.5
    Input the longitude of coordinate 2: 25.5

    The output is suppose to be: 1480.0848451069087 km

    But my output was: 4157.795646651634

    Not sure what's wrong. I think I have to convert it or something?

  2. #2
    Super Moderator Norm's Avatar
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    Default Re: Compute the distance between two points on the surface of earth

    My output is: The distance between points (x1, y1) and (x2, y2) is 3839.512066956892

    Finding the correct formula and then coding it can be a pain.

    One problem probably is the args for the trig methods:
    a - an angle, in radians.
    You need to convert the degrees to radians.
    If you don't understand my answer, don't ignore it, ask a question.

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    Default Re: Compute the distance between two points on the surface of earth

    Quote Originally Posted by Norm View Post

    One problem probably is the args for the trig methods:

    You need to convert the degrees to radians.
    Yes, that was what I was thinking. I was unsure at first if my output was in degrees or radians by default. So how would I do the conversions?

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    Super Moderator Norm's Avatar
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    Default Re: Compute the distance between two points on the surface of earth

    So how would I do the conversions?
    Multiply the degrees by radians/degree
    If you don't understand my answer, don't ignore it, ask a question.

  5. #5
    Super Moderator Norm's Avatar
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    Default Re: Compute the distance between two points on the surface of earth

    So how would I do the conversions?
    Multiply the degrees by radians/degree
    Check the Math class for a method
    If you don't understand my answer, don't ignore it, ask a question.

  6. #6
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    Default Re: Compute the distance between two points on the surface of earth

    Quote Originally Posted by Norm View Post
    Multiply the degrees by radians/degree
    Check the Math class for a method
    There was a mistake in the formula. It was suppose to be arccos, not arctan. I did that by accident. I made two new classes, the first one has the fixed formula with the degrees to radian conversion, and the other is using a nested class. They yield different outputs, but the nested class one is closer to the desired output when I input the following:

    Input Data:
    Input the latitude of coordinate 1: 25
    Input the longitude of coordinate 1: 35
    Input the latitude of coordinate 2: 35.5
    Input the longitude of coordinate 2: 25.5


    Expected Output

    The distance between those points is: 1480.0848451069087 km


    import java.lang.Math;  
     
    import java.util.Scanner;  
     
     
     
    class RicMain  
     
    {  
     
        public static void main(String args[])  
     
        {  
     
            Scanner ip = new Scanner(System.in);  
     
            double x1, x2, y1, y2, a, d;  
     
     
     
            a = 6371.01;  //a is the radius of the sphere. 
     
                         //radius of Earth is 6371.01 km.  
     
     
     
            System.out.print("Input the latitude of coordinate 1: ");  
     
            x1 = ip.nextDouble();  
     
            System.out.print("Input the longitude of coordinate 1: ");  
     
            y1 = ip.nextDouble();  
     
            System.out.print("Input the latitude of coordinate 2: ");  
     
            x2 = ip.nextDouble();  
     
            System.out.print("Input the longitude of coordinate 2: ");  
     
            y2 = ip.nextDouble();  
     
            //x1 and x2 are the latitude (x-axis) in degrees.  
     
            //y1 and y2 are the longitude (y-axis) in degrees. 
     
     
     
            //d is the great circle distance (distance between the two points (x1, y1) and (x2, y2).  
     
            d = a * Math.acos((Math.cos(x1)*Math.cos(x2)*Math.cos(y1 - y2)) + (Math.sin(x1)*Math.sin(x2)));  
     
            System.out.println("\nThe distance between points (x1, y1) and (x2, y2) is " + Math.toRadians(d) + " km");  
     
        }  
     
    }

    import java.lang.Math;  
     
    import java.util.Scanner;  
     
     
     
    class RicMain  
     
    {  
     
        public static void main(String args[])  
     
        {  
     
     
     
            Scanner ip = new Scanner(System.in); 
     
            double x1, y1, x2, y2; 
     
     
     
            System.out.print("Input the latitude of coordinate 1: "); 
     
            x1 = ip.nextDouble();  
     
            System.out.print("Input the longitude of coordinate 1: ");  
     
            y1 = ip.nextDouble();  
     
            System.out.print("Input the latitude of coordinate 2: ");  
     
            x2 = ip.nextDouble();  
     
            System.out.print("Input the longitude of coordinate 2: ");  
     
            y2 = ip.nextDouble();  
     
            //x1 and x2 are the latitude (x-axis) and measured in degrees.  
     
            //y1 and y2 are the longitude (y-axis) and measured in degrees.  
     
     
     
            System.out.println("\nThe distance between points (x1, y1) and (x2, y2) is " + d(x1, y1, x2, y2, y2) + "km");  
     
        }  
     
     
     
        //this inner class converts points to radians. 
     
        //Math.toRadians() converts degrees into radians. 
     
        public static double d(double x1, double x2, double y1, double y2, double a) 
     
        { 
     
            x1 = Math.toRadians(x1); 
     
            y1 = Math.toRadians(y1); 
     
            x2 = Math.toRadians(x2); 
     
            y2 = Math.toRadians(y2); 
     
     
     
            a = 6371.01; //radius of Earth is 6371.01 km. 
     
                         //a is the radius of the sphere. 
     
     
     
            return a * Math.acos((Math.cos(x1)*Math.cos(x2)*Math.cos(y1 - y2)) + (Math.sin(x1)*Math.sin(x2)));  
     
            //the great circle distance (distance between the two points (x1, y1) and (x2, y2). 
     
            //is given in degrees 
     
        } 
     
    }

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