On-Line Computer Graphics Notes
ROTATION ABOUT THE Z-AXIS

Overview

Rotation about the z-axis is similar to rotation specified in two-dimensional space as in the three-dimensional rotation, the z-coordinate must remain constant.

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Specification of the Rotation Matrix

The transformation for rotation of $\theta$ radians about the $z$-axis is given by the $4 \times 4$ matrix

$$R _ {z; \theta } \; = \; \left[ \begin{array}{cccc} \cos\th... ... \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \\ \end{array}\right]$$

If this transformation is applied to the point $(x,y,z)$, we obtain

$$\left[ \begin{array}{cccc} x & y & z & 1 \end{array}\right] \left... ...cos\theta - y\sin\theta & x\sin\theta + y\cos\theta & z & 1 \end{array}\right]$$

The effect of this transform is illustrated by the following figure:

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