Step by Step solution about How to resolve the algorithm Haversine formula step by step in the C programming language

This C code calculates the distance between two points on Earth's surface using the Haversine formula. It is a method of calculating the great-circle distance between two points on a sphere.

1. Header Includes:

   • #include <stdio.h>: For input/output functions like printf.
   • #include <stdlib.h>: For exit function.
   • #include <math.h>: For mathematical functions like sin, cos, and asin.

2. Constants:

   • #define R 6371: Radius of the Earth in kilometers.
   • #define TO_RAD (3.1415926536 / 180): Conversion factor from degrees to radians.

3. dist Function:

   • Input: Four double-precision floating-point numbers: th1, ph1, th2, and ph2. These represent the latitudes and longitudes of two points on Earth in decimal degrees.
   • Return: The distance between the two points in kilometers, calculated using the Haversine formula.
   • Formula:

     dist = 2 * R * asin(sqrt(dx^2 + dy^2 + dz^2) / 2)
     

     where:
     • dx = cos(ph1) * cos(th1) - cos(th2)
     • dy = sin(ph1) * cos(th1)
     • dz = sin(th1) - sin(th2)

4. main Function:

   • Calculates the distance between two points on Earth using the dist function:
     • Nashville, TN: (36.12, -86.67)
     • Los Angeles, CA: (33.94, -118.4)
   • Prints the distance in both kilometers and miles, converting kilometers to miles using a factor of 1.609344.

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

#define R 6371
#define TO_RAD (3.1415926536 / 180)
double dist(double th1, double ph1, double th2, double ph2)
{
	double dx, dy, dz;
	ph1 -= ph2;
	ph1 *= TO_RAD, th1 *= TO_RAD, th2 *= TO_RAD;

	dz = sin(th1) - sin(th2);
	dx = cos(ph1) * cos(th1) - cos(th2);
	dy = sin(ph1) * cos(th1);
	return asin(sqrt(dx * dx + dy * dy + dz * dz) / 2) * 2 * R;
}

int main()
{
	double d = dist(36.12, -86.67, 33.94, -118.4);
	/* Americans don't know kilometers */
	printf("dist: %.1f km (%.1f mi.)\n", d, d / 1.609344);

	return 0;
}