Bullet-Hell Tool (Unity C#) - Rotate Half-Circle of Objects / Projectiles Towards Directional Vector2

Question

_Greetings
Greetings. I am working on c# script for a 'bullet-hell' tool in Unity and I have gotten stuck trying to produce a crescent / half-circle of objects - that turns toward the traveling direction. The scripts spawn a perfect half-circle every time and keep the objects there, no matter object-amount. No problem there, the circle is however never turned towards the right direction.

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_Question
What I am trying to achieve is for the half-circle to point towards the travel-direction of the centerObject. This travel direction is described via a Vector2 between (1,1) and (-1,-1). How can I use this vector to turn the half-circle in the direction of travel?

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There are multiple instances of InitializeOrbit, each responsible for its own half-circle and with a corresponding move direction Vector2.

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_Code
In the first script, the 'theta' is first calculated, whereafter the objects are spawned.

public void InitializeOrbit()
{
    for (int i = 0; i < numberOfOrbits; i++)
    {
         float theta = (1 * Mathf.PI / numberOfOrbits) * i;
         Instantiate(OrbitPrefab, orbitLocation, transform.rotation);
    }
}

And in the second, the theta is used to calculate the position of the individual objects.

public void OrbitSource ()
{
    Vector2 offset = new Vector2(Mathf.Sin(theta) * orbitRadius, Mathf.Cos(theta) * orbitRadius);
    transform.position = (Vector2)centerTransform.position + offset;
}

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I hope I have provided proper information, thanks in advance. I have tried reading How to place spheres in a half circle shape between 2 points - But have sadly not been able to use this information correctly to attain my desired result.

Answer 1

I managed to write a solution myself. A lot of information has been found in this Stack Overflow question, which was a great help. Here's the script:

public void InitializeOrbitProjectiles()
    {
        Vector3 posA = new Vector3(projectile.direction.y, -projectile.direction.x) + transform.position * projectile.orbitRadius;
        Vector3 posB = new Vector3(-projectile.direction.y, projectile.direction.x) + transform.position * projectile.orbitRadius;

        var centerDirection = Quaternion.LookRotation((posB - posA).normalized);
        float directionAngle = Angle(projectile.direction);

        for (int i = 0; i < projectile.numberOfOrbits; i++)
        {

            float angle = (projectile.orbitCircle * Mathf.PI / projectile.numberOfOrbits) * i;

            float x = Mathf.Sin(angle) * projectile.orbitRadius;
            float z = Mathf.Cos(angle) * projectile.orbitRadius;
            Vector3 pos = new Vector3(0, 0, 0);

            Debug.Log("directionAngle " + directionAngle);

            if ((directionAngle >= 0 && directionAngle < 90) || (directionAngle >= 271 && directionAngle < 360))
                pos = new Vector3(0, x, z);
            else if (directionAngle >= 90 && directionAngle < 91)
                pos = new Vector3(x, 0, z);
            else if (directionAngle >= 91 && directionAngle < 270)
                pos = new Vector3(0, -x, z);
            else if (directionAngle >= 270 && directionAngle < 271)
                pos = new Vector3(-x, 0, z);

            pos = centerDirection * pos;

            Instantiate(projectileOrbitPrefab, transform.position + pos, transform.rotation);

        }
    }

And the orbitSource script:

public void OrbitSource()
    {
        transform.position = centerTransform.position + pos;
    }