夹紧 rotation/quaternion

Question

仍在研究 VR 交互，我希望能够旋转对象，但我遇到了问题。

例如，我想 open/close 在 VR 中用我的手来 open/close 笔记本电脑的上半部分。为了实现这一目标，我正在做的是，我把前锋放在这样的位置：

我正在使用 position, forward, up 创建一个平面。然后获取我的VR控制器对应的平面上最近的点，然后使用transform.LookAt.

这很好用，但我希望能够夹住旋转，所以我不能旋转太多（见视频结尾）。

我一直在尝试一切，使用 eulersAngle 和四元数，但我做不到。

我制作了一些助手（用于显示 localEulerAngles 的文本，以及转换为 LookAt，这样我就不必使用 VR 耳机，因为它变得非常乏味）

这是一段视频，展示了正在发生的事情：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

假设显示器的父转换是笔记本电脑的 body/keyboard。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 "center of rotation" 向量（例如，标记为 C 的灰色向量），该向量是父对象的局部变量，以及一个角度（例如，110 度，在每个紫色向量和灰色矢量）。例如：

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

然后，就可以把它"wants"的正向向量带过去，求出RotationRangeCenter的世界方向和那个点的符号夹角，然后夹到±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，找到与该角度对应的方向。最后，旋转显示器，使其前向与夹紧的前向对齐，右侧不变。您可以使用叉积找到显示器的向上旋转，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));

如果有人试图将监视器拖到 "boundaries" 之外太远，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) 插值到 clampedAngle，以便在限制之间移动：

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));

Answer 2

@Ruzihm 的回答只需稍作调整即可奏效！老实说，我自己也做不到。

如果有人感兴趣，这里是为 VR 更新的完整代码：

using UnityEngine;

public class JVRLookAtRotation : MonoBehaviour, IJVRControllerInteract
{

    [SerializeField] private Transform toRotate;

    [SerializeField] private Vector3 minRotationDelta;
    [SerializeField] private Vector3 maxRotationDelta;

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

    // No clue where does this come from
    private Vector3 _localRotationRangeCenter = new Vector3(0, 0.999f, 0.044f);

    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 right = toRotate.right;
        Vector3 rotatePosition = toRotate.position;
        Vector3 pos1 = rotatePosition + up;
        Vector3 pos2 = rotatePosition + forward;
        Plane p = new Plane(rotatePosition, pos1, pos2);
        _targetPosition = p.ClosestPointOnPlane(_jvrController.CurrentPositionWorld);

        Vector3 worldRotationRangeCenter = toRotate.parent.TransformDirection(_localRotationRangeCenter);
        Vector3 targetForward = _targetPosition - rotatePosition;

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

        float clampedAngle = Mathf.Clamp(targetAngle, minRotationDelta.x, maxRotationDelta.x);

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

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

    }

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

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

夹紧 rotation/quaternion

Clamping rotation/quaternion

c#

math

quaternions

unity3d