LocationDistance ( latitude1 ; longitude1 ; latitude2 ; longitude2 )

Distance between two locations given by coordinates

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Jeremy Bante

https://github.com/jbante/

Sample input:

LocationDistance (
37.7749296 ; -122.419416; // San Francisco
40.7143528 ; -74.0059731 // New York
)

Sample output:

4139112.9605735081163149
// ~2572 miles

Function definition: (Copy & paste into FileMaker's Edit Custom Function window)

/*******************************************************************************
 * LocationDistance ( latitude1 ; longitude1 ; latitude2 ; longitude2 )
 * Calculates the distance between two points on the surface of the Earth. This
 * function assumes that coordinates are in the WGS84 coordinate system.
 *
 * @parameter latitude1: Latitude of the first point
 * @parameter longitude1: Longitude of the first point
 * @parameter latitude2: Latitude of the second point
 * @parameter longitude2: Longitude of the second point
 *
 * @return The distance between the two points, in meters.
 *
 * @history 2012-09-26 - Jeremy Bante <http://scr.im/jbante> - Created
 * @history 2014-09-15 - Jeremy Bante <http://scr.im/jbante> - Using the
 * Andoyer-Lambert-Thomas formula approximating distances on an ellipsoid
 * instead of a sphere to improve accuracy.
 *
 * @see http://www.dtic.mil/dtic/tr/fulltext/u2/703541.pdf
 * @see http://en.wikipedia.org/wiki/World_Geodetic_System
 ******************************************************************************/

Let ( [
	_equatorialRadius = 6378137 ;	// meters
	_flattening = .0033528106647475 ;	// 1 / 298.257223563

	_parametricStartLatitude =
		Atan (
			( 1 - _flattening ) * Tan ( Radians ( latitude1 ) )
		) ;
	_parametricEndLatitude =
		Atan ( ( 1 - _flattening ) * Tan ( Radians ( latitude2 ) ) ) ;
	_latitudeMean =
		( _parametricStartLatitude + _parametricEndLatitude ) / 2 ;
	_sin_latitudeMean = Sin ( _latitudeMean ) ;
	_halfLatitudeDifference =
		( _parametricEndLatitude - _parametricStartLatitude ) / 2 ;
	_sin_halfLatitudeDifference = Sin ( _halfLatitudeDifference ) ;
	_cos_halfLatitudeDifference = Cos ( _halfLatitudeDifference ) ;
	_l =
		_sin_halfLatitudeDifference ^ 2
		+ ( _cos_halfLatitudeDifference ^ 2 - _sin_latitudeMean ^ 2 )
		* Sin ( Radians ( longitude2 - longitude1 ) / 2 ) ^ 2 ;
	_cos_d = 1 - 2 * _l ;
	_d = Acos ( _cos_d ) ;
	_sin_d = Sin ( _d ) ;
	_uu =
		2 * _sin_latitudeMean ^ 2
		* _cos_halfLatitudeDifference ^ 2 / ( 1 - _l ) ;
	_vv =
		2
		* _sin_halfLatitudeDifference ^ 2
		* Cos ( _latitudeMean ) ^ 2
		/ _l ;
	_x = _uu + _vv ;
	_t = _d / _sin_d ;
	_e = 2 * _cos_d ;
	_y = _uu - _vv ;
	_dd = 4 * _t ^ 2 ;
	_a = _dd * _e ;
	_c = _t - .5 * ( _a - _e ) ;
	_delta1_d = .25 * _flattening * ( _t * _x - _y ) ;
	_delta2_d =
		( _flattening ^ 2 / 64 )
		* (
			_x * ( _a + _c * _x )
			- _y * ( 2 * _dd + _e * _y )
			+ _dd * _x * _y
		) ;
	_distance =
		_equatorialRadius * _sin_d * ( _t - _delta1_d + _delta2_d )
] ;
	_distance
)

Calculates the distance between two points on the surface of the Earth. The calculation used is typically accurate to within several centimeters.

Comments

		Ros, Calgary Jan 3, 2015
Very useful, ...thank you...!

Note: these functions are not guaranteed or supported by BrianDunning.com. Please contact the individual developer with any questions or problems.

LocationDistance ( latitude1 ; longitude1 ; latitude2 ; longitude2 )

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