一個角度軸如何轉換向量以匹配另一個方向？

Question

我正在為一個學校項目制作太空游戲，而我的飛船的AI則依賴向另一艘飛船移動的能力。 我當前的實現無法正常工作，因為它會將飛船旋轉到目標矢量的兩個方向，因此偶爾攻擊的飛船將朝着完全相反的方向前進，而其他時候它將向正確的方向走。 任何反饋將不勝感激！

//ship heading (already calculated)
Vector3f heading /* = ... */;
heading.normalize();

//direction of enemy ship relative to ours
Vector3d direction = new Vector3f(enemy.x - ship.x, enemy.y - ship.y, enemy.z - ship.z);
direction.normalize();

//angle between vectors
float angle = heading.angle(direction);

//axis to rotate upon
Vector3f axis = new Vector3f();
axis.cross(heading, direction);
axis.normalize();

//initialize matrix to hold rotation
Matrix4f rot = new Matrix4f();
rot.setIdentity();

//rotate the ship if we are more than 10 deg off
if (angle > Math.toRadians(10)) {
    rot.setRotation(new AxisAngle4f(axis, rotationVelocity * deltaTime));
}

Answer 1

好吧，我已經找到了一種更好的方法，它涉及一些線性插值。

以下內容保持不變：

//ship heading (already calculated)
Vector3f heading /* = ... */;
heading.normalize();

//direction of enemy ship relative to ours
Vector3d direction = new Vector3f(enemy.x - ship.x, enemy.y - ship.y, enemy.z - ship.z);
direction.normalize();

//angle between vectors
float angle = heading.angle(direction);

現在，我計算要插值到方向矢量的航向矢量的百分比：

//calculate angle to rotate
float deltaRotation = rotationVelocity * deltaTime;

//calcuate percent of rotation 
float percent = Math.min(deltaRotation / angle, 1.0f);

//create interpolated vector representing the new forward direction
Vector3f inter = new Vector3f(heading.x + percent * (direction.x - heading.x), heading.y + percent * (direction.y - heading.y), heading.z + percent * (direction.z - heading.z));
inter.normalize();

現在我們可以創建新的旋轉矩陣：

//the object's default forward size without any transformations
Vector3f forward = new Vector3f(0.0f, 0.0f, 1.0f);

//rotation axis
Vector3f axis = new Vector3f();
axis.cross(forward, inter);
axis.normalize();

//New rotation matrix to be applied
Matrix4f rotationMatrix = new Matrix4f();
rotationMatrix.setIdentity();
rotationMatrix.setRotation(new AxisAngle4f(axis, forward.angle(inter)));

現在，我的船始終面向正確的方向！ :)