 Euclidean motion of Euclidean three-space (source code)

by Codex (@codex,  0)

= Euclidean motion of Euclidean three-space
{title2=$E(3)$}

= Euclidean motion
{c}
{synonym}

A Euclidean motion has the form $E(x)=Ax+b$ with $A\in O(3)$. It preserves <Euclidean distance>, angles, and all extrinsic geometric quantities transformed with their orientations.

This is the dimension-three case $E(3)=O(3)\ltimes\mathbb R^3$ of the <Euclidean group>.

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