three.js 中的四元数旋转在旋转超过 90° 时变得混乱

Question

我正在使用四元数使用双指触摸事件对 THREE.Mesh 对象进行捏合-旋转-缩放。这是我第一次使用这种旋转方法，并且由于我确定有些属性的四元数我似乎无法理解，所以当总触摸拖动旋转时，旋转逐渐开始到处抖动超过约 90° 的物体。然后，当再次拖回 90° 以下时，它逐渐 returns 到原始的平滑旋转，尽管明显是非线性的。（90° 只是一个猜测）。

我完全被难住了。这是我用来旋转对象的代码 obj:

  // global state
var 
      // keeps track of original object scale
    pinchScale = new THREE.Vector3(),

      // current first touch
    touch1 = new THREE.Vector2(),

      // current second touch
    touch2 = new THREE.Vector2(),

      // first touch at touch start
    touch1OnHold = new THREE.Vector2(),

      // second touch at touch start
    touch2OnHold = new THREE.Vector2(),

      // keeps track of total held rotation at last fired touchmove event
    angularHoldPrev = new THREE.Quaternion();

  ⋮

  // key-value pairs inside an addEventListener utility
touchstart: function (event) {
  event.preventDefault();
  if ( event.touches.length === 1 ) {
    …
  } else if ( event.touches.length === 2 ) {
    touch1OnHold.set(event.touches[0].pageX, event.touches[0].pageY);
    touch2OnHold.set(event.touches[1].pageX, event.touches[1].pageY);
    angularHoldPrev.set(0, 0, 0, 1)
  }
},
touchmove: function (event) {
  event.preventDefault();
  if ( event.touches.length === 1 ) {
    …
  } else if ( event.touches.length === 2 ) {
    touch1.set(event.touches[0].pageX, event.touches[0].pageY);
    touch2.set(event.touches[1].pageX, event.touches[1].pageY);
    var 
          // get touch spread at present event firing, and at the start of current hold
        touchDiff = touch2.clone().sub(touch1),
        touchDiffOnHold = touch2OnHold.clone().sub(touch1OnHold),

          // camera is on z-axis; get this axis regardless of obj orientation
        axis1 = new THREE.Vector3(0, 0, 1).applyQuaternion(obj.quaternion.clone().inverse()),

          // get a touch rotation around this axis
        rot1 = new THREE.Quaternion().setFromAxisAngle(axis1, (Math.atan2(touchDiffOnHold.y, touchDiffOnHold.x) - Math.atan2(touchDiff.y, touchDiff.x))).normalize(),

          // get touch barycentre at present event firing, and at the start of current hold
        touchCentre = touch1.clone().add(touch2).multiplyScalar(.5),
        touchCentreOnHold = touch1OnHold.clone().add(touch2OnHold).multiplyScalar(.5),

          // get axis of touch barycentre movement on the xy plane, regardless of obj orientation
        axis2 = new THREE.Vector3(touchCentre.y - touchCentreOnHold.y, touchCentre.x - touchCentreOnHold.x, 0).applyQuaternion(obj.quaternion.clone().inverse()),

          // get a rotation proportional to magnitude of touch movement
        rot2 = new THREE.Quaternion().setFromAxisAngle(axis2, axis2.length() * rotationSensitivity).normalize(),

          // combine the two rotations
        rot = rot1.multiply(rot2);

      // undo last rotation if not the empty quaternion
    if (!angularHoldPrev.equals(new THREE.Quaternion())) obj.quaternion.multiply(angularHoldPrev.inverse());

      // perform the currently calculated rotation
    obj.quaternion.multiply(rot);

      // save this rotation for next event firing
    angularHoldPrev.copy(rot);

      // resize object according to change in touch spread
    obj.scale.copy(pinchScale.clone().multiplyScalar(touchDiff.length() / touchDiffOnHold.length()))
  }
},
touchend: function (event) {
  event.preventDefault();

    // reset original object scale
  pinchScale.copy(obj.scale)
}

如果我能为所有两点触控输入保持比例旋转提供任何线索，将不胜感激。干杯。

Answer 1

我通过使所有 touchmove 旋转增量而不是相对于 touchstart 来让它工作，它实际上清理了一些东西。 rotV 是我为动画循环设置的 angular 速度变量，当您四处移动时，它会为对象提供良好的惯性踢动。（感谢@WestLangley 的优化建议）

var touch1 = new THREE.Vector2(),
    touch2 = new THREE.Vector2(),
    touch1Prev = new THREE.Vector2(),
    touch2Prev = new THREE.Vector2(),
    rotV = new THREE.Quaternion(),

    touchDiff = new THREE.Vector2(),
    touchDiffPrev = new THREE.Vector2(),
    touchCentre = new THREE.Vector2(),
    touchCentrePrev = new THREE.Vector2(),
    axis1 = new THREE.Vector3(),
    axis2 = new THREE.Vector3(),
    rot1 = new THREE.Quaternion(),
    rot2 = new THREE.Quaternion(),
    adjq = new THREE.Quaternion();

⋮

touchstart: function (event) {
  event.preventDefault();
  if ( event.touches.length === 1 ) {
    …
  } else if ( event.touches.length === 2 ) {
    touch1Prev.set(event.touches[0].pageX, event.touches[0].pageY);
    touch2Prev.set(event.touches[1].pageX, event.touches[1].pageY)
  }
},
touchmove: function (event) {
  event.preventDefault();
  adjq.copy(obj.quaternion).inverse();
  if ( event.touches.length === 1 ) {
    …
  } else if ( event.touches.length === 2 ) {
    touch1.set(event.touches[0].pageX, event.touches[0].pageY);
    touch2.set(event.touches[1].pageX, event.touches[1].pageY);

    touchDiff.copy(touch2).sub(touch1);
    touchDiffPrev.copy(touch2Prev).sub(touch1Prev);
    axis1.set(0, 0, 1).applyQuaternion(adjq);
    rot1.setFromAxisAngle(axis1, (Math.atan2(touchDiffPrev.y, touchDiffPrev.x) - Math.atan2(touchDiff.y, touchDiff.x))).normalize();

    touchCentre.copy(touch1).add(touch2).multiplyScalar(.5);
    touchCentrePrev.copy(touch1Prev).add(touch2Prev).multiplyScalar(.5);
    axis2.set(touchCentre.y - touchCentrePrev.y, touchCentre.x - touchCentrePrev.x, 0).applyQuaternion(adjq);
    rot2.setFromAxisAngle(axis2, axis2.length() * rotationSensitivity * 10).normalize();

    obj.quaternion.multiply(rot1.multiply(rot2));
    rotV.multiply(rot1.slerp(adjq.set(0, 0, 0, 1), .9));
    obj.scale.multiplyScalar(touchDiff.length() / touchDiffPrev.length());

    touch1Prev.copy(touch1);
    touch2Prev.copy(touch2)
  }
},
touchend: function (event) {
  event.preventDefault()
}

我仍然希望我知道是什么导致了最初的问题 :P

three.js 中的四元数旋转在旋转超过 90° 时变得混乱

Quaternion rotation in three.js going haywire when rotating past about 90°

javascript

three.js

rotation

multi-touch

quaternions