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Returns the "distance" in radians (about the spheres centre) between two positions.

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Interface

#include <codecogs/maths/geometry/spherical/angulardistance.h>

using namespace Maths::Geometry::Spherical;

double distance(const Position &start, const Position &end, double radToDist=3437.7475)

Overview

Calculates the angular between two points on the surface of a sphere relative to the centre of the sphere.

This calculation is made using:

$dist = cos^{-1} \left [ sin(a_{lat}) sin(b_{lat}) + cos(a_{lat}) cos(b_{lat}) cos(b_{long} - a_{long}) \right ]$

(1)

where a and b are the start and end location.

Example 1

#include <stdio.h>
#include <codecogs/geometry/spherical/angularDistance.h>

int main()
{
  Position start(10,-90);
  Position end(45,20);
  printf("Angular Distance in Radians = %lf", angularDistance(start, end)); 
	return 0;
}

Output:

Angular Distance in Radians = 1.686437

Parameters

start

the first position [Latitude, Longitude].

end

the second position [latitude, Longitude].

Returns

the distance in radian about the center of the sphere.

FUNCTION

distance

Applies a simple conversion to the distance calculated by angularDistance to give a more conventional measure of distance according to the specified conversion ratio. This is simple the circumference of the sphere divided by $2 pi$ . For example, with the planet earth on degree is divided into 60, which is called 1 minute of arc. This is also one nautical mile. Therefore to convert radian to nautical miles (knots) you multiply by:

$\frac{360.0 \cdot 60}{2 \pi}$

(2)

<table> <tr><td align="middle"><strong>Description</strong></td><td align="middle"><strong>radToDist</strong></td></tr> <tr><td>Nautical Mile on Earth</td><td>3437.7475 knots/radian</td></tr> <tr><td>Miles on Earth</td><td>3956.0881 miles/radian</td></tr> <tr><td>kilometers on Earth</td><td>6366.7070 km/radian</td></tr> </table>

Example 1

#include <stdio.h>
#include <codecogs/geometry/spherical/angulardistance.h>

int main()
{
  Position start(10,-90);
  Position end(45,20);
  printf("\nKnots = %lf", distance(start, end)); 
  printf("\nMiles = %lf", distance(start, end, 3956.0881)); 
	return 0;
}

Output:

Knots = 5797.543498
Miles = 6671.692101

Parameters

start

the first position [Latitude, Longitude].

end

the second position [latitude, Longitude].

radToDist

Default Value = 3437.7475

Returns

the distance to new position.