Google Maps Polygons self intersecting detection

I'm trying to implement a polygon self intersection algorithm from Google Maps API V3 polygons.
The goal is just to detect if yes or no, a simple polygon drawn by the user is self crossing.

I have found this very interesting link, but it assumes that coordinates of the polygon's vertices are given on geoJSON format. However, this isn't my case ; I'm only able to retrieve polygons coordinates using polygon.getPath() into a polygoncomplete event.

This is how i retrieve the coordinates :

google.maps.event.addDomListener(drawingManager, 'polygoncomplete', function(polygon)
{
    var polygonBounds = polygon.getPath();
    var coordinates = [];

    for(var i = 0 ; i < polygonBounds.length ; i++)
    {            
        vertice = {
                      "Latitude" : polygonBounds.getAt(i).lat(),
                      "Longitude" : polygonBounds.getAt(i).lng()
                  }

        coordinates.push(vertice );
    }
}

How can I transform these coordinates, given by polygon.getpath() into geoJSON format ?
Is there any better way to detect if a Google Maps polygon is self-intersecting ? If so, could you please share some code sample and not just a mathematical explaination ?

PS : I've seen this link but without any code sample, I'm a little bit lost.

You don't need to convert them to GeoJSON to use the jsts library, you need to convert them from google.maps.LatLng objects to jsts.geom.Coordinates. Instead of using this:

var geoJSON2JTS = function(boundaries) {
  var coordinates = [];
  for (var i = 0; i < boundaries.length; i++) {
    coordinates.push(new jsts.geom.Coordinate(
        boundaries[i][1], boundaries[i][0]));
  }
  return coordinates;
};

Use this, which will convert coordinates in a google.maps.Polygon path to the JTS format:

var googleMaps2JTS = function(boundaries) {
  var coordinates = [];
  for (var i = 0; i < boundaries.getLength(); i++) {
    coordinates.push(new jsts.geom.Coordinate(
        boundaries.getAt(i).lat(), boundaries.getAt(i).lng()));
  }
  return coordinates;
};

then change "findSelfIntersects" like this:

/**
 * findSelfIntersects
 *
 * Detect self-intersections in a polygon.
 *
 * @param {object} google.maps.Polygon path co-ordinates.
 * @return {array} array of points of intersections.
 */
var findSelfIntersects = function(googlePolygonPath) {
  var coordinates = googleMaps2JTS(googlePolygonPath);
  var geometryFactory = new jsts.geom.GeometryFactory();
  var shell = geometryFactory.createLinearRing(coordinates);
  var jstsPolygon = geometryFactory.createPolygon(shell);

  // if the geometry is aleady a simple linear ring, do not
  // try to find self intersection points.
  var validator = new jsts.operation.IsSimpleOp(jstsPolygon);
  if (validator.isSimpleLinearGeometry(jstsPolygon)) {
    return;
  }

  var res = [];
  var graph = new jsts.geomgraph.GeometryGraph(0, jstsPolygon);
  var cat = new jsts.operation.valid.ConsistentAreaTester(graph);
  var r = cat.isNodeConsistentArea();
  if (!r) {
    var pt = cat.getInvalidPoint();
    res.push([pt.x, pt.y]);
  }
  return res;
};

proof of concept fiddle (credit to HoffZ)

code snippet:

var mapOptions = {
  zoom: 16,
  center: new google.maps.LatLng(62.1482, 6.0696)
};

var drawingManager = new google.maps.drawing.DrawingManager({
  drawingControl: false,
  polygonOptions: {
    editable: true
  }
});

var googleMaps2JTS = function(boundaries) {
  var coordinates = [];
  for (var i = 0; i < boundaries.getLength(); i++) {
    coordinates.push(new jsts.geom.Coordinate(
      boundaries.getAt(i).lat(), boundaries.getAt(i).lng()));
  }
  coordinates.push(coordinates[0]);
  console.log(coordinates);
  return coordinates;
};

/**
 * findSelfIntersects
 *
 * Detect self-intersections in a polygon.
 *
 * @param {object} google.maps.Polygon path co-ordinates.
 * @return {array} array of points of intersections.
 */
var findSelfIntersects = function(googlePolygonPath) {
  var coordinates = googleMaps2JTS(googlePolygonPath);
  var geometryFactory = new jsts.geom.GeometryFactory();
  var shell = geometryFactory.createLinearRing(coordinates);
  var jstsPolygon = geometryFactory.createPolygon(shell);

  // if the geometry is aleady a simple linear ring, do not
  // try to find self intersection points.
  var validator = new jsts.operation.IsSimpleOp(jstsPolygon);
  if (validator.isSimpleLinearGeometry(jstsPolygon)) {
    return;
  }

  var res = [];
  var graph = new jsts.geomgraph.GeometryGraph(0, jstsPolygon);
  var cat = new jsts.operation.valid.ConsistentAreaTester(graph);
  var r = cat.isNodeConsistentArea();
  if (!r) {
    var pt = cat.getInvalidPoint();
    res.push([pt.x, pt.y]);
  }
  return res;
};


var map = new google.maps.Map(document.getElementById("map"), mapOptions);
drawingManager.setDrawingMode(google.maps.drawing.OverlayType.POLYGON);
drawingManager.setMap(map);
google.maps.event.addListener(drawingManager, 'polygoncomplete', function(polygon) {
  //var polyPath = event.overlay.getPath();
  var intersects = findSelfIntersects(polygon.getPath());
  console.log(intersects);
  if (intersects && intersects.length) {
    alert('Polygon intersects itself');
  } else {
    alert('Polygon does not intersect itself');
  }
});

#map {
  width: 500px;
  height: 400px;
}

<script src="https://maps.google.com/maps/api/js?libraries=drawing"></script>
<script src="https://cdn.rawgit.com/bjornharrtell/jsts/gh-pages/1.4.0/jsts.min.js"></script>
<p>
  Draw a polygon on the map
</p>

<div id="map">

</div>