angular Distance

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

Contents

Interface
AngularDistance
Distance
Page Comments

Dependents

Interface

C++

AngularDistance

doubleangularDistance(	const Position&	`start`
	const Position&	`end`	)

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.

Parameters

start	the first Position [Latitude, Longitude].
end	the second Position [latitude, Longitude].

Returns

the distance in radian about the center of the sphere.

Source Code

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Distance

doubledistance(	const Position&	`start`
	const Position&	`end`
	double	`radToDist` `= 3437.7475`	)

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 $\inline 2 pi$ . 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 muliply 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

Position start(10,-90);
Position end(45,20);
printf("\nKnots = %lf", distance(start, end)); 
printf("\nMiles = %lf", distance(start, end, 3956.0881));

Parameters

start	Constant
end	a Position reference designating the target location at [Latitude,Longitude].
radToDist	Default Value = 3437.7475

Returns

a Range argument representing the distance to new position, also equal to the 'distance' parameter.

Source Code

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double	`angularDistance` (const Position &start, const Position &end) Returns the "distance" in radians (about the spheres centre) between two positions.
double	`distance` (const Position &start, const Position &end, double radToDist=3437.7475) Returns the distance from the start position to the 'end' position.