sine movement at any angle

I'm working on a 2D game. I have enemy spawn points at all directions around the viewport. All the enemies will pass through the centre of the viewport. What I'm trying to do is make some enemies move in a sine wave. But the enemies could come from any spawn point. Here's an image that hopefully will explain what I'm trying to do. Different colours mark some of the wished paths. I have done some research but haven't found a solution yet. The closest I came was the solution described here. http://answers.unity3d.com/questions/305484/sine-movement.html That works fine in one direction.

Here's my current code

 using UnityEngine;
 using System.Collections;
 
 public class SineMove : MonoBehaviour {
 
     private GameObject center;
 
     private Vector3 difference;
 
     public float CurveSpeed = 5;
     public float MoveSpeed = 0;
     public float fTime = 2;
 
     Vector3 vLastPos = Vector3.zero;
     
     // Use this for initialization
     void Start () 
     {
         center = GameObject.FindWithTag("CenterTarget");
         difference = transform.position - center.transform.position;
 
     }
     
     // Update is called once per frame
     void Update () 
     {
 
         fTime += Time.deltaTime * CurveSpeed;
         
         Vector3 vSin = new Vector3(Mathf.Sin(fTime), -Mathf.Sin(fTime), 0);
         Vector3 vLin = new Vector3(MoveSpeed, MoveSpeed, 0);
         transform.position -= (vSin + vLin) * Time.deltaTime;
 
         //Tried using difference but it didn't work
         //transform.position -= (difference+vSin) *0.2f*Time.deltaTime;
 
                 //vLastPos Is only for Debug.Draw
         vLastPos = transform.position;
         Debug.DrawLine(vLastPos, transform.position, Color.green, 100);
     }
 
 }
 

Any help much appreciated.