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

Overview

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

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Specification of the Rotation Matrix

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

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

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

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

This transformation is illustrated in the following figure.

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