Unity - Projectile Motion, find the angle needed to hit coordinates x,y

Question

Plenty of questions asked around the same topic, but nothing seems to be working for me.

The problem is simple, a player and an enemy are on the x,y plane. I want to launch my projectile at a calculated angle in such way that the projectile will hit the enemy at it's coordinates.

I've tried implementing both

Angle of Reach and Angle required to hit x,y

Both of these implementation end up doing the same for me; Shooting but not hitting the target in this manner

Any help or pointers would be much appreciated! Thank you

Here is the code:

public Rigidbody projectile;
public float projectileSpeed;
public float Firerate = 9f;
private float nextfire;

private GameObject enemy;
private float gravity = Physics.gravity.y;
private Vector3 directionalVector;

// Start is called before the first frame update
void Start()
{
    enemy = GameObject.FindGameObjectWithTag("enemy");

}


void Update()
{
    directionalVector = enemy.transform.position - transform.position;

}
void FixedUpdate()
{

    nextfire = Time.time + (1 / Firerate);

    float projectileSpeed2 = projectileSpeed * projectileSpeed;
    float projectileSpeed4 = projectileSpeed2 * projectileSpeed2;
    float x = enemy.transform.position.x;
    float y = enemy.transform.position.y;
    float x2 = x * x;



    float theta = Mathf.Atan(projectileSpeed2-Mathf.Sqrt(projectileSpeed4-gravity*(gravity*x2+2*y*projectileSpeed2))/gravity*x);
    print(theta);

    Vector3 releaseVector = (Quaternion.AngleAxis(theta, Vector3.up) * directionalVector).normalized;

    Debug.DrawRay(transform.position, releaseVector, Color.red,0.5f);
    Rigidbody instantiatedProjectile = Instantiate(projectile, transform.position, transform.rotation) as Rigidbody;
    instantiatedProjectile.velocity = releaseVector * projectileSpeed;
}

}

Answer 1

After fighting this for a while I found a solution.

In the end I ended up using the Angle of Reach. The second error was that Mathf.Atan returns radians and not degrees, while Quantion.AngleAxis takes in angles. The third and the final one was the fact that Unity uses left hand coordinate system as opposed to the usual right hand system which I was used to.

Here is the final piece of code:

public class TargetAndShoot : MonoBehaviour
{
    public Rigidbody projectile;
    public float projectileSpeed;
    public float firerate;
    private float nextfire;

    private GameObject enemy;
    private float gravity = Physics.gravity.y;


    // Start is called before the first frame update
    void Start()
    {
        enemy = GameObject.FindGameObjectWithTag("enemy");

    }


    void Update()
    {
        if (Time.time >= nextfire)
        {
            nextfire = Time.time + (1 / firerate);
            float distance = enemy.transform.position.x - transform.position.x;
            Vector3 directionalVector = enemy.transform.position - transform.position;

            float v2 = projectileSpeed * projectileSpeed;
            float v4 = v2 * v2;

            float x = enemy.transform.position.x;
            float x2 = x * x;
            float y = enemy.transform.position.y;

            float theta = 0.5f*Mathf.Asin((gravity * distance) / (projectileSpeed * projectileSpeed));
            Vector3 releaseVector = (Quaternion.AngleAxis(theta * Mathf.Rad2Deg, -Vector3.forward) * directionalVector).normalized;
            Debug.DrawRay(transform.position, releaseVector*5, Color.cyan, 0.5f);

            Rigidbody instantiatedProjectile = Instantiate(projectile, transform.position, transform.rotation) as Rigidbody;
            instantiatedProjectile.velocity = releaseVector * projectileSpeed;
        }
    }

}