Definition:Affine Frame

Definition
Let $\mathcal E$ be an affine space with difference space $V$.

An affine frame in $\mathcal E$ is an ordered tuple $\left(p_0,e_1,\ldots,e_n\right)$, where
 * $p_0$ is an element of $\mathcal E$ called the origin
 * $\left(e_1,\ldots,e_n\right)$ is a basis for $V$

Equivalently, an affine frame may be given by the set of $n+1$ points
 * $\left( q_0,\ldots, q_n \right) = \left( p_0, p_0 + e_1, \ldots, p_0 + e_n \right)$

The frame $\left(p_0,e_1,\ldots,e_n\right)$ is then recovered by
 * $\left( q_0, q_1 - q_0 ,\ldots, q_n - q_0 \right)$