如何将球扔到平面上的特定点？

Question

我正在尝试设计一个弹射机构，用于将球射向特定点。例如，球的起始位置为x=0，y=.5，z=0，我希望它最终停留在x=10，y=0，z=20。目前我正在使用：

RigidBody.AddForce(new Vector3 (10, 15, 20) * thrust);

我正在将“y”元素平均到x和z之间，但是推力似乎是最难计算的。我尝试通过试错法估计它，但那可能不是正确的解决方案。

- Alex

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你必须进行计算或猜测和检查，除非你想修改物理学。 - ʇolɐǝz ǝɥʇ qoq

Answer 1

我通过计算初始速度，利用起点和目标位置的已知信息创建了一个解决方案。变量“transform”是球在3D空间开始其运动的玩家手部的变换参考。该脚本将导致抛射物沿着类似于此路径http://en.wikipedia.org/wiki/Trajectory_of_a_projectile飞向目标位置。

例如:

public class BallisticLauncherTest : MonoBehaviour
{

    public GameObject ballGameObject;
    public Transform target;


    // Use this for initialization
    void Start()
    {
        ThrowBallAtTargetLocation(target.position, 10f);    
    }

    // Throws ball at location with regards to gravity (assuming no obstacles in path) and initialVelocity (how hard to throw the ball)
    public void ThrowBallAtTargetLocation(Vector3 targetLocation, float initialVelocity)
    {
        Vector3 direction = (targetLocation - transform.position).normalized;
        float distance = Vector3.Distance(targetLocation, transform.position);

        float firingElevationAngle = FiringElevationAngle(Physics.gravity.magnitude, distance, initialVelocity);
        Vector3 elevation = Quaternion.AngleAxis(firingElevationAngle, transform.right) * transform.up;
        float directionAngle = AngleBetweenAboutAxis(transform.forward, direction, transform.up);
        Vector3 velocity = Quaternion.AngleAxis(directionAngle, transform.up) * elevation * initialVelocity;

        // ballGameObject is object to be thrown
        ballGameObject.rigidbody.AddForce(velocity, ForceMode.VelocityChange);
    }

    // Helper method to find angle between two points (v1 & v2) with respect to axis n
    public static float AngleBetweenAboutAxis(Vector3 v1, Vector3 v2, Vector3 n)
    {
        return Mathf.Atan2(
            Vector3.Dot(n, Vector3.Cross(v1, v2)),
            Vector3.Dot(v1, v2)) * Mathf.Rad2Deg;
    }

    // Helper method to find angle of elevation (ballistic trajectory) required to reach distance with initialVelocity
    // Does not take wind resistance into consideration.
    private float FiringElevationAngle(float gravity, float distance, float initialVelocity)
    {
        float angle = 0.5f * Mathf.Asin((gravity * distance) / (initialVelocity * initialVelocity)) * Mathf.Rad2Deg;
        return angle;
    }
}

- Jayson Ash

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嗨，似乎不起作用，而且缺少FiringElevationAngle方法（我在那里放了“45”值）。你能测试一下看看它是否对你有用吗？ - Alex

我添加了缺失的FiringElevationAngle方法，将所有代码放入一个完整的脚本中，并进行了正确性测试。 - Jayson Ash