计算机图形：绕任意轴旋转

当对象绕着不平行于任何一个坐标轴的轴旋转时, 即x, y, z。然后, 需要进行其他转换。首先, 需要对齐, 然后将对象恢复到原始位置。需要执行以下步骤

1. 将对象转换为原点
2. 旋转对象, 使对象的轴与任何坐标轴重合。
3. 围绕要重合的坐标轴进行旋转。
4. 反向应用旋转, 使旋转回到原始位置。

Matrix for representing three-dimensional rotations about the Z axis

Matrix for representing three-dimensional rotations about the X axis

Matrix for representing three-dimensional rotations about the Y axis

Following figure show the original position of object and position of object after rotation about the x-axis

5. Apply inverse translation to bring rotation axis to the original position.

For such transformations, composite transformations are required. All the above steps are applied on points P’ and P”.Each step is explained using a separate figure.

Step1: Initial position of P’ and P”is shown

Step2: Translate object P’ to origin

Step3: Rotate P” to z axis so that it aligns along the z-axis

Step4: Rotate about around z- axis

Step5: Rotate axis to the original position

Step6: Translate axis to the original position.

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