How to make the camera move in the direction of view?

Question

C++ / C#

How to make the camera move in the direction of view?
I tried from point to point, but when moving from one point to another, it starts to fly along an incomprehensible trajectory.
I used LookAt to point the camera at a point.

using UnityEngine;
using System.Collections;

public class camera : MonoBehaviour {

  public GameObject point;
  public GameObject point2;
  public float speed;
  public bool touch;
  Vector3 vec;
  Vector3 moveDirection;
  void Start () {
    touch = false;
    vec = point.transform.position;
    transform.LookAt (vec);
  

  
  }
  
  // Update is called once per frame
  void FixedUpdate () {

    if (!touch) {
      transform.Translate (Vector3.Normalize (vec - transform.position) * Time.deltaTime * speed);
      //transform.LookAt (vec);
      Debug.Log (touch);
    } else {
      Debug.Log(touch);
      //transform.Translate (Vector3.Normalize (vec - transform.position) * Time.deltaTime * speed);
      transform.Rotate(new Vector3(0,-0.8f,0)* Time.deltaTime * speed);
      if(Mathf.Abs(transform.rotation.y) > 0.6 && Mathf.Abs(transform.rotation.y) < 0.7)
      {
        touch = false;
        vec = point2.transform.position;
        transform.LookAt (vec);
      }
    //	Debug.Log("rot : " + transform.rotation.x);
    //	Debug.Log("rot : " + transform.rotation.y);
      //Debug.Log("rot : " + transform.rotation.z);
    //	Debug.Log("loc : " + transform.localRotation);

      /*transform.LookAt (vec);
      Debug.Log("dw");
      touch = false;
      vec = point2.transform.position;*/

    }


  }

  void OnTriggerEnter(Collider camer)
  {
    touch = true;
    //Debug.Log("dwad");
  }

}

In this code, I'm flying to the first point, after the collision of the colliders, the camera stops, turns and switches to the position of the second point, but it doesn't fly straight, as to the first point, but in an arc...