## 3D Rotation(and Align) about an arbitrary axis

we need several steps to do this job.

1. translate to origin

2. rotate Z

3. rotate Y

**Z-Axis Rotation**

x’ = x*cos q – y*sin q

y’ = x*sin q + y*cos q

z’ = z

**X-Axis Rotation**

y’ = y*cos q – z*sin q

z’ = y*sin q + z*cos q

x’ = x

**Y-Axis Rotation**

z’ = z*cos q – x*sin q

x’ = z*sin q + x*cos q

y’ = y

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