Google Maps API - different map style for polygon

I want to achieve the effect similar to what is presented here:

inside Android google map. The polygon should have a different map style (json file) than the rest of the map. Is there a way of doing that? I would even accept having two different maps (one under the other) and cutting the polygon out of the top map. Would that be possible?

That effect is possible with Polygon.setHoles() or PolygonOptions.addHole() methods. You should create gray transparent polygon for all map (from -90 to 90 degrees of latitude and from -180 to 180 of longitude) with holes for each of your terrain location. Something like this:

public class MainActivity extends AppCompatActivity implements OnMapReadyCallback {

    private static final String TAG = MainActivity.class.getSimpleName();
    private GoogleMap mGoogleMap;
    private MapFragment mMapFragment;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        mMapFragment = (MapFragment) getFragmentManager()
                .findFragmentById(R.id.map_fragment);
        mMapFragment.getMapAsync(this);
    }

    @Override
    public void onMapReady(GoogleMap googleMap) {
        mGoogleMap = googleMap;

        List<List<LatLng>> holes = new ArrayList<>();

        // "hole" for Hyde Park
        List<LatLng> hole = new ArrayList<>();
        hole.add(new LatLng(51.509869, -0.191208));
        hole.add(new LatLng(51.513287, -0.158464));
        hole.add(new LatLng(51.505540, -0.151769));
        hole.add(new LatLng(51.502178, -0.174471));
        hole.add(new LatLng(51.502444, -0.187989));
        holes.add(hole);

        // "hole" for Regent's Park
        hole = new ArrayList<>();
        hole.add(new LatLng(51.530226, -0.167685));
        hole.add(new LatLng(51.534924, -0.163737));
        hole.add(new LatLng(51.537566, -0.151849));
        hole.add(new LatLng(51.535964, -0.146914));
        hole.add(new LatLng(51.525325, -0.145625));
        hole.add(new LatLng(51.523589, -0.155538));
        holes.add(hole);

        mGoogleMap.addPolygon(createPolygonWithHoles(holes));

        mGoogleMap.animateCamera(CameraUpdateFactory.newLatLngZoom(new LatLng(51.519454, -0.168869), 14));
    }

    private static List<LatLng> createBoundsOfEntireMap() {
        final float delta = 0.01f;

        return new ArrayList<LatLng>() {{
            add(new LatLng(90 - delta, -180 + delta));
            add(new LatLng(0, -180 + delta));
            add(new LatLng(-90 + delta, -180 + delta));
            add(new LatLng(-90 + delta, 0));
            add(new LatLng(-90 + delta, 180 - delta));
            add(new LatLng(0, 180 - delta));
            add(new LatLng(90 - delta, 180 - delta));
            add(new LatLng(90 - delta, 0));
            add(new LatLng(90 - delta, -180 + delta));
        }};
    }

    static PolygonOptions createPolygonWithHoles(List<List<LatLng>> holes) {
        PolygonOptions polyOptions = new PolygonOptions()
                .fillColor(0x33000000)
                .addAll(createBoundsOfEntireMap())
                .strokeColor(0xFF000000)
                .strokeWidth(5);

        for (List<LatLng> hole : holes) {
            polyOptions.addHole(hole);
        }

        return polyOptions;
    }

}

and you get something like that:

Also you need bitmap circles as markers for polygon vertexes or draw it as Circle objects.

Update

For "hole-in-hole" case and "night-and-day" you should change .fillColor(0x33000000) to more dark, e.g. .fillColor(0xDD000000) and just add polygon with hole over "first" polygon. Something like this:

@Override
public void onMapReady(GoogleMap googleMap) {
    mGoogleMap = googleMap;

    List<List<LatLng>> holes = new ArrayList<>();

    // "hole" for Hyde Park
    List<LatLng> hole = new ArrayList<>();
    hole.add(new LatLng(51.509869, -0.191208));
    hole.add(new LatLng(51.513287, -0.158464));
    hole.add(new LatLng(51.505540, -0.151769));
    hole.add(new LatLng(51.502178, -0.174471));
    hole.add(new LatLng(51.502444, -0.187989));
    holes.add(hole);

    // "hole" for Regent's Park
    hole = new ArrayList<>();
    hole.add(new LatLng(51.530226, -0.167685));
    hole.add(new LatLng(51.534924, -0.163737));
    hole.add(new LatLng(51.537566, -0.151849));
    hole.add(new LatLng(51.535964, -0.146914));
    hole.add(new LatLng(51.525325, -0.145625));
    hole.add(new LatLng(51.523589, -0.155538));
    holes.add(hole);

    mGoogleMap.addPolygon(createPolygonWithHoles(holes));

    List<LatLng> holesInHolesPoly = new ArrayList<>();
    holesInHolesPoly.add(new LatLng(51.508184, -0.177805));
    holesInHolesPoly.add(new LatLng(51.509759, -0.164373));
    holesInHolesPoly.add(new LatLng(51.504549, -0.162399));
    holesInHolesPoly.add(new LatLng(51.503453, -0.177934));

    List<LatLng> holesInHolesHole = new ArrayList<>();
    holesInHolesHole.add(new LatLng(51.505883, -0.172999));
    holesInHolesHole.add(new LatLng(51.507992, -0.171025));
    holesInHolesHole.add(new LatLng(51.506308, -0.169738));

    hole = new ArrayList<>();
    hole.add(new LatLng(51.530226, -0.167685));

    PolygonOptions holeInHoles = new PolygonOptions()
            .fillColor(0xDD000000)
            .addAll(holesInHolesPoly)
            .addHole(holesInHolesHole)
            .strokeColor(0xFF000000)
            .strokeWidth(5);

    mGoogleMap.addPolygon(holeInHoles);

    mGoogleMap.animateCamera(CameraUpdateFactory.newLatLngZoom(new LatLng(51.519454, -0.168869), 14));
}

and you are got something like that:

It's not a solution, but really good workaround. Or you can set "night" style for whole map and use custom TileProvider or GroundOverlay with "day" bitmap. Anyway - seems there are no "normal" way to create custom style for polygon part of the map.