Mapsでルートのシミュレーションがしたい

現在MapKit.frameworkを使って地図機能を実装しているのですが、目的地にピンを留めた後に現在地からその目的地までのルートをシミュレーションしたいです。しかしどうすればいいか分かりません。
詳しくは以下のページにある動画のようにしたいです。（3Dでなくて2Dで構いません）

【裏技】Googleマップのルート検索で「3D」をオンにするとアニメーションが見られます

この動画のようにルートに沿ってピンを走らせるにはどうすればいいのでしょうか？
現在以下のようにコードを実装しており、現在地から目的地までの線引き等はできています。

Swift
1class ViewController: UIViewController, CLLocationManagerDelegate {
2    
3    @IBOutlet weak var mapView: MKMapView!
4    var lm: CLLocationManager! = nil
5    var fromCoordinate: CLLocationCoordinate2D?
6    var toCoordinate: CLLocationCoordinate2D?
7
8    override func viewDidLoad() {
9        super.viewDidLoad()
10        
11        setCoreLocation()
12        addLongPressGesture()
13    }
14
15    override func didReceiveMemoryWarning() {
16        super.didReceiveMemoryWarning()
17    }
18    
19    //MARK: ViewDidLoadPreference
20    
21    func setCoreLocation() {
22        lm = CLLocationManager()
23        lm.delegate = self
24        
25        lm.requestAlwaysAuthorization()
26        lm.desiredAccuracy = kCLLocationAccuracyBest
27        lm.distanceFilter = 300
28        lm.startUpdatingLocation()
29    }
30    
31    func addLongPressGesture() {
32        let myLongPressGesture = UILongPressGestureRecognizer(target: self, action: #selector(ViewController.longPressGesture(_:)))
33        myLongPressGesture.minimumPressDuration = 1.0
34        myLongPressGesture.allowableMovement = 150
35        
36        mapView.addGestureRecognizer(myLongPressGesture)
37    }
38    
39    //MARK: GestureRecognizer
40    
41    func longPressGesture(sender: UILongPressGestureRecognizer) {
42        if sender.state != UIGestureRecognizerState.Ended {
43            let touchLocation = sender.locationInView(mapView)
44            let locationCoordinate = mapView.convertPoint(touchLocation,toCoordinateFromView: mapView)
45            toCoordinate = CLLocationCoordinate2D(latitude: locationCoordinate.latitude, longitude: locationCoordinate.longitude)
46            
47            setPointAnnotation(toCoordinate!)
48            
49            routeSearch()
50        }
51    }
52    
53    //MARK: CoreLocationDelegate
54
55    func locationManager(manager: CLLocationManager, didUpdateToLocation newLocation: CLLocation, fromLocation oldLocation: CLLocation){
56        fromCoordinate = CLLocationCoordinate2D(latitude: newLocation.coordinate.latitude, longitude: newLocation.coordinate.longitude)
57        
58        guard let coodinate = fromCoordinate else {
59            return
60        }
61        
62        let region = MKCoordinateRegionMake(coodinate, MKCoordinateSpanMake(0.01, 0.01))
63        mapView.setRegion(region, animated:true)
64        mapView.userTrackingMode = MKUserTrackingMode.FollowWithHeading
65    }
66    
67    func locationManager(manager: CLLocationManager, didFailWithError error: NSError) {
68        NSLog("Error")
69    }
70    
71    //MARK: MapKit
72    
73    func routeSearch() {
74        let fromPlacemark = MKPlacemark(coordinate:fromCoordinate!, addressDictionary:nil)
75        let toPlacemark = MKPlacemark(coordinate:toCoordinate!, addressDictionary:nil)
76        
77        let fromItem = MKMapItem(placemark:fromPlacemark);
78        let toItem = MKMapItem(placemark:toPlacemark);
79        
80        let request = MKDirectionsRequest()
81        request.source = fromItem
82        request.destination = toItem
83        request.requestsAlternateRoutes = true;
84        request.transportType = MKDirectionsTransportType.Walking
85        
86        let directions = MKDirections(request: request)
87        directions.calculateDirectionsWithCompletionHandler { [unowned self] response, error in
88            guard let unwrappedResponse = response else { return }
89            
90            for route in unwrappedResponse.routes {
91                self.mapView.addOverlay(route.polyline)
92                self.mapView.setVisibleMapRect(route.polyline.boundingMapRect, animated: true)
93                
94                self.title = String(Int(round(route.distance / 100))) + "km   " + String(Int(round(route.expectedTravelTime / 60))) + "分"
95            }
96        }
97    }
98    
99    func mapView(mapView: MKMapView!, rendererForOverlay overlay: MKOverlay!) -> MKOverlayRenderer! {
100        let route: MKPolyline = overlay as! MKPolyline
101        let routeRenderer = MKPolylineRenderer(polyline:route)
102        routeRenderer.lineWidth = 5.0
103        routeRenderer.strokeColor = UIColor.redColor()
104        return routeRenderer
105    }
106    
107    func setPointAnnotation(coordinate: CLLocationCoordinate2D) {
108        let annotation = MKPointAnnotation()
109        annotation.coordinate = coordinate
110        self.mapView.addAnnotation(annotation)
111    }
112
113}