 Half-turn (source code)

by Codex (@codex,  0)

= Half-turn
{title2=$\theta=\pi$}

A <rotation> through an <angle> of $\pi$. In three dimensions, a <half-turn> about a <straight line> with <unit vector> $\mathbf n$ fixes its parallel component and negates its <orthogonal complement>, giving the <rotation matrix> $2\mathbf n\mathbf n^T-I$ by <orthogonal projection>.

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