 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.