/// <summary>
/// Reference for Predictive Aiming:
/// https://www.gamasutra.com/blogs/KainShin/20090515/83954/Predictive_Aim_Mathematics_for_AI_Targeting.php
/// </summary>
protected Vector3 GetPredictiveAimDirection(NpcController npc)
{
if (npc == null)
{
return(new Vector3());
}
var bulletSpeed = HandController.GetProjectileSpeed();
var bulletSpeedSq = bulletSpeed * bulletSpeed;
var bulletOrigin = HandController.GetWeaponPosition();
var enemyInitialPosition = npc.transform.root.position;
var enemyVelocity = npc.GetVelocity();
var enemySpeed = enemyVelocity.magnitude;
var enemySpeedSq = enemySpeed * enemySpeed;
var enemyToBullet = bulletOrigin - enemyInitialPosition;
var enemyToBulletDistance = enemyToBullet.magnitude;
var enemyToBulletDistanceSq = enemyToBulletDistance * enemyToBulletDistance;
var enemyToBulletDirection = enemyToBullet.normalized;
var enemyVelocityDirection = enemyVelocity.normalized;
//Law of Cosines: A*A + B*B - 2*A*B*cos(theta) = C*C
//A is distance from bullet to enemy (known value: enemyToBulletDistance)
//B is distance traveled by enemy until impact (enemySpeed * t (time))
//C is distance traveled by bullet until impact (bulletSpeed * t (time))
var cosTheta = Vector3.Dot(enemyToBulletDirection, enemyVelocityDirection);
var a = bulletSpeedSq - enemySpeedSq;
var b = 2.0f * enemyToBulletDistance * enemySpeed * cosTheta;
var c = -enemyToBulletDistanceSq;
var discriminant = b * b - 4.0f * a * c;
var uglyNumber = Mathf.Sqrt(discriminant);
var t0 = 0.5f * (-b + uglyNumber) / a;
var t1 = 0.5f * (-b - uglyNumber) / a;
var time = Mathf.Min(t0, t1);
if (time < Mathf.Epsilon)
{
time = Mathf.Max(t0, t1);
}
var bulletVelocity = enemyVelocity + -enemyToBullet / time;
return(bulletVelocity);
}