Carousel or Swipe Menu

I want to do a specific kind of effect, a demo can be found HERE. It has a set of image(menu) that can be carouseled by swiping. It has bullet points to denote the currently selected menu. It also show the currently centered menu to be larger than the others.

I'm not sure what this effect is called, but I wish to know how to do it in Unity 5.

Currently I have something like this:

 // menu items
 public GameObject Quest;
 public GameObject Vortex;
 public GameObject RaidBattle;
 public GameObject Randall;
 public GameObject Arena;

 // menu item bullets
 public GameObject bulletQuest;
 public GameObject bulletVortex;
 public GameObject bulletRaidBattle;
 public GameObject bulletRandall;
 public GameObject bulletArena;

 // other public
 public GameObject centerPoint;

 // private
 private GameObject firstItem;
 private GameObject lastItem;
 private GameObject chosenItem;

 private bool isHolding = false;

 // quest is always the center menu on load
 void Start () {
     chosenItem = Quest;
 }

 void Update () {
     Vector3 mousePos = Camera.main.ScreenToWorldPoint(Input.mousePosition);
     Vector2 touchPos = new Vector2(mousePos.x, mousePos.y);

     // left click (should be touch)
     if (Input.GetMouseButtonDown (0) && !isHolding) {
         // check if collided with a sprite
         if (chosenItem.GetComponent<BoxCollider2D>() == Physics2D.OverlapPoint(touchPos)) {
             isHolding = true;
         }
     }

     // release left click
     if (Input.GetMouseButtonUp (0) && isHolding) isHolding = false;

     // holding on
     if (isHolding) {
         transform.localPosition = new Vector3(mousePos.x, transform.localPosition.y, 1f);
     }

     // check collision between center and a menu
     Debug.Log (centerPoint.GetComponent<BoxCollider2D>()) ;
 }

But I'm already starting to get confused on what to do next. I guess I need to steply grow and shrink the localScale of the gameObjects but:

• How do I know if which one is currently in the center?

• How do I make it snap to the center?

• How do I consider the force of the swipe to make it revolve per menu item?