Just like it's important to predict a projectile's landing point, it's also important to develop intelligent agents capable of aiming projectiles. It wouldn't be fun if our rugby-player agents aren't capable of passing the ball.
Thanks to our previous hard work, this recipe is a real piece of cake:
- Create the
GetFireDirectionfunction:public static Vector3 GetFireDirection (Vector3 startPos, Vector3 endPos, float speed) { // body } - Solve the corresponding quadratic equation:
Vector3 direction = Vector3.zero; Vector3 delta = endPos - startPos; float a = Vector3.Dot(Physics.gravity, Physics.gravity); float b = -4 * (Vector3.Dot(Physics.gravity, delta) + speed * speed); float c = 4 * Vector3.Dot(delta, delta); if (4 * a * c > b * b) return direction; float time0 = Mathf.Sqrt((-b + Mathf.Sqrt(b * b - 4 * a * c)) / (2*a)); float time1 = Mathf.Sqrt((-b - Mathf.Sqrt(b * b - 4 * a * c)) / (2*a)); - If shooting the projectile is feasible given the parameters, return a non-zero direction vector:
float time; if (time0 < 0.0f) { if (time1 < 0) return direction; time = time1; } else { if (time1 < 0) time = time0; else time = Mathf.Min(time0, time1); } direction = 2 * delta - Physics.gravity * (time * time); direction = direction / (2 * speed * time); return direction;
Given a fixed speed, we solve the corresponding quadratic equation in order to obtain the desired direction (when at least one time value is available), which doesn't need to be normalized because we already normalized the vector while setting up the projectile.
Take into account that we are returning a blank direction when time is negative; it means that the speed is not sufficient. One way to overcome this is to define a function that tests different speeds and then shoots the projectile.
Another relevant improvement is to add an extra parameter of the type bool for those cases when we have two valid times (which means two possible arcs), and we need to shoot over an obstacle such as a wall:
if (isWall)
time = Mathf.Max(time0, time1);
else
time = Mathf.Min(time0, time1);