nLab
barycenter

Barycenter of a simplex

Definition

If $\sigma =\{v_0,\dots ,v_q\}\in K_q$, the set of $q$-simplices of a simplicial complex, $K$, then its barycentre, $b(\sigma )$, is the point

$$b(\sigma )=\sum _{0\le i\le q}\frac{1}{q+1}{v}_i\in \mid K\mid .$$b(\sigma) = \sum_{0\leq i \leq q}\frac{1}{q + 1} v_i \in |K|.

For the use of barycenters in the barycentric subdivision, see classical triangulation or

• wikipedia: barycentric subdivision, barycentric coordinates

• barycentric coordinates homepage

• Wolframworld: [[barycentric coordinates](http://mathworld.wolfram.com/BarycentricCoordinates.html)