Emulating 3d trajectory in top-down 2d game?

Question

As the title suggests, I am wondering if it's possible to emulate a 3d arrow trajectory to a top-down 2d game? If you would look at this clip of Age of Empires 2 game, especially when archers are firing from bottom to top. Can the parabola/arc of the trajectory (in that certain view angle) be emulated in a 2d orthographic, top-down game? So that the arrows would look like they're in 3d space. I know it's tricky but I wonder if there's some computation available for this.

If you could point me in the right direction or some sample code I would be very grateful. I've only implemented this projectile motion in a side-scroll view.

Thank you in advance.

Answer 1

I created this version which uses a target position and t (time 0-1).

I would loop this function in an update function if (t < 1) t would increase by projectileSpeed * deltaTime in the update after the function was called:

AS THE PROJECTILE

const float projectileHeight = 10f;
const float projectileSpeed = 5f;

Vector3 startPos;
Vector3 endPos;
float fireLerp = 1;

void FireProjectile(Vector3 firePoint, Vector3 targetPos)
{
    startPos = firePoint;
    endPos = targetPos;

    // Setting the fire lerp to 0 will begin the fire animation
    fireLerp = 0;
}

void Update()
{
    if (fireLerp < 1)
    {
        Vector3 newProjectilePos = CalculateTrajectory(startPos, endPos, fireLerp);
        transform.position = newProjectilePos;

        fireLerp += projectileSpeed * Time.deltaTime;
    }
}

Vector3 CalculateTrajectory(Vector3 firePos, Vector3 targetPos, float t)
{
    Vector3 linearProgress = Vector3.Lerp(firePos, targetPos, t);
    float perspectiveOffset = Mathf.Sin(t * Mathf.PI) * projectileHeight;

    Vector3 trajectoryPos = linearProgress + (Vector3.up * perspectiveOffset);
    return trajectoryPos;
}

Answer 2

Store the Z coordinate and move object as if it was in 3D space. When drawing on screen, add object's Z to Y (you can multiply Z by some constant to make world look 'flatter').