= Edge vector
For endpoints with position <vectors> $p_i,p_j$ in an affine Euclidean <SPACE>, the directed <edge vector> from $i$ to $j$ is $e_{ij}=p_j-p_i$. Reversing orientation changes its sign, while translating both endpoints leaves it unchanged.
For a triangle, $e_{12}+e_{23}+e_{31}=0$. Its side <lengths> are the <norms> of the corresponding <edge vectors>, and dot products determine angles. Choosing an orientation is essential: an undirected <edge> alone specifies the pair of opposite <vectors>, rather than one of them. Edge differences also describe how a scalar or vector field changes across a mesh.
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