You can switch on a set using array literals as cases in Swift! Can be really useful to avoid many if/else if statements.

class RoadTile: Tile {
    var connectedDirections = Set<Direction>()

    func render() {
        switch connectedDirections {
        case [.up, .down]:
            image = UIImage(named: "road-vertical")
        case [.left, .right]:
            image = UIImage(named: "road-horizontal")
        default:
            image = UIImage(named: "road")
        }
    }
}