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    <p>Thanks to mimi and this great article <a href="http://www.movable-type.co.uk/scripts/latlong.html" rel="nofollow noreferrer">http://www.movable-type.co.uk/scripts/latlong.html</a> but they don't give the whole picture. Here is a detail one. All this points are collected using Google Earth using Placemark to mark the locations. Make sure lat/long are set to decimal degrees in Preferences.</p> <pre><code>lat A = 3.222895 lon A = 101.719751 lat B = 3.222895 lon B = 101.719751 lat C = 3.224972 lon C = 101.722932 Earth radius, R = 6371 </code></pre> <p><strong>1. First you have to find the bearing from A to C and A to B.</strong><br> Bearing formula </p> <pre><code>bearingAC = atan2( sin(Δλ)*cos(φ₂), cos(φ₁)*sin(φ₂) − sin(φ₁)*cos(φ₂)*cos(Δλ) ) bearingAB = atan2( sin(Δλ)*cos(φ₂), cos(φ₁)*sin(φ₂) − sin(φ₁)*cos(φ₂)*cos(Δλ) ) </code></pre> <p>φ is latitude, λ is longitude, R is earth radius</p> <p><strong>2. Find A to C distance using spherical law of cosines</strong> </p> <pre><code>distanceAC = acos( sin(φ₁)*sin(φ₂) + cos(φ₁)*cos(φ₂)*cos(Δλ) )*R </code></pre> <p><strong>3. Find cross-track distance</strong> </p> <pre><code>distance = asin(sin(distanceAC/ R) * sin(bearingAC − bearing AB)) * R </code></pre> <p><strong>Objective-C code</strong> </p> <pre><code>double lat1 = 3.227511; double lon1 = 101.724318; double lat2 = 3.222895; double lon2 = 101.719751; double lat3 = 3.224972; double lon3 = 101.722932; double y = sin(lon3 - lon1) * cos(lat3); double x = cos(lat1) * sin(lat3) - sin(lat1) * cos(lat3) * cos(lat3 - lat1); double bearing1 = radiansToDegrees(atan2(y, x)); bearing1 = 360 - ((bearing1 + 360) % 360); double y2 = sin(lon2 - lon1) * cos(lat2); double x2 = cos(lat1) * sin(lat2) - sin(lat1) * cos(lat2) * cos(lat2 - lat1); double bearing2 = radiansToDegrees(atan2(y2, x2)); bearing2 = 360 - ((bearing2 + 360) % 360); double lat1Rads = degreesToRadians(lat1); double lat3Rads = degreesToRadians(lat3); double dLon = degreesToRadians(lon3 - lon1); double distanceAC = acos(sin(lat1Rads) * sin(lat3Rads)+cos(lat1Rads)*cos(lat3Rads)*cos(dLon)) * 6371; double min_distance = fabs(asin(sin(distanceAC/6371)*sin(degreesToRadians(bearing1)-degreesToRadians(bearing2))) * 6371); NSLog(@"bearing 1: %g", bearing1); NSLog(@"bearing 2: %g", bearing2); NSLog(@"distance AC: %g", distanceAC); NSLog(@"min distance: %g", min_distance); </code></pre> <p>Actually there's a library for this. You can find it here <a href="https://github.com/100grams/CoreLocationUtils" rel="nofollow noreferrer">https://github.com/100grams/CoreLocationUtils</a></p>
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