**Rotating**

**In order to rotate a shape within most software, a rotational axis must first be defined. Similarly, within mathematics, an initial geometry is ‘plugged into’ a rotation matrix. Below are a series of templates to rotate a shape around each axis (x, y, z). The x _{a},y_{a}, z_{a} within each of the templates below are the initial descriptions of the original shape, prior to its rotation. For example, a cylinder is defined by a parametric equation where x_{a} = cos(u), y_{a} = sin(u), and z_{a} = v. To rotate the cylinder, insert each of these definitions into the templates below.**

**Typically, we speak and think about rotation in terms of degrees, not radians. This guide has been written in radians, but it is easy to move between the two units. Some common ...**

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