java - 将对象旋转到面点

Question

我想旋转一个物体以面对一个我有点麻烦的点。

所以我从一个以零为底并在 y 轴上对齐的对象开始。

我想旋转它，使物体的顶部朝向目的地

到目前为止，我的流程是: 给定轴 A

1. 找到我的位置和我的注视位置之间的距离:D
2. 创建一个方向 vector :V = D.normalize()
3. 找到正确的 vector :R = A cross D
4. 求上 vector :U = D cross R
5. 找到向上和方向之间的角度:ANGLE = acos((U dot D)/(U.length * D.length))
6. 按每个轴上的方向缩放的角度旋转

这是它的代码表示。我不确定这到底有什么问题我已经在纸上解决了，据我所知，这种方法应该有效，但绘制时结果完全不正确。如果有人看到任何缺陷并能指出我正确的方向，那就太好了。

    Vector3 distance = new Vector3(from.x, from.y, from.z).sub(to.x, to.y, to.z);
    final Vector3 axis = new Vector3(0, 1, 0);
    final Vector3 direction = distance.clone().normalize();

    final Vector3 right = (axis.clone().cross(direction));
    final Vector3 up = (distance.clone().cross(right));

    float angle = (float) Math.acos((up.dot(direction)/ (up.length() * direction.length()))); 
    bondObject.rotateLocal(angle, direction.x , direction.y, direction.z);

Answer 1

这里的基本思想如下。

• 确定物体朝向的方向:directionA
• 确定对象应该面向哪个方向:directionB
• 确定这些方向之间的角度:rotationAngle
• 确定旋转轴:rotationAxis

这是修改后的代码。

Vector3 distance = new Vector3(from.x, from.y, from.z).sub(to.x, to.y, to.z);

if (distance.length() < DISTANCE_EPSILON)
{
    //exit - don't do any rotation
    //distance is too small for rotation to be numerically stable
}

//Don't actually need to call normalize for directionA - just doing it to indicate
//that this vector must be normalized.
final Vector3 directionA = new Vector3(0, 1, 0).normalize();
final Vector3 directionB = distance.clone().normalize();

float rotationAngle = (float)Math.acos(directionA.dot(directionB));

if (Math.abs(rotationAngle) < ANGLE_EPSILON)
{
    //exit - don't do any rotation
    //angle is too small for rotation to be numerically stable
}

final Vector3 rotationAxis = directionA.clone().cross(directionB).normalize();

//rotate object about rotationAxis by rotationAngle