Function for the Google Maps API V3 that returns a LatLng object representing the midpoint of a complex polyline (taken in as an array of points). Also requires midpoint distance, but this is easily calculable from the array of points.

googleMapsPolylineMidpoint.js

getMidpoint: function(points, midpointDistance) {
  var tempDistance = midpointDistance;
  var midpointLatLng;

  // We go through each segment of the line
  for (var i = 0; i < points.length - 1; i++) {
    var segment = points.slice(i, i + 2);
    var length = google.maps.geometry.spherical.computeLength(segment);
    tempDistance = tempDistance - length;

    // If we're at zero or below, we've found the line where our midpoint exists
    if (tempDistance <= 0) {
      // We've gone past the midpoint so we need to back up.
      var midpointLength = tempDistance + length;

      // The proportion of the current segment where our midpoint exists
      var percentage = midpointLength / length;

      midpointLatLng = google.maps.geometry.spherical.interpolate(segment[0], segment[1], percentage);
      break;
    }
  }

  if (typeof midpointLatLng === 'undefined') {
    // we don't have a midpoint for this polyline, something went very wrong
    return false;
  } else {
    return midpointLatLng;
  }
}