Objective-C implementation of the Haversine formula and Spherical Law of Cosines used to find the distance between two GPS coordinates. Also, methods are available to find initial and final bearing from GPS coordinates.
The haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes. It is a special case of a more general formula in spherical trigonometry, the law of haversines, relating the sides and angles of spherical triangles. (http://en.wikipedia.org/wiki/Haversine_formula)
In spherical trigonometry, the law of cosines (also called the cosine rule for sides) is a theorem relating the sides and angles of spherical triangles, analogous to the ordinary law of cosines from plane trigonometry. (http://en.wikipedia.org/wiki/Spherical_law_of_cosines)
"If performance is an issue and accuracy less important, for small distances Pythagoras’ theorem can be used on an equirectangular projection." - http://www.movable-type.co.uk/scripts/latlong.html
// Test coordinates // Nantucket Memorial Airport (KACK) CGFloat latitude1 = 41.2531111; CGFloat longitude1 = -70.0603056; // Block Island Airport (KBID) CGFloat latitude2 = 41.1681111; CGFloat longitude2 = -71.5778333; // Logan International Airport (KBOS) CGFloat latitude1 = 42.3629722; CGFloat longitude1 = -71.0064167; // San Francisco International (KSFO) CGFloat latitude2 = 37.6191050; CGFloat longitude2 = -122.3752372; // Setup ZFHaversine *distanceAndBearing = [[ZFHaversine alloc] init]; [distanceAndBearing setLatitude1:latitude1]; [distanceAndBearing setLongitude1:longitude1]; [distanceAndBearing setLatitude2:latitude2]; [distanceAndBearing setLongitude2:longitude2]; // Setup with coordinates ZFHaversine *distanceAndBearing = [[ZFHaversine alloc] initWithLatitude1:latitude1 longitude1:longitude1 latitude2:latitude2 longitude2:longitude2]; // __Optional__: Change the default distance formula from Haversine to the Spherical Law Of Cosines [distanceAndBearing setFormulaMode:sphericalFormula]; // ... or the equirectangular approximation distance formula // Note: with this formula, the further apart the two points are, // the more incorrect the distance gets //[distanceAndBearing setFormulaMode:equirectangularFormula]; // Results for Distance NSLog(@"Kilos %f", [distanceAndBearing kilos]); NSLog(@"Meters %f", [distanceAndBearing meters]); NSLog(@"Nautial Miles %f", [distanceAndBearing nauticalMiles]); NSLog(@"Miles %f", [distanceAndBearing miles]); NSLog(@"Yards %f", [distanceAndBearing yards]); NSLog(@"Feet %f", [distanceAndBearing feet]); // Results for Initial and Final Bearing NSLog(@"Initial Bearing %f", [distanceAndBearing initialBearing]); NSLog(@"Final Bearing %f", [distanceAndBearing finalBearing]);
Steve Foster @flightblog
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