http://williams.best.vwh.net/avform.htm

avform.js

      function toRad(degree) { return degree * Math.PI / 180; }
      function toDeg(radian) { return radian * 180 / Math.PI; }

      // round floating point errors
      function rnd( float ){
        return (Math.floor(100000 * float) / 100000).toFixed(5);
      }

      function assert( a, b ){
        switch( typeof a ){
          case 'number':
            if( a % 1 !== 0 ) console.log( rnd(a) == rnd(b) ? '✓': '✖', rnd(a), rnd(b), a, b ); // float
            else console.log( a == b ? '✓': '✖', a, b ); // int
            break;
          default:
            console.log( a == b ? '✓': '✖', a, b );
        }
      }

      function dist( a, b ){
        return Math.acos( Math.sin( a.lat ) * Math.sin( b.lat ) +
          Math.cos( a.lat ) * Math.cos( b.lat ) * Math.cos( a.lon - b.lon ));
      }

      function course( a, b, d ){
        return Math.acos(
          ( Math.sin( b.lat ) - Math.sin( a.lat ) * Math.cos( d )) /
          ( Math.sin( d ) * Math.cos( a.lat ) )
        );
      }

      function xTrack( d, crs1, crs2 ){
        return Math.asin( Math.sin( d ) * Math.sin( crs1 - crs2 ) );
      }

      function aTrack( d, xtd ){
        return Math.acos( Math.cos( d ) / Math.cos( xtd ) );
      }

      function aTrackSimple( d, xtd ){
        return Math.asin( Math.sqrt( Math.pow( Math.sin( d ), 2 ) - Math.pow( Math.sin( xtd ), 2 ) ) / Math.cos( xtd ) );
      }

      function interpolate( d, f, a, b ){
        var A = Math.sin( (1-f) * d ) / Math.sin( d );
        // assert( A, 0.62588 );
        var B = Math.sin( f * d ) / Math.sin( d );
        // assert( B, 0.422735 );
        var X = A * Math.cos( a.lat ) * Math.cos( a.lon ) + B * Math.cos( b.lat ) * Math.cos( b.lon );
        // assert( X, -0.157344 );
        var Y = A * Math.cos( a.lat ) * Math.sin( a.lon ) + B * Math.cos( b.lat ) * Math.sin( b.lon );
        // assert( Y, 0.764745 );
        var Z = A * Math.sin( a.lat ) + B * Math.sin( b.lat );
        // assert( Z, 0.624826 );
        return {
          lat: Math.atan2( Z, Math.sqrt( Math.pow( X, 2 ) + Math.pow( Y, 2 ) ) ),
          lon: Math.atan2( Y, X )
        }
      }

      // we travel from JFK to LAX and end up at D
      var LAX = { lon: 118.4, lat: 33.95, rad: { lat: 0, lon: 0 } };
      var JFK = { lon: 73.7833, lat: 40.6333, rad: { lat: 0, lon: 0 } };
      var LOST = { lon: 116.5, lat: 34.5, rad: { lat: 0, lon: 0 } };

      LAX.rad.lat = toRad( LAX.lat );
      LAX.rad.lon = toRad( LAX.lon );
      JFK.rad.lat = toRad( JFK.lat );
      JFK.rad.lon = toRad( JFK.lon );

      assert( LAX.rad.lat, 0.592539 );
      assert( LAX.rad.lon, 2.066470 );
      assert( JFK.rad.lat, 0.709186 );
      assert( JFK.rad.lon, 1.287762 );

      LOST.rad.lat = toRad( LOST.lat );
      LOST.rad.lon = toRad( LOST.lon );

      assert( LOST.rad.lat, 0.6021386 );
      assert( LOST.rad.lon, 2.033309 );

      var dist_AD = dist( LAX.rad, LOST.rad );
      assert( dist_AD, 0.02905 );

      var crs_AD = course( LAX.rad, LOST.rad, dist_AD );
      assert( crs_AD, 1.22473 );

      //---
      var dist_AB = dist( LAX.rad, JFK.rad );
      assert( dist_AB, 0.62358 );

      var crs_AB = course( LAX.rad, JFK.rad, dist_AB );
      assert( crs_AB, 1.15003 );
      //---

      var xtd = xTrack( dist_AD, crs_AD, crs_AB );
      assert( xtd, 0.00216747 );

      var atd = aTrack( dist_AD, xtd );
      assert( atd, 0.0289691 );

      var atd2 = aTrackSimple( dist_AD, xtd );
      assert( atd2, 0.0289691 );

      var forty = interpolate( dist_AB, 0.4, LAX.rad, JFK.rad );
      assert( forty.lat, 0.674909 );
      assert( forty.lon, 1.77371 );