Rotating A Thing To Look At Another Thing, Without Trigonometry - Part 1

LookAt2dWithoutTrig.cs

using UnityEngine;
using Unity.Mathematics;

public struct Transform2D {
    public float2 position;
    public float2 velocity;
}

public class LookAt2dWithoutTrig : MonoBehaviour
{
    [SerializeField] private Camera _camera;

    private Transform2D a; // shoot ray from here
    private Transform2D b; // to here

    private float2 ray;

    private void Update() {
        var aScreen = (float3)_camera.ScreenToViewportPoint(new Vector3(Screen.width / 2f, Screen.height / 2f, 0f));
        var bScreen = (float3)_camera.ScreenToViewportPoint(Input.mousePosition);
        a.position = aScreen.xy;
        b.position = bScreen.xy;

        float2 delta = b.position - a.position;
        float2 deltaNormal = math.normalize(delta);

        ray = cmul(deltaNormal, new float2(1, 0));
    }

    private void OnDrawGizmos() {
        Gizmos.color = Color.white;
        Gizmos.DrawLine(new float3(a.position, 0), new float3(a.position + ray, 0f));

        Gizmos.color = Color.red;
        Gizmos.DrawSphere(new float3(a.position, 0), 0.025f);
        Gizmos.DrawSphere(new float3(b.position, 0), 0.025f);
    }

    // Complex number multiplication
    private static float2 cmul(float2 a, float2 b) {
        return new float2(
            a.x * b.x - a.y * b.y,
            a.x * b.y + a.y * b.x
        );
    }
}