Make a bowling ball spin on a swipe path

I have the code to be able to find the swipe, but how do I go about making sure that my ball follows this curve?

Here is my SwipeCode
LineRender.cs
public class LineRender : MonoBehaviour {

	public Color c1 = Color.red;
	public Color c2 = Color.yellow;
	
	private GameObject lineGO;
	private LineRenderer lineRenderer;
	private int i = 0;
	
	
	void Start()
	{
		lineGO = new GameObject("Line");
		lineGO.AddComponent<LineRenderer>();
		lineRenderer = lineGO.GetComponent<LineRenderer>();
		lineRenderer.material = new Material(Shader.Find("Mobile/Particles/Additive"));
		lineRenderer.SetColors(c1, c2);
		lineRenderer.SetWidth(0.3F, 0);
		lineRenderer.SetVertexCount(0);
	}
	
	void Update()
	{		
		if (Input.touchCount > 0)
		{
			Touch touch = Input.GetTouch(0);
			
			if(touch.phase == TouchPhase.Moved)
			{
				lineRenderer.SetVertexCount(i+1);
				Vector3 mPosition = new Vector3(Input.mousePosition.x, Input.mousePosition.y, 15);				
				lineRenderer.SetPosition(i, Camera.main.ScreenToWorldPoint(mPosition));
				i++;
			}
			
			if(touch.phase == TouchPhase.Ended)
			{
				/* Remove Line */
				
				lineRenderer.SetVertexCount(0);
				i = 0;
			}
		} 
		else {
			MouseSwipe();
		}
	}
	
	void MouseSwipe(){
		if(Input.GetMouseButton(0))
		{
			lineRenderer.SetVertexCount(i+1);
			Vector3 mPosition = new Vector3(Input.mousePosition.x, Input.mousePosition.y, 15);
			lineRenderer.SetPosition(i, Camera.main.ScreenToWorldPoint(mPosition));
			i++;
			
		}
		else{
			/* Remove Line */			
			lineRenderer.SetVertexCount(0);
			i = 0;
		}
		
	}
}

My Launch code for the ball
public class DragLaunch : MonoBehaviour {

	private Ball ball;
	private float startTime, endTime;
	private Vector3 dragStart, dragEnd;
		
	// Use this for initialization
	void Start () {
		ball = GetComponent<Ball>();
	}
	
	public void MoveStart (float amount){
		if(! ball.inPlay){
			float xPos = Mathf.Clamp(ball.transform.position.x + amount, -50f, 50f);
			float yPos = ball.transform.position.y;
			float zPos = ball.transform.position.z;			
			ball.transform.position = new Vector3 (xPos,yPos, xPos);
		}
	}
	
	public void DragStart(){
		if(! ball.inPlay){
			//Capture time & position of drag start
			dragStart = Input.mousePosition;
			startTime = Time.time;
		}
	}
	
	public void DragEnd(){
		if(! ball.inPlay){
			//Launch the ball
			dragEnd = Input.mousePosition;
			endTime = Time.time;
			float dragDuration = endTime - startTime;
			
			float launchSpeedX = (dragEnd.x - dragStart.x) / dragDuration;
			float launchSpeedZ = (dragEnd.y - dragStart.y) / dragDuration;
			
			Vector3 launchVelocity = new Vector3(launchSpeedX, 0, launchSpeedZ);
			ball.Launch(launchVelocity);
		}
	}
}

This is a nice post. Plz make your research more strong about coding. go bowling alley