将球体 a 旋转到自身的 b 点

我试图弄清楚如何将球体从 A 点旋转到 B 点。我找到了一些Unity3d代码：

Quaternion rot = Quaternion.FromToRotation (pointA, pointB);
sphere.transform.rotation *= rot; //Multiply rotations to get the resultant rotation

via http://answers.unity3d.com/questions/21921/rotate-point-a-on-sphere-to-point-b-on-sphere.html http://answers.unity3d.com/questions/21921/rotate-point-a-on-sphere-to-point-b-on-sphere.html但我不知道如何在 Three.js 中实现它。

这是我的代码：

var s = sphere mesh
var va = 1st start vector
var vb = 2nd end vector;

var qa = new THREE.Quaternion(va.x, va.y, va.z, 1);
var qb = new THREE.Quaternion(vb.x, vb.y, vb.z, 1);
var qc = new THREE.Quaternion();

THREE.Quaternion.slerp(qa, qb, qc, 1);

s.useQuaternion = true;
s.quaternion = qc;

Thanks!

Assume the sphere is centered at the origin and A and B are normalized (i.e. unit length). Then compute the cross product http://en.wikipedia.org/wiki/Cross_product C = A×B. This is your vector representing your rotation axis. The angle for your rotation is given by θ = cos-1(A∙B) where A∙B is the dot product http://en.wikipedia.org/wiki/Dot_product of the unit vectors A and B. Note that the angle in this case is typically in radians, not degrees.

如果球体以某个点为中心P不在原点或其半径不是单位长度，您必须在导出旋转之前平移和缩放 A 和 B。这看起来像：

A' ← (A-P)/|A-P|     // Normalized version of A
B' ← (B-P)/|B-P|     // Normalized version of B
V ← A'×B'            // Axis about which to rotate the system
θ ← cos-1(A'∙B')      // Angle by which to rotate

然后您可以使用V and θ作为构造四元数的参数，您将使用它来定义旋转。此旋转将以原点为中心，因此在应用它之前，请先平移 -P，然后应用旋转，然后再平移 P。

需要注意的是：这里可能存在符号错误。如果不起作用，那是因为叉积的符号与点积的符号不匹配。如果这是一个问题，只需颠倒叉积中参数的顺序即可修复它。