Start of camera math

using System.Collections;
using System.Collections.Generic;
using UnityEngine;

[RequireComponent(typeof(Camera))]
public class CameraSceneRender : MonoBehaviour
{
    private Vector3 targetPos => targetObject.transform.position;

    [SerializeField]
    private GameObject targetObject;

    private Camera camera;
    private Vector3 p => camera.transform.position;

    private Vector3 viewDir => camera.transform.forward;
    private Vector3 viewUp => camera.transform.up;
    private Vector3 viewRight => camera.transform.right;

    private Vector3 straight => targetPos - p;
    private Vector3 targetDir => straight.normalized;
    // distance along viewing direction to plane intercting the target
    private float d => Vector3.Dot(targetDir, viewDir) * straight.magnitude;

    private Vector3 viewCentre => p + viewDir * d;

    private float theta => camera.fieldOfView;
    private float phi => camera.fieldOfView / 2;
    private float tanTheta => Mathf.Tan(theta * Mathf.Deg2Rad);
    private float tanPhi => Mathf.Tan(phi * Mathf.Deg2Rad);

    private float b => tanPhi * d;
    // vectors aligning up and right sized for the frustum
    private Vector3 u => viewRight * frustumWidth;
    private Vector3 v => viewUp * b;

    private Vector3 tr => viewCentre + u + v;
    private Vector3 tl => viewCentre - u + v;
    private Vector3 br => viewCentre + u - v;
    private Vector3 bl => viewCentre - u - v;

    private float frustumHeight => d * Mathf.Tan(camera.fieldOfView * 0.5f * Mathf.Deg2Rad);
    private float frustumWidth => frustumHeight * camera.aspect;

    // This is the red line
    private Vector3 comp => targetPos - viewCentre;
    private Vector3 compDir => comp.normalized;
    private float uCompAlignment => Vector3.Dot(viewRight, compDir);
    private float vCompAlignment => Vector3.Dot(viewUp, compDir);
    private Vector3 uPrime => viewRight * comp.magnitude * uCompAlignment;
    private Vector3 vPrime => viewUp * comp.magnitude * vCompAlignment;

    private Vector3 trPrime => viewCentre + uPrime + vPrime;
    private Vector3 tlPrime => viewCentre - uPrime + vPrime;
    private Vector3 brPrime => viewCentre + uPrime - vPrime;
    private Vector3 blPrime => viewCentre - uPrime - vPrime;

    // Start is called before the first frame update
    void Start()
    {
        camera = GetComponent<Camera>();
    }

    // Update is called once per frame
    void Update()
    {
        drawTargets();
        drawFrustum();
        drawTheoreticalFrustum();
    }

    private void drawTargets()
    {
        Debug.DrawLine(p, targetPos, Color.white);
        Debug.DrawLine(p, viewCentre, Color.blue);
        Debug.DrawLine(viewCentre, viewCentre + u, Color.blue);
        Debug.DrawLine(viewCentre, viewCentre + v, Color.blue);
    }

    private void drawFrustum()
    {
        Debug.DrawLine(p, tr, Color.green);
        Debug.DrawLine(p, tl, Color.green);
        Debug.DrawLine(p, br, Color.green);
        Debug.DrawLine(p, bl, Color.green);

        Debug.DrawLine(tr, tl, Color.green);
        Debug.DrawLine(tr, br, Color.green);
        Debug.DrawLine(bl, br, Color.green);
        Debug.DrawLine(bl, tl, Color.green);
    }

    private void drawTheoreticalFrustum()
    {
        //Debug.DrawLine(p, tr, Color.green);
        //Debug.DrawLine(p, tl, Color.green);
        //Debug.DrawLine(p, br, Color.green);
        //Debug.DrawLine(p, bl, Color.green);
        Debug.DrawLine(viewCentre, targetPos, Color.red);
        Debug.DrawLine(viewCentre, viewCentre + uPrime, Color.red);
        Debug.DrawLine(viewCentre, viewCentre + vPrime, Color.red);

        Debug.DrawLine(trPrime, tlPrime, Color.red);
        Debug.DrawLine(trPrime, brPrime, Color.red);
        Debug.DrawLine(blPrime, brPrime, Color.red);
        Debug.DrawLine(blPrime, tlPrime, Color.red);
    }
}