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How To Draw Path Between Two Location Coordinates Using OSRM Routing Machine in OpenLayers?
How To Draw Path Between Two Location Coordinates Using OSRM  Routing Machine in OpenLayers ?

That is very similar to how the route is added in this example https://openlayers.org/en/latest/examples/feature-move-animation.html
For the route in the OSRM example http://project-osrm.org/docs/v5.7.0/api/#route-service the code would be
const coordinates = [
  [13.38886, 52.517037],
  [13.397634, 52.529407],
  [13.428555, 52.523219],
];

fetch(
  'https://router.project-osrm.org/route/v1/driving/' +
    coordinates.join(';') +
    '?overview=full&geometries=polyline6'
).then(function (response) {
  response.json().then(function (result) {
    const polyline = result.routes[0].geometry;

    const route = new Polyline({
      factor: 1e6,
    }).readGeometry(polyline, {
      dataProjection: 'EPSG:4326',
      featureProjection: map.getView().getProjection(),
    });
    const routeFeature = new Feature({
      type: 'route',
      geometry: route,
    });

    const vectorLayer = new VectorLayer({
      source: new VectorSource({
        features: [routeFeature],
      }),
      style: new Style({
        stroke: new Stroke({
          width: 4,
          color: 'red',
        }),
      }),
    });

    map.addLayer(vectorLayer);
    map.getView().fit(routeFeature.getGeometry());
  });
});

Working example https://codesandbox.io/s/osrm-route-xci7vf

<!DOCTYPE html>
<html>
  <head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
    <title>OpenLayers 3 - OSRM Polyline Route</title>
    <meta name="robots" content="noindex, nofollow">
    <meta name="googlebot" content="noindex, nofollow">
    <meta name="viewport" content="width=device-width, initial-scale=1">
    <script type="text/javascript" src="https://cdnjs.cloudflare.com/ajax/libs/ol3/3.10.1/ol.min.js"></script>
    <link rel="stylesheet" type="text/css" href="https://cdnjs.cloudflare.com/ajax/libs/ol3/3.10.1/ol.min.css">
    <script id="insert"></script>
  </head>
  <body>
    <div id="map"></div>
    <div id="msg">Click to add a point.</div>
    <script type="text/javascript">
      var points = [],
        msg_el = document.getElementById('msg'),
        url_osrm_nearest = 'https://router.project-osrm.org/nearest/v1/driving/',
        url_osrm_route = 'https://router.project-osrm.org/route/v1/driving/',
        icon_url = 'https://cdn.rawgit.com/openlayers/ol3/master/examples/data/icon.png',
        vectorSource = new ol.source.Vector(),
        vectorLayer = new ol.layer.Vector({
          source: vectorSource
        }),
        styles = {
          route: new ol.style.Style({
            stroke: new ol.style.Stroke({
              width: 6, color: [40, 40, 40, 0.8]
            })
          }),
          icon: new ol.style.Style({
            image: new ol.style.Icon({
              anchor: [0.5, 1],
              src: icon_url
            })
          })
        };
      var map = new ol.Map({
        target: 'map',
        layers: [
          new ol.layer.Tile({
            source: new ol.source.OSM()
          }),
          vectorLayer
        ],
        view: new ol.View({
          center: [-5685003, -3504484],
          zoom: 11
        })
      });
      map.on('click', function (evt) {
        utils.getNearest(evt.coordinate).then(function (coord_street) {
          var last_point = points[points.length - 1];
          var points_length = points.push(coord_street);

          utils.createFeature(coord_street);

          if (points_length < 2) {
            msg_el.innerHTML = 'Click to add another point';
            return;
          }
          //get the route
          var point1 = last_point.join();
          var point2 = coord_street.join();

          fetch(url_osrm_route + point1 + ';' + point2).then(function (r) {
            return r.json();
          }).then(function (json) {
            if (json.code !== 'Ok') {
              msg_el.innerHTML = 'No route found.';
              return;
            }
            msg_el.innerHTML = 'Route added';
            utils.createRoute(json.routes[0].geometry);
          });
        });
      });
      var utils = {
        getNearest: function (coord) {
          var coord4326 = utils.to4326(coord);
          return new Promise(function (resolve, reject) {
            //make sure the coord is on street
            fetch(url_osrm_nearest + coord4326.join()).then(function (response) {
              // Convert to JSON
              return response.json();
            }).then(function (json) {
              if (json.code === 'Ok') resolve(json.waypoints[0].location);
              else reject();
            });
          });
        },
        createFeature: function (coord) {
          var feature = new ol.Feature({
            type: 'place',
            geometry: new ol.geom.Point(ol.proj.fromLonLat(coord))
          });
          feature.setStyle(styles.icon);
          vectorSource.addFeature(feature);
        },
        createRoute: function (polyline) {
          // route is ol.geom.LineString
          var route = new ol.format.Polyline({
            factor: 1e5
          }).readGeometry(polyline, {
            dataProjection: 'EPSG:4326',
            featureProjection: 'EPSG:3857'
          });
          var feature = new ol.Feature({
            type: 'route',
            geometry: route
          });
          feature.setStyle(styles.route);
          vectorSource.addFeature(feature);
        },
        to4326: function (coord) {
          return ol.proj.transform([
            parseFloat(coord[0]), parseFloat(coord[1])
          ], 'EPSG:3857', 'EPSG:4326');
        }
      };
    </script>
  </body>
</html>

