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);
         }
     }
 }