在 THREE.js 中使用四元数设置矢量的全局旋转

Question

我想使用四元数设置矢量的绝对全局旋转。

假设我有一个函数f(v, q)，它将向量v 旋转到四元数q。

THREE.Vector3 有一个 .applyQuaternion 函数，它对向量应用旋转，但这是相对旋转。例如，函数调用f(f(v, q), q) 将应用q 两次。相反，我希望f(f(v, q), q) = f(v, q) 因为q 是向量的绝对旋转。

我知道我可以计算一些deltaQ = currentQ.premultiply(q.inverse())，然后调用.applyQuaternion，但是我不知道如何查询currentQ，或者向量的当前旋转，以便我可以“撤消”它并应用新的四元数。

感谢您的帮助！

编辑：

理想情况下，我希望围绕世界坐标空间中定义的点旋转，这就是为什么我有object.worldToLocal 和object.localToWorld 调用。然而，当我进行这些转换时，轨道物体飞离了地图。

const scene = new THREE.Scene();
const camera = new THREE.PerspectiveCamera( 75, window.innerWidth/window.innerHeight, 0.1, 1000 );

const renderer = new THREE.WebGLRenderer();
renderer.setSize( window.innerWidth, window.innerHeight );
document.body.appendChild( renderer.domElement );
/* const orbitControls = new THREE.OrbitControls(camera, renderer.domElement); */

// CONSTRUCT ORBITER
const orbitGeometry = new THREE.SphereGeometry(0.1, 32, 32);
const orbitMaterial = new THREE.MeshBasicMaterial({colors: 0xff0000});
const orbiter = new THREE.Mesh(orbitGeometry, orbitMaterial);

// CONSTRUCT GLOBAL AXES
const xDir = new THREE.Vector3(1, 0, 0);
const yDir = new THREE.Vector3(0, 1, 0);
const zDir = new THREE.Vector3(0, 0, 1);
const origin = new THREE.Vector3(0, 0, 0);
const xArrowWorld = new THREE.ArrowHelper(xDir, origin, 3, 0xFF00FF);
const yArrowWorld = new THREE.ArrowHelper(yDir, origin, 3, 0xffff00);
const zArrowWorld = new THREE.ArrowHelper(zDir, origin, 3, 0x00b7eb);
const worldAxes = new THREE.Group();
worldAxes.add(xArrowWorld);
worldAxes.add(yArrowWorld);
worldAxes.add(zArrowWorld);


// CONSTRUCT MARKER
const sphereGeometry = new THREE.SphereGeometry(0.1, 32, 32);
const sphereMaterial = new THREE.MeshBasicMaterial({color: 0xffffff});
const marker = new THREE.Mesh(sphereGeometry, sphereMaterial);

// scene.add(axes);
scene.add(marker);
scene.add(orbiter);
scene.add(worldAxes);

camera.position.z = 5;
camera.position.y = 3;
camera.position.x = 3;
camera.lookAt(worldAxes.position);

marker.position.set(1, 0, 0);

function rotateEuler(object, point, eulerX, eulerY, eulerZ, isExtrinsic = false) {
    if (isExtrinsic) {
        object.rotation.order = 'ZYX';
    } else {
        object.rotation.order = 'XYZ';
    }
    const q = new THREE.Quaternion();
    const eul = new THREE.Euler(eulerX, eulerY, eulerZ, object.rotation.order);
    q.setFromEuler(eul);
    rotateQuaternionAroundPoint(object, point, q);
}

function rotateQuaternionAroundPoint(object, point, q) {

    object.rotation.set(0, 0, 0)
    object.position.set(0, 0, 0);

    object.localToWorld(object.position);
    object.position.sub(point);
    object.position.applyQuaternion(q);
    object.position.add(point);
    object.worldToLocal(object.position);

}

let rotY = 0;
let rotationPoint = marker.localToWorld(marker.position.clone());

function animate() {
    requestAnimationFrame( animate );

    rotY += 0.01;

    rotateEuler(orbiter, rotationPoint, 0, rotY, 0, true);

    renderer.render( scene, camera );
}

animate();

<script src="https://cdnjs.cloudflare.com/ajax/libs/three.js/110/three.min.js"></script>

Answer 1

执行此操作的最简单方法是将Vector3 重置为其初始状态，然后将四元数应用于此重置向量。这会从方程中删除任何先前的旋转。例如，假设向量的默认状态是指向'UP'：

function f(v, q) {
    v.set(0, 1, 0);
    v.applyQuaternion(q);
    return v;
}