基于角度的弹丸轨迹

Question

在我的 3D 游戏（自上而下的射击游戏）中，我尝试这样做：当您在 map 的特定区域上单击鼠标按钮（点上光线投射）时 -> 从枪中射出一枪 -> 弹丸飞入具有一定路径且与鼠标指针距离相同的枪管方向（但不是方向）。 我已经有了计算弹丸轨迹的源代码。 帮助使射弹沿枪管的方向飞行，但使用鼠标位置射线投射显示的距离，而不是鼠标位置方向。

```private void FireCannonAtPoint(Vector3 point)
{
    var velocity = BallisticVelocity(point, _angle);

    GameObject projectile = Instantiate(_projectile, _shootPoint.transform.position, Quaternion.identity) as GameObject;
            projectile.GetComponent<Rigidbody>().velocity = velocity;
}

private Vector3 BallisticVelocity(Vector3 destination, float angle)
{
    Vector3 dir = destination - _shootPoint.transform.position; 
    float height = dir.y;
    dir.y = 0; 
    float dist = dir.magnitude; 
    float a = angle * Mathf.Deg2Rad; 
    dir.y = dist * Mathf.Tan(a); 
    dist += height / Mathf.Tan(a); 

    float velocity = Mathf.Sqrt(dist * Physics.gravity.magnitude / Mathf.Sin(2 * a));
    return velocity * dir.normalized; 
}```

Answer 1

枪管：3D 中的段[turret_end_1, turret_end2] ，其中turret_end_1是炮塔上子弹离开的点。

屏幕：焦点F和屏幕平面，命名为screen_plane 。

# From 3D to 2D: projection from 3D space on the screen_plane:
Mouse = [mouse_x, mouse_y] # given on the screen_plane
B1 = project_on_screen_plane(turret_end_1)
B2 = project_on_screen_plane(turret_end_2)

# Calculations in 2D, i.e. on the screen_plane
U = B1-B2
U = ( dot_product(Mouse-B1, U) / dot_product(U, U) ) * U
U = B1 + U # this is the point you are looking for on the screen


# From 2D back to 3D: connect the focal point with the point U on the screen plane
# to form a line and find its intersection point in 3D with the line B1 B2
# aligned with the turret.
# line through F with directing vector Vector_from_F_to(U)
# line through B1 with directing vector B1-B2

V = intersect( F,  Vector_from_F_to(U),  B1,  B1-B2 ) # the point you are looking for in 3D