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OL3: GetFeature from Layers by Coordinate

I want to get the Feature of a Layer by coordinate. Furthermore I want to open this feature in a popup, which I have solved so far by an onclick event. But I want to realize by giving the coordinates of a feature and opening the popup of the featue.

I have a layer with the map and a layer with the features:

if (trackMap != null) {
  for (var i = 0; i < trackMap.length; i++) {
    var trackInfo = trackMap[i];
    lat = parseFloat(trackInfo.lat);
    lon = parseFloat(trackInfo.lon);

    var layergpx = new ol.layer.Vector({
      source: new ol.source.Vector({
        parser: new ol.parser.GPX(),
        url: '${contextRoot}/gps/gpx2' + trackInfo.url
      })
    });
    layers.push(layergpx);
  }
}

I want to get the feature of this layer in another Javascript function.

How I open a pop up by clicking on the map:

/**
 * The Click Event to show the data
 */
var element = document.getElementById('popup');
var popup = new ol.Overlay({
      element: element,
      positioning: ol.OverlayPositioning.BOTTOM_CENTER,
      stopEvent: false
});
map.addOverlay(popup);

map.on('singleclick', function(evt) {
  map.getFeatures({
    pixel: evt.getPixel(),
    layers: vectorLayers,
    success: function(layerFeatures) {
      var feature = layerFeatures[0][0];
      if (feature) {
        var geometry = feature.getGeometry();
        var coord = geometry.getCoordinates();
        popup.setPosition(coord);
        $(element).popover({
          'placement': 'top',
          'html': true,
          'content': feature.get('desc')
        });
        $(element).popover('show');
      } else {
        $(element).popover('destroy');
      }
    }
  });
});

But I want this feature not to be opened by clicking on it on the map, but by entering a coordinate in a textfield and the map opens this pop up, like in the onclick event.

Take a look at this example to see if it helps you: http://openlayers.org/en/latest/examples/kml.html

var displayFeatureInfo = function(pixel) {
  map.getFeatures({
    pixel: pixel,
    layers: [vector],
    success: function(featuresByLayer) {
      var features = featuresByLayer[0];
      var info = [];
      for (var i = 0, ii = features.length; i < ii; ++i) {
        info.push(features[i].get('name'));
      }
      document.getElementById('info').innerHTML = info.join(', ') || '&nbsp';
    }
  });

map.getFeatures() has this success callback where it delivers the features of the layers specified in layers: [vector]. Customize it at will to get what you need.

=== Update ===

In the OpenLayers 3's Map object you have a function: getPixelFromCoordinate

/**
 * @param {ol.Coordinate} coordinate Coordinate.
 * @return {ol.Pixel} Pixel.
 */
ol.Map.prototype.getPixelFromCoordinate = function(coordinate) {
  var frameState = this.frameState_;
  if (goog.isNull(frameState)) {
    return null;
  } else {
    var vec2 = coordinate.slice(0, 2);
    return ol.vec.Mat4.multVec2(frameState.coordinateToPixelMatrix, vec2, vec2);
  }
};

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