OrbitalCamera.cs

using UnityEngine;

public class OrbitalCamera : MonoBehaviour {

	public GameObject lookAt;

	public float followSpeed = 3.5f;
	public float minAngle = -45.0f;
	public float maxAngle = 60.0f;

	private float distance = 0.0f;
	private float lookH = 0.0f;
	private float lookV = 0.0f;

	void Start () {
		distance = (transform.position - lookAt.transform.position).magnitude;
	}

	void Update () {

		lookH = (lookH + Input.GetAxis ("Mouse X")) % 360;
		lookV = Mathf.Clamp (lookV + Input.GetAxis ("Mouse Y") * (-1), minAngle, maxAngle);

	}

	void LateUpdate () {

		Move ();

	}

	private void Move () {

		Quaternion rotation = Quaternion.Euler (lookV, lookH, 0);
		Vector3 nextPosition = lookAt.transform.position + rotation * new Vector3 (0, 0, - distance);

		transform.position = Vector3.Lerp (
			transform.position, nextPosition, followSpeed * Time.deltaTime
		);
		transform.LookAt (lookAt.transform.position);

	}
}