Lock enemy's y-axis when using Vector3.MoveTowards to follow the player

Question

I am using the following code to make a zombie move towards me, but when playing the scene the zombie seems to be moving towards me, but also off the ground and not fixed on the y-axis

 public GameObject ThePlayer;
public float TargetDistance;
public float AllowedRange = 10;
public GameObject TheEnemy;
public float EnemySpeed;
public int AttackTrigger;
public RaycastHit Shot;

void Update()
{
    transform.LookAt(ThePlayer.transform);
    if (Physics.Raycast(transform.position, transform.TransformDirection(Vector3.forward), out Shot))
    {
        TargetDistance = Shot.distance;
        if (TargetDistance < AllowedRange)
        {
            EnemySpeed = 0.01f;
            if (AttackTrigger == 0)
            {
                //TheEnemy.GetComponent<Animation>().Play("Walking");
                transform.position = Vector3.MoveTowards(transform.position, ThePlayer.transform.position, EnemySpeed);
            }
        }
        else
        {
            EnemySpeed = 0;
            //TheEnemy.GetComponent<Animation>().Play("Idle");
        }
    }

    if (AttackTrigger == 1)
    {
        EnemySpeed = 0;
        //TheEnemy.GetComponent<Animation>().Play("Attacking");
    }
}

void OnTriggerEnter()
{
    AttackTrigger = 1;
}

void OnTriggerExit()
{
    AttackTrigger = 0;
}

What can i do to ensure that it is sticking to the y axis at all times

Answer 1

The reason this is happening is because Vector3.MoveTowards will move all axes toward the target.

You can specifically exclude changes to the Y axis by creating a new target Vector3 having the Y axis set to the value it should stay at.

transform.position = Vector3.MoveTowards(
    transform.position,
    new Vector3(
        ThePlayer.transform.position.x,
        transform.position.y,
        ThePlayer.transform.position.z
    ),
    EnemySpeed
);

The above code creates a new Vector3 target where the Y axis is the same as the current position instead of the target, preventing Vector3.MoveTowards from changing the Y axis at all.

Answer 2

You can break out the Vector3 target parameter of Vector3.MoveTowards to prevent movement on the y-axis. Simply set the y value of the target position to the same y value as the current position. For example:

Vector3 currentPosition = transform.position;
Vector3 targetPosition = new Vector3(ThePlayer.transform.position.x, transform.position.y, ThePlayer.transform.position.z);

transform.position = Vector3.MoveTowards(currentPosition, targetPosition, EnemySpeed);

Answer 3

The other answers are great. But if you have a RigidBody attached, you can freeze the y rotation via constraints. Then no code change would be necessary.