c# - 夹紧旋转/四元数

Question

仍在进行 VR 交互，我希望能够旋转对象，但我面临一个问题。

例如，我想在 VR 中用手打开/关闭笔记本电脑的上部。为了实现这一目标，我正在做的是我像这样放置前锋:



我正在使用位置、向前、向上创建一个平面。然后获取与我的 VR Controller 对应的平面上最近的点，然后使用 transform.LookAt。

这工作正常，但我希望能够夹紧旋转，所以我不能旋转太多(见视频结尾)。

我一直在尝试一切，使用 eulerAngle 和 Quaternion，但我无法做到。

我做了一些助手(显示localEulerAngles的文本，以及LookAt的转换，所以我不必使用VR耳机，因为它变得非常乏味)

这是一个显示正在发生的事情的视频:https://www.youtube.com/watch?v=UfN97OpYElk

这是我的代码:

using UnityEngine;

public class JVRLookAtRotation : MonoBehaviour, IJVRControllerInteract
{

    [SerializeField] private Transform toRotate;

    [SerializeField] private Vector3 minRotation;
    [SerializeField] private Vector3 maxRotation;

    [Header("Rotation contraints")]
    [SerializeField] private bool lockX;
    [SerializeField] private bool lockY;
    [SerializeField] private bool lockZ;

    private JVRController _jvrController;
    private bool _isGrabbed;
    private Vector3 _targetPosition;
    private Vector3 _tmp;

    public Transform followTransform;

    private void LateUpdate()
    {

        /*
        if (!_isGrabbed) return;

        if (_jvrController.Grip + _jvrController.Trigger < Rules.GrabbingThreshold)
        {
            _isGrabbed = false;
            _jvrController.StopGrabbing();
            _jvrController = null;
            return;
        }

        */

        Vector3 up = toRotate.up;
        Vector3 forward = toRotate.forward;
        Vector3 pos0 = toRotate.position;
        Vector3 pos1 = pos0 + up;
        Vector3 pos2 = pos0 + forward;
        Plane p = new Plane(pos0, pos1, pos2);

        // Using followTransform just to no have to use VR, otherwise it's the controller pos
        _targetPosition = p.ClosestPointOnPlane(followTransform.position);

        toRotate.LookAt(_targetPosition, up);

        /*
        _tmp = toRotate.localEulerAngles;
        _tmp.x = Mathf.Clamp(WrapAngle(_tmp.x), minRotation.x, maxRotation.x);
        _tmp.y = WrapAngle(_tmp.y);
        _tmp.z = WrapAngle(_tmp.z);
        toRotate.localRotation = Quaternion.Euler(_tmp);
        */

    }

    public void JVRControllerInteract(JVRController jvrController)
    {
        if (_isGrabbed) return;
        if (!(jvrController.Grip + jvrController.Trigger > Rules.GrabbingThreshold)) return;

        _jvrController = jvrController;
        _jvrController.SetGrabbedObject(this);
        _isGrabbed = true;
    }

    private static float WrapAngle(float angle)
    {
        angle%=360;
        if(angle >180)
            return angle - 360;

        return angle;
    }

    private static float UnwrapAngle(float angle)
    {
        if(angle >=0)
            return angle;

        angle = -angle%360;

        return 360-angle;
    }
}

Answer 1

假设显示器的父变换是笔记本电脑的主体/键盘。父级的局部轴如下所示:



为了描述运动范围，您可以定义一个“旋转中心”向量(例如，标记为 C 的灰色向量)，它是父对象的局部和一个角度(例如，每个紫色向量和灰色向量之间的 110 度)。例如:

[SerializeField] private Vector3 LocalRotationRangeCenter = new Vector3(0f, 0.94f, 0.342f);
[SerializeField] private float RotationRangeExtent = 110f;

然后，你可以取它“想要”去的前向向量，找到 RotationRangeCenter的世界方向之间的有符号角。和那个点，然后把它夹在± RotationRangeExtent :

Vector3 worldRotationRangeCenter = toRotate.parent.TransformDirection(RotationRangeCenter);

Vector3 targetForward = _targetPosition - toRotate.position;

float targetAngle = Vector3.SignedAngle(worldRotationRangeCenter, targetForward, 
        toRotate.right);

float clampedAngle = Mathf.Clamp(targetAngle, -RotationRangeExtent, RotationRangeExtent);

然后，找到对应于该角度的方向。最后，旋转显示器，使其向前与夹住的向前对齐，并且其右侧不会改变。您可以使用叉积来查找监视器的状态，然后使用 Quaternion.LookRotation找到相应的旋转:

Vector3 clampedForward = Quaternion.AngleAxis(clampedAngle, toRotate.right)
        * worldRotationRangeCenter;

toRotate.rotation = Quaternion.LookRotation(clampedForward, 
        Vector3.Cross(clampedForward, toRotate.right));

如果有人试图将显示器拖离“边界”太远，它将从一个限制传送到另一个限制。如果这不是您想要的行为，您可以考虑从 SignedAngle(worldRotationRangecenter, targetForward, toRotate.right) 进行插值至 clampedAngle , 对于极限之间的运动:

private float angleChangeLimit = 90f; // max angular speed

// ...

Vector3 worldRotationRangeCenter = toRotate.parent.TransformDirection(RotationRangeCenter);

Vector3 targetForward = _targetPosition - toRotate.position;

float targetAngle = Vector3.SignedAngle(worldRotationRangeCenter, targetForward, 
        toRotate.right);

float clampedAngle = Mathf.Clamp(targetAngle, -RotationRangeExtent, RotationRangeExtent);

float currentAngle = Vector3.SignedAngle(worldRotationRangeCenter, toRotate.forward, 
        toRotate.right);

clampedAngle = Mathf.MoveTowards(currentAngle, clampedAngle, 
        angleChangeLimit * Time.deltaTime);

Vector3 clampedForward = Quaternion.AngleAxis(clampedAngle, toRotate.right)
        * worldRotationRangeCenter;

toRotate.rotation = Quaternion.LookRotation(clampedForward, 
        Vector3.Cross(clampedForward, toRotate.right));