SmoothFollowC.cs

using UnityEngine;
using System.Collections;

public class SmoothFollowC : MonoBehaviour {

	// The target we are following
	public Transform target;
	// The distance in the x-z plane to the target
	public float distance = 10.0f;
	// the height we want the camera to be above the target
	public float height = 5.0f;
	// How much we 
	public float heightDamping = 2.0f;
	public float rotationDamping = 3.0f;

	// Use this for initialization
	void Start () {
	
	}
	
	// Update is called once per frame
	void LateUpdate () {
		if (!target)
			return;
		
		// Calculate the current rotation angles
		var wantedRotationAngle = target.eulerAngles.y;
		var wantedHeight = target.position.y + height;
		
		var currentRotationAngle = transform.eulerAngles.y;
		var currentHeight = transform.position.y;
		
		// Damp the rotation around the y-axis
		currentRotationAngle = Mathf.LerpAngle (currentRotationAngle, wantedRotationAngle, rotationDamping * Time.deltaTime);
		
		// Damp the height
		currentHeight = Mathf.Lerp (currentHeight, wantedHeight, heightDamping * Time.deltaTime);
		
		// Convert the angle into a rotation
		var currentRotation = Quaternion.Euler (0, currentRotationAngle, 0);
		
		// Set the position of the camera on the x-z plane to:
		// distance meters behind the target
		transform.position = target.position;
		transform.position -= currentRotation * Vector3.forward * distance;
		
		// Set the height of the camera
		transform.position = new Vector3(transform.position.z, currentHeight, transform.position.z);
		
		// Always look at the target
		transform.LookAt (target);
	}
}