Camera Follow (Not Exact)

I’d like my camera to follow the player through my 2D game. Right now I have this:

public GameObject player;

private Vector3 offset;

void Start()
{
    offset = transform.position - player.transform.position;
}

void LateUpdate()
{
    transform.position = player.transform.position + offset;
}

It works but is too exact as it’s constantly updating the camera to the player’s position. I’d like it to translate the camera left/right/up when the camera gets close to the edge of what’s currently visible.

Any help would be much appreciated.

the unity standard assets has one already

if you don’t want to download it here is it

using System;
using UnityEngine;

namespace UnityStandardAssets._2D
{
    public class Camera2DFollow : MonoBehaviour
    {
        public Transform target;
        public float damping = 1;
        public float lookAheadFactor = 3;
        public float lookAheadReturnSpeed = 0.5f;
        public float lookAheadMoveThreshold = 0.1f;

        private float m_OffsetZ;
        private Vector3 m_LastTargetPosition;
        private Vector3 m_CurrentVelocity;
        private Vector3 m_LookAheadPos;

        // Use this for initialization
        private void Start()
        {
            m_LastTargetPosition = target.position;
            m_OffsetZ = (transform.position - target.position).z;
            transform.parent = null;
        }


        // Update is called once per frame
        private void Update()
        {
            // only update lookahead pos if accelerating or changed direction
            float xMoveDelta = (target.position - m_LastTargetPosition).x;

            bool updateLookAheadTarget = Mathf.Abs(xMoveDelta) > lookAheadMoveThreshold;

            if (updateLookAheadTarget)
            {
                m_LookAheadPos = lookAheadFactor*Vector3.right*Mathf.Sign(xMoveDelta);
            }
            else
            {
                m_LookAheadPos = Vector3.MoveTowards(m_LookAheadPos, Vector3.zero, Time.deltaTime*lookAheadReturnSpeed);
            }

            Vector3 aheadTargetPos = target.position + m_LookAheadPos + Vector3.forward*m_OffsetZ;
            Vector3 newPos = Vector3.SmoothDamp(transform.position, aheadTargetPos, ref m_CurrentVelocity, damping);

            transform.position = newPos;

            m_LastTargetPosition = target.position;
        }
    }
}